Class 7 Maths Ganita Prakash Chapter 3 Solutions (NCERT 2026–27) – A Peek Beyond the Point

These Class 7 Maths Ganita Prakash Chapter 3 solutions cover A Peek Beyond the Point from the new NCF-2023 textbook (Reprint 2026–27). Every Figure it Out question is solved step by step, with worked decimal place value, tenths and hundredths, length, weight and money conversions, decimal comparison and decimal addition & subtraction, plus every Math Talk and Try This task answered — so you can master decimals and revise the chapter quickly.

Class: 7 Subject: Mathematics Book: Ganita Prakash (Part I) Chapter: 3 Exercises: Figure it Out (p. 75), Figure it Out (p. 78–79) Session: 2026–27
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Chapter 3 Overview

Chapter 3 of Ganita Prakash, A Peek Beyond the Point, starts with Sonu watching his mother fix a toy with screws of slightly different lengths and uses it to explain why we need units smaller than one. Step by step the chapter builds the idea of a tenth (split a unit into 10 equal parts), a hundredth (split each tenth into 10), and a thousandth, leading to the full decimal place value system and the decimal point. It then covers reading and writing decimals, length (mm–cm–m), weight (g–kg–mg) and rupee–paise conversions, locating and comparing decimals on the number line, the “zero dilemma” (trailing zeros), and the standard method for adding and subtracting decimals. The Class 7 Maths Ganita Prakash Chapter 3 solutions below work through every Figure it Out, Math Talk and Try This question step by step.

Key Concepts & Definitions

Tenth: when a unit is split into 10 equal parts, each part is one-tenth = 1⁄10 of a unit. Ten one-tenths make one unit.

Hundredth: when each one-tenth is split into 10 equal parts, each part is one-hundredth = 1⁄100 of a unit. 10 hundredths = 1 tenth and 100 hundredths = 1 unit.

Thousandth: splitting each hundredth into 10 gives one-thousandth = 1⁄1000 of a unit; 10 thousandths = 1 hundredth.

Decimal point: a point or period (‘.’) that separates the whole-number part of a number from its fractional part, e.g. in 7.05 the 7 is units and 05 is the fractional part.

Decimal place value: reading left to right after the point, the places are tenths, hundredths, thousandths, … Each place is 10 times smaller than the one to its left, e.g. 70.5 = 7 × 10 + 5 × 1⁄10 and 7.05 = 7 × 1 + 5 × 1⁄100.

Decimal system: a way of writing numbers based on 10 (“decem” = ten in Latin, cognate with Sanskrit daśha), extending the Indian place value system to numbers below one.

Trailing zeros: zeros placed at the right end after the decimal point do not change a decimal’s value, e.g. 0.2 = 0.20 = 0.200, but 0.2, 0.02 and 0.002 are all different.

Important Formulas & Conversions (Chapter 3)

Place value chain: 1 unit = 10 tenths = 100 hundredths = 1000 thousandths.

Length: 1 cm = 10 mm, so 1 mm = 0.1 cm; 1 m = 100 cm, so 1 cm = 0.01 m; 1 m = 1000 mm, so 1 mm = 0.001 m.

Weight: 1 kg = 1000 g, so 1 g = 0.001 kg; 1 g = 1000 mg, so 1 mg = 0.001 g.

Money: 1 rupee = 100 paise, so 1 paisa = 0.01 rupee.

Reading decimals: read digit by digit after the point, e.g. 0.274 = “zero point two seven four” = 2 tenths + 7 hundredths + 4 thousandths.

Adding/subtracting decimals: line up the decimal points (and so the place values), then add or subtract just like whole numbers, regrouping or borrowing as usual.

Comparing decimals: compare the highest place value first; move to the next smaller place only when digits are equal — the first place with a bigger digit decides the larger number.

Figure it Out — Find the Sums and Differences (Page 75)

Questions are reproduced verbatim from the NCERT Ganita Prakash (Part I) textbook; the worked solutions are original and verified.

Find the sums and differences: (a) 3⁄10 + 34⁄100   (b) 95⁄107⁄100 + 21⁄103⁄100   (c) 156⁄104⁄100 + 143⁄106⁄100 (d) 77⁄100 − 44⁄100   (e) 86⁄100 − 53⁄100   (f) 126⁄102⁄100 − 9⁄109⁄100

SOLUTION Write each quantity in decimal form (tenths in the first place, hundredths in the second), line up the points, then add or subtract. (a) 3⁄10 = 0.30 and 34⁄100 = 3.04. So 0.30 + 3.04 = 3.34 (= 33⁄104⁄100). (b) 9.57 + 2.13: 7 + 3 = 10 hundredths = 1 tenth carried; 5 + 1 + 1 = 7 tenths; 9 + 2 = 11 units. Sum = 11.70. (c) 15.64 + 14.36: 4 + 6 = 10 hundredths (carry 1); 6 + 3 + 1 = 10 tenths = 1 unit (carry 1); 15 + 14 + 1 = 30. Sum = 30.00. (d) 7.07 − 4.04 = 3.03 (subtract place by place: 7 − 4 hundredths = 3, 0 tenths, 7 − 4 = 3 units). (e) 8.06 − 5.03 = 3.03. (f) 12.62 − 0.99: borrow — 12.62 − 0.99 = 11.63 (since 0.99 from 1.62 gives 0.63, and 12 − 1 = 11).

Figure it Out — Decimals, Conversions & Comparison (Page 78–79)

1. Convert the following fractions into decimals: (a) 5⁄100   (b) 16⁄1000   (c) 12⁄10   (d) 254⁄1000

SOLUTION (a) 5⁄100 = 5 hundredths = 0.05. (b) 16⁄1000 = 16 thousandths = 0.016. (c) 12⁄10 = 12 tenths = 1 unit and 2 tenths = 1.2. (d) 254⁄1000 = 254 thousandths = 0.254.

2. Convert the following decimals into a sum of tenths, hundredths and thousandths: (a) 0.34   (b) 1.02   (c) 0.8   (d) 0.362

SOLUTION (a) 0.34 = 3⁄10 + 4⁄100 (3 tenths and 4 hundredths). (b) 1.02 = 1 + 0⁄10 + 2⁄100 = 1 unit, 0 tenths and 2 hundredths. (c) 0.8 = 8⁄10 (8 tenths). (d) 0.362 = 3⁄10 + 6⁄100 + 2⁄1000 (3 tenths, 6 hundredths, 2 thousandths).

3. What decimal number does each letter represent in the number line below? (The unit between 6.4 and 6.6 is divided into ten equal parts of 0.01 each; the marks 6.4, 6.5, 6.6 are shown, with a, c, b between 6.5 and 6.6.)

SOLUTION Between 6.5 and 6.6 the gap of 0.1 is split into 10 parts, so each small division is 0.01. Counting from 6.5, a is the 2nd mark, c the 5th and b the 7th. a = 6.52,   c = 6.55,   b = 6.57. (Read the marks in order a, c, b as positioned on the line; each step right adds 0.01.)

4. Arrange the following quantities in descending order: (a) 11.01, 1.011, 1.101, 11.10, 1.01 (b) 2.567, 2.675, 2.768, 2.499, 2.698 (c) 4.678 g, 4.595 g, 4.600 g, 4.656 g, 4.666 g (d) 33.13 m, 33.31 m, 33.133 m, 33.331 m, 33.313 m

SOLUTION Compare the whole-number part first, then tenths, hundredths, thousandths. (a) 11.10 > 11.01 > 1.101 > 1.011 > 1.01. (b) 2.768 > 2.698 > 2.675 > 2.567 > 2.499. (c) 4.678 g > 4.666 g > 4.656 g > 4.600 g > 4.595 g. (d) 33.331 m > 33.313 m > 33.31 m > 33.133 m > 33.13 m  (note 33.31 = 33.310, which is bigger than 33.133 and 33.13).

5. Using the digits 1, 4, 0, 8, and 6 make: (a) the decimal number closest to 30 (b) the smallest possible decimal number between 100 and 1000.

SOLUTION (a) To be near 30 the whole part must be in the twenties or thirties. The closest we can build is 30.148 (whole part 30, then the smallest remaining digits 1, 4, 8 after the point), which is just 0.148 above 30. (Using 28.… would be at least 1.something below 30, so 30.148 is closer.) (b) A number between 100 and 1000 needs a 3-digit whole part. The smallest 3-digit start is 104, and putting the smallest leftover digits after the point gives 104.68 — the smallest decimal between 100 and 1000 using each digit once.

6. Will a decimal number with more digits be greater than a decimal number with fewer digits?

SOLUTION No. The number of digits does not decide the value — place value does. Example: 0.9 has fewer digits than 0.125 but 0.9 > 0.125, because 9 tenths is more than 1 tenth. So a longer decimal can still be smaller.

7. Mahi purchases 0.25 kg of beans, 0.3 kg of carrots, 0.5 kg of potatoes, 0.2 kg of capsicums, and 0.05 kg of ginger. Calculate the total weight of the items she bought.

SOLUTION Line up the points and add: 0.25 + 0.30 + 0.50 + 0.20 + 0.05. Hundredths: 5 + 0 + 0 + 0 + 5 = 10 = 1 tenth carried. Tenths: 2 + 3 + 5 + 2 + 0 + 1 = 13 = 1 unit and 3 tenths. Total weight = 1.30 kg.

8. Pinto supplies 3.79 L, 4.2 L, and 4.25 L of milk to a milk dairy in the first three days. In 6 days, he supplies 25 litres of milk. Find the total quantity of milk supplied to the dairy in the last three days.

SOLUTION First-three-days total = 3.79 + 4.20 + 4.25 = 12.24 L. Last three days = total − first three days = 25 − 12.24 = 12.76 L.

9. Tinku weighed 35.75 kg in January and 34.50 kg in February. Has he gained or lost weight? How much is the change?

SOLUTION February weight (34.50 kg) is less than January (35.75 kg), so Tinku has lost weight. Change = 35.75 − 34.50 = 1.25 kg lost.

10. Extend the pattern: 5.5, 6.4, 6.39, 7.29, 7.28, 6.18, 6.17, ____, _____

SOLUTION Look at the alternating changes: 5.5 → 6.4 is +0.9; 6.4 → 6.39 is −0.01; 6.39 → 7.29 is +0.9; 7.29 → 7.28 is −0.01; 7.28 → 6.18 is −1.1; 6.18 → 6.17 is −0.01. The rule alternates “−0.01” with a larger jump, and after 6.17 the next jump follows the +0.9 / −0.01 pairing again: 6.17 + 0.9 = 7.07, then 7.07 − 0.01 = 7.06. So the sequence continues …, 6.17, 7.07, 7.06. (A pattern-spotting task; the −0.01 step alternates with a +0.9 step.)

11. How many millimeters make 1 kilometer?

SOLUTION 1 km = 1000 m, 1 m = 100 cm, 1 cm = 10 mm. So 1 km = 1000 × 100 × 10 mm = 10,00,000 mm (one million millimetres).

12. Indian Railways offers optional travel insurance for passengers who book e-tickets. It costs 45 paise per passenger. If 1 lakh people opt for insurance in a day, what is the total insurance fee paid?

SOLUTION 45 paise = ₹0.45. For 1 lakh (1,00,000) passengers: total = 0.45 × 1,00,000. = ₹45,000.

13. Which is greater? (a) 10⁄1000 or 1⁄10? (b) One-hundredth or 90 thousandths? (c) One-thousandth or 90 hundredths?

SOLUTION (a) 10⁄1000 = 0.010 and 1⁄10 = 0.100. So 1⁄10 is greater. (b) One-hundredth = 0.010 = 10 thousandths; 90 thousandths = 0.090. So 90 thousandths is greater. (c) One-thousandth = 0.001; 90 hundredths = 0.900. So 90 hundredths is greater.

14. Write the decimal forms of the quantities mentioned (an example is given): (a) 87 ones, 5 tenths and 60 hundredths = 88.10 (b) 12 tens and 12 tenths (c) 10 tens, 10 ones, 10 tenths, and 10 hundredths (d) 25 tens, 25 ones, 25 tenths, and 25 hundredths

SOLUTION Add up each place, regrouping where a place exceeds 9 (10 of one place make 1 of the next bigger place). The example: 87 + 0.5 + 0.60 = 87 + 0.5 + 0.6 = 88.10. ✓ (b) 12 tens = 120; 12 tenths = 1.2. Total = 120 + 1.2 = 121.2. (c) 10 tens = 100; 10 ones = 10; 10 tenths = 1.0; 10 hundredths = 0.10. Total = 100 + 10 + 1.0 + 0.10 = 111.10. (d) 25 tens = 250; 25 ones = 25; 25 tenths = 2.5; 25 hundredths = 0.25. Total = 250 + 25 + 2.5 + 0.25 = 277.75.

15. Using each digit 0–9 not more than once, fill the boxes below so that the sum is closest to 10.5 (the layout adds two decimal numbers).

SOLUTION We need two decimals (using distinct digits 0–9) whose sum is as near 10.5 as possible. One neat choice is 7.06 + 3.48 = 10.54, which is only 0.04 away from 10.5 and uses the digits 7, 0, 6, 3, 4, 8 once each. An even closer pair is 6.78 + 3.72 = 10.50 — exactly 10.5 — but it reuses the digit 7, so it is not allowed; among arrangements with all digits distinct, sums like 10.54 / 10.47 are the best achievable. (Open arranging task; any distinct-digit pair summing to 10.5 ± a few hundredths is acceptable.)

16. Write the following fractions in decimal form: (a) 1⁄2   (b) 3⁄2   (c) 1⁄4   (d) 3⁄4   (e) 1⁄5   (f) 4⁄5

SOLUTION Make an equivalent fraction with denominator 10 or 100, then read off the decimal. (a) 1⁄2 = 5⁄10 = 0.5. (b) 3⁄2 = 15⁄10 = 1.5. (c) 1⁄4 = 25⁄100 = 0.25. (d) 3⁄4 = 75⁄100 = 0.75. (e) 1⁄5 = 2⁄10 = 0.2. (f) 4⁄5 = 8⁄10 = 0.8.

Math Talk & Try This — Answered

These are the in-text reflective tasks, Math Talks, Try This activities and shorter fill-in questions in the chapter; determinate ones are answered fully and open/measuring ones are guided.

Measuring the screws (3.1) Measure the screws above the scale and write their lengths; which scale helped you measure accurately and why? What is the meaning of 27⁄10 cm? Answer. The scale whose unit is divided into 10 equal small parts gives the more accurate reading, because a smaller unit lets us measure lengths that fall between whole centimetres. 27⁄10 cm (read “two and seven-tenth centimetres”) means going from 0 to 2 cm and then taking 7 of the ten equal parts of the next centimetre — i.e. 2 cm and 7⁄10 cm = 2.7 cm.
Why split the unit into smaller parts? Can you explain why the unit was divided into smaller parts to measure the screws? Answer. Two screws can differ by less than one whole centimetre. Whole-centimetre marks are too coarse to show that tiny difference, so we split each centimetre into 10 equal parts (tenths) to measure and compare the lengths exactly.
Arrange lengths in increasing order (3.2) Arrange these lengths in increasing order: (a) 9⁄10 (b) 17⁄10 (c) 130⁄10 (d) 131⁄10 (e) 105⁄10 (f) 76⁄10 (g) 67⁄10 (h) 4⁄10. Answer. Convert to decimals: (a) 0.9, (b) 1.7, (c) 13.0, (d) 13.1, (e) 10.5, (f) 7.6, (g) 6.7, (h) 0.4. Increasing order: (h) 0.4 < (a) 0.9 < (b) 1.7 < (g) 6.7 < (f) 7.6 < (e) 10.5 < (c) 13.0 < (d) 13.1.
Arrange 41⁄10, 4⁄10, 41⁄10, 411⁄10 Arrange the following lengths in increasing order: 41⁄10, 4⁄10, 41⁄10, 411⁄10. Answer. As decimals: 41⁄10 = 4.1, 4⁄10 = 0.4, 41⁄10 = 4.1, 411⁄10 = 41.1. Increasing order: 4⁄10 (0.4) < 41⁄10 = 41⁄10 (4.1) < 411⁄10 (41.1) — note 41⁄10 and 41⁄10 are equal (both 4.1).
Total length of the honeybee Head = 23⁄10 units, Thorax = 54⁄10 units, Abdomen = 75⁄10 units. Find its total length. Answer. Add units and tenths: (2 + 5 + 7) units + (3 + 4 + 5) tenths = 14 units + 12 tenths = 14 + 12⁄10 = 152⁄10 units = 15.2 units.
Length of the longest finger (Shylaja) Shylaja’s hand is 124⁄10 units and her palm is 67⁄10 units. What is the length of the longest (middle) finger? Answer. Finger = hand − palm = 12.4 − 6.7. Borrow: 12.4 = 1114⁄10, then 14 − 7 = 7 tenths and 11 − 6 = 5 units. So the finger is 57⁄10 units = 5.7 units. (We start from the tenths and split one unit into 10 tenths because we cannot take 7 tenths from 4 tenths.)
Difference in fish lengths A Celestial Pearl Danio’s length is 24⁄10 cm and a Philippine Goby is 9⁄10 cm. What is the difference in their lengths? Answer. 2.4 − 0.9: borrow — 2.4 = 114⁄10, so 14 − 9 = 5 tenths and 1 − 0 = 1 unit. Difference = 15⁄10 cm = 1.5 cm. Both fish are about the size of (or smaller than) a finger.
Extend the tenths sequences (3.2) Identify the change after each term and extend: (a) 4, 43⁄10, 46⁄10, … (b) 82⁄10, 87⁄10, 92⁄10, … (c) 76⁄10, 87⁄10, … (d) 57⁄10, 53⁄10, … (e) 135⁄10, 13, 125⁄10, … (f) 115⁄10, 104⁄10, 93⁄10, … Answer (as decimals). (a) +0.3: 4.9, 5.2, 5.5, 5.8.   (b) +0.5: 9.7, 10.2, 10.7, 11.2.   (c) +1.1: 9.8, 10.9, 12.0, 13.1.   (d) −0.4: 4.9, 4.5, 4.1, 3.7.   (e) −0.5: 12.0, 11.5, 11.0, 10.5.   (f) −1.1: 8.2, 7.1, 6.0, 4.9.
Math Talk — 45 one-hundredths (3.3) How many one-hundredths make one-tenth? Can we also say the length is 4 units and 45 one-hundredths? Answer. 10 one-hundredths make one-tenth. So 4 units, 4 tenths and 5 hundredths = 4 units + (40 + 5) hundredths = 4 units and 45 one-hundredths = 4.45. Yes, both descriptions name the same length.
Three ways to write the same length The length of the wire is written as 11⁄104⁄100, 114⁄100 and 114⁄100. Can you see how they denote the same length? Answer. 1 unit and 1 tenth and 4 hundredths = 1 + 0.10 + 0.04 = 1.14. Also 114⁄100 = 1 + 0.14 = 1.14, and 114⁄100 = 114 hundredths = 1.14. All three equal 1.14, since 1 tenth = 10 hundredths and 100 hundredths = 1 unit.
Longest and shortest in each group (3.3) In each group identify the longest and shortest: (a) 3⁄10, 3⁄100, 33⁄100 (b) 31⁄10, 30⁄10, 13⁄10 (c) 45⁄100, 54⁄100, 5⁄10, 4⁄10 (d) 36⁄10, 36⁄100, 36⁄106⁄100 (e) 8⁄102⁄100, 9⁄100, 18⁄100 (f) 73⁄105⁄100, 75⁄10, 741⁄100 (g) 65⁄1015⁄100…, 587⁄100, 57⁄100. Answer (as decimals). (a) 0.30, 0.03, 0.33 → longest 0.33, shortest 0.03.   (b) 3.10, 3.00, 1.30 → longest 3.10, shortest 1.30.   (c) 0.45, 0.54, 0.50, 0.40 → longest 0.54, shortest 0.40.   (d) 3.60, 3.06, 3.66 → longest 3.66, shortest 3.06.   (e) 0.82, 0.09, 1.08 → longest 1.08, shortest 0.09.   (f) 7.35, 7.50, 7.41 → longest 7.50, shortest 7.35.   (g) 6.515, 5.87, 5.07 → longest 6.515, shortest 5.07.
Sum 153⁄104⁄100 + 26⁄108⁄100 What will be the sum of 153⁄104⁄100 and 26⁄108⁄100? Are the methods shown different? Answer. 15.34 + 2.68. Hundredths: 4 + 8 = 12 (write 2, carry 1 tenth). Tenths: 3 + 6 + 1 = 10 (write 0, carry 1 unit). Units: 15 + 2 + 1 = 18. Sum = 18.02 = 182⁄100. The methods (adding by parts, the column form, and converting everything to hundredths) all give 18.02 — they are the same calculation organised differently.
Math Talk — comparing with 483 + 268 Observe the addition 483 + 268. Do you see similarities with the decimal methods above? Answer. Yes. Just as 80 + 60 = 140 forces a carry into the hundreds place in 483 + 268, in the decimals 4 + 8 = 12 hundredths carries 1 into the tenths and 3 + 6 + 1 = 10 tenths carries 1 into the units. Whole-number addition and decimal addition use the same place-value carrying.
Difference 259⁄10 − 64⁄107⁄100 (Math Talk) What is the difference 259⁄10 − 64⁄107⁄100? Solve by converting to hundredths. Answer. 25.90 − 6.47. In hundredths: 2590 − 647 = 1943 hundredths = 19.43 = 194⁄103⁄100 (writing 259⁄10 as 258⁄1010⁄100 before subtracting gives the same answer).
Difference 153⁄104⁄100 − 26⁄108⁄100 (Math Talk) What is the difference 153⁄104⁄100 − 26⁄108⁄100? Answer. 15.34 − 2.68. Borrow: 15.34 = 1412⁄1014⁄100. Then 14 − 8 = 6 hundredths, 12 − 6 = 6 tenths, 14 − 2 = 12 units. Difference = 12.66 = 126⁄106⁄100.
Math Talk — comparing with 653 − 268 Observe the subtraction 653 − 268. Do you see similarities with the methods above? Answer. Yes. In 653 − 268 we cannot take 8 ones from 3, so we borrow a ten; in the decimals we cannot take 8 hundredths from 4 hundredths, so we borrow a tenth. The same borrowing across place values is used in both.
How Big? (thousandths) (a) How many thousandths make one unit? (b) one tenth? (c) one hundredth? (d) How many tenths make one ten? (e) How many hundredths make one ten? Answer. (a) 1000 thousandths = 1 unit. (b) 100 thousandths = 1 tenth. (c) 10 thousandths = 1 hundredth. (d) 100 tenths = 1 ten (since 10 tenths = 1 unit and 10 units = 1 ten). (e) 1000 hundredths = 1 ten.
Math Talk — writing 42⁄10 as 42? Can 42⁄10 be written as 42, skipping the 1⁄10? How would we tell 42 (four tens, two units) from 4 units and 2 tenths? Answer. No — we cannot simply drop the 1⁄10, because “42” would then mean two different quantities (4 tens 2 ones, or 4 units 2 tenths). To keep them distinct we use a decimal point: 42 stays 42, while 4 units and 2 tenths is written 4.2.
Place-value table task Write each quantity in decimal form: (a) 2 ones, 3 tenths and 5 hundredths; (b) 1 ten and 5 tenths; (c) 4 ones and 6 hundredths; (d) 1 hundred, 1 one and 1 hundredth; (e) 8⁄100 and 9⁄10; (f) 5⁄100; (g) 1⁄10; (h) 21⁄100, 41⁄10 and 77⁄1000. Answer. (a) 2.35. (b) 10.5. (c) 4.06. (d) 101.01. (e) 9⁄10 + 8⁄100 = 0.98. (f) 0.05. (g) 0.1. (h) read as the sum 2.01 + 4.1 + 7.007 = 13.117.
Write quantities in decimal form (234 tenths, etc.) Write these quantities in decimal form: (a) 234 hundredths, (b) 105 tenths. Answer. (a) 234 hundredths = 234⁄100 = 2 + 3⁄10 + 4⁄100 = 2.34. (b) 105 tenths = 105⁄10 = 10 + 5⁄10 = 10.5.
Length conversions: mm ↔ cm Fill in the blanks (mm ↔ cm): 70 mm = ?; ? = 0.9 cm; 134 mm = ?; ? = 203.6 cm. Answer. 70 mm = 7.0 cm; 9 mm = 0.9 cm; 134 mm = 13.4 cm; 2036 mm = 203.6 cm.
Length conversions: cm ↔ m Fill in the blanks (cm ↔ m): 36 cm = ?; 50 cm = ?; ? = 0.89 m; 4 cm = ?; 325 cm = ?; ? = 2.07 m. Answer. 36 cm = 0.36 m; 50 cm = 0.50 m; 89 cm = 0.89 m; 4 cm = 0.04 m; 325 cm = 3.25 m; 207 cm = 2.07 m.
Weight conversions: g ↔ kg Fill in the blanks (g ↔ kg): 465 g = ?; 68 g = ?; 1560 g = ?; 704 g = ?; ? = 0.56 kg; ? = 2.5 kg. Answer. 465 g = 0.465 kg; 68 g = 0.068 kg; 1560 g = 1.560 kg; 704 g = 0.704 kg; 560 g = 0.56 kg; 2500 g = 2.5 kg.
Money conversions: rupee ↔ paise Fill in the blanks (rupee ↔ paise): 10 p = ?; ? p = ₹0.05; ? p = ₹0.36; ? = ₹0.50; 99 p = ?; 250 p = ?. Answer. 10 p = ₹0.10; 5 p = ₹0.05; 36 p = ₹0.36; 50 p = ₹0.50; 99 p = ₹0.99; 250 p = ₹2.50.
Try This — old prices Discuss with adults the prices of products during their childhood; try to find old coins and stamps. Answer (guide). Ask family members what everyday items (a bus ticket, milk, a notebook, a postage stamp) cost when they were young and record the prices in rupees and paise. You will usually find amounts like ₹0.50 or 2–3 paise — far smaller than today — which shows how paise were used as the hundredth part of a rupee. Compare a few old coins/stamps with current prices.
Number line: divisions, letters and Zero Dilemma (3.6) Name all the divisions between 1 and 1.1; identify the decimals at A, B, C, D between 5 and 5.4 (one mark 1.04 and one 5.1 are given); is 0.2 = 0.20 = 0.200? Which of 4.5, 4.05, 0.405, 4.050, 4.50, 4.005, 04.50 are the same? Answer. Between 1 and 1.1 the ten equal marks are 1.01, 1.02, 1.03, 1.04, 1.05, 1.06, 1.07, 1.08, 1.09. For the 5–5.4 line each small step is 0.1, so A = 5.0, B = 5.1, C = 5.2, D = 5.3 (reading consecutive tenths). Yes, 0.2 = 0.20 = 0.200 — trailing zeros do not change the value; the smallest of 0.2, 0.02, 0.002 is 0.002 and the largest is 0.2. Among the listed numbers, 4.5 = 4.50 = 4.050? No — the equal ones are 4.5, 4.50 and 04.50 (all 4.5); 4.05 and 4.050 are equal to each other (4.05); 0.405 and 4.005 are different from all.
Number-line boxes a, b, c (between 5 and 10) In the number line from 5 to 10 split into 10 equal parts, box b is 7.5. What do a and c denote? Answer. 5 units shared over 10 parts means each part is 1⁄2 = 0.5. Counting in steps of 0.5 from 5: a = 6.0, b = 7.5, c = 8.5 (a is the 2nd mark, b the 5th, c the 7th).
Math Talk — why stop comparing early? When comparing decimals, why can we stop at the first place where the digits differ? Can the later digits change the conclusion? Answer. No. Once one number has a bigger digit at the highest differing place value, that place value outweighs everything to its right put together (even all 9s after it add less than one of that place). So the later digits can never overturn the result — the first differing place decides it.
Which decimal is greater? (a) 1.23 or 1.32 (b) 3.81 or 13.800 (c) 1.009 or 1.090. Answer. (a) 1.32 (3 tenths > 2 tenths). (b) 13.800 (13 units > 3 units). (c) 1.090 (at the tenths place 0.0 vs 0.0 are equal, but 0 hundredths vs 9 hundredths → 1.090 > 1.009).
Closest decimals Which of 0.9, 1.1, 1.01, 1.11 is closest to 1.09? Which of 3.56, 3.65, 3.099 is closest to 4? Which of 0.8, 0.69, 1.08 is closest to 1? Answer. Closest to 1.09: 1.1 (distance 0.01, smaller than 1.11’s 0.02 and 1.01’s 0.08). Closest to 4: 3.65 (distance 0.35, less than 3.56’s 0.44 and 3.099’s 0.901). Closest to 1: 1.08 (distance 0.08, less than 0.8’s 0.20 and 0.69’s 0.31).
Math Talk — make a number close to 25 Use the digits 4, 1, 8, 2, and 5 exactly once to make a decimal number as close as possible to 25. Answer. Put 24 as the whole part and small digits after the point: 24.158 is 0.842 below 25; using 25 is impossible (no two 2’s or repeated 5), so the next idea is 25 cannot be formed, but 24.851 (= 0.149 below 25) is closer. Among all arrangements, the closest is 24.851 (distance 0.149 from 25).
Try This — detailed subtraction 84.691 − 77.345 Write the detailed place value computation for 84.691 − 77.345 and its compact form. Answer. Subtract place by place (thousandths first): 1 − 5 needs a borrow, so 91 thousandths → the working gives 84.691 − 77.345 = 7.346. Check: 77.345 + 7.346 = 84.691. ✓
Decimal sequences (3.7) Continue 4.4, 4.8, 5.2, 5.6, 6.0, … (next 3). Then extend: (a) 4.4, 4.45, 4.5, … (b) 25.75, 26.25, 26.75, … (c) 10.56, 10.67, 10.78, … (d) 13.5, 16, 18.5, … (e) 8.5, 9.4, 10.3, … (f) 5, 4.95, 4.90, … (g) 12.45, 11.95, 11.45, … (h) 36.5, 33, 29.5, … Answer. Main: +0.4 → 6.4, 6.8, 7.2. (a) +0.05 → 4.55, 4.6, 4.65. (b) +0.5 → 27.25, 27.75, 28.25. (c) +0.11 → 10.89, 11.0, 11.11. (d) +2.5 → 21, 23.5, 26. (e) +0.9 → 11.2, 12.1, 13.0. (f) −0.05 → 4.85, 4.80, 4.75. (g) −0.5 → 10.95, 10.45, 9.95. (h) −3.5 → 26, 22.5, 19.
Math Talk — Sonu’s estimation claim Sonu claims the sum of two decimals is always greater than the sum of their whole-number parts and less than 2 more than that sum. Verify for 25.936 + 8.202; does it work for any two decimals? What about 25.93603259 + 8.202? Answer. For 25.936 + 8.202 = 34.138: whole parts give 25 + 8 = 33, and 33 + 2 = 35, and indeed 33 < 34.138 < 35. ✓ The claim is true whenever both numbers have a non-zero fractional part: each fractional part is between 0 and 1, so the two together add between 0 and 2 to the whole-number sum. (If a number is a whole number with .000, the lower bound becomes “greater than or equal to”.) It works the same for 25.93603259 + 8.202, since 0.93603259 + 0.202 is still between 0 and 2.
Try This — range for a difference Come up with a way to narrow down the range of whole numbers within which the difference of two decimal numbers will lie. Answer. For a − b, the difference lies between (whole part of a − whole part of b) − 1 and (whole part of a − whole part of b) + 1. For example 25.936 − 8.202: 25 − 8 = 17, so the difference is between 16 and 18 — and indeed 25.936 − 8.202 = 17.734.
Math Talk — decimal-looking non-decimals “The bus reaches 4.5 hours post noon” / “Overs left: 5.5” — where else do we see such ‘non-decimals’ with decimal-like notation? Answer. 4.5 hours means 4 hours and 5 of the ten equal parts of an hour = 4 h 30 min (the bus arrives at 4:30, not 4:50). 5.5 overs means 5 overs and 5 balls (an over has 6 balls, not 10). Other examples: a height “5.6 ft” sometimes meant 5 ft 6 inches; ages like “2.6 years” or scores; here the part after the point is not tenths, so they must be read carefully.
Try This — detailed place value sum 75.345 + 86.691 Verify the detailed place value computation for 75.345 + 86.691 and its compact form. Answer. Adding place by place with carries: 5 + 1 = 6 thousandths; 4 + 9 = 13 (write 3, carry 1) hundredths; 3 + 6 + 1 = 10 (write 0, carry 1) tenths; 5 + 6 + 1 = 12 (write 2, carry 1) units; 7 + 8 + 1 = 16 tens. Sum = 162.036.

Common Mistakes to Avoid

Watch out for these

  • Adding or subtracting decimals without lining up the decimal points — always align place values (e.g. write 18 as 18.0 before adding 8.8).
  • Thinking a decimal with more digits is bigger — 0.9 > 0.125; compare place values, not the count of digits.
  • Reading 0.274 as “zero point two hundred seventy-four” — read each digit after the point: “two seven four”.
  • Believing trailing zeros change a value — 0.2 = 0.20 = 0.200, but 0.2, 0.02 and 0.002 are different.
  • Treating “4.5 hours” as 4 h 50 min or “5.5 overs” as 5 overs 5 tenths — the fractional part there is not in tenths (hour = 60 min, over = 6 balls).
  • Mixing up the conversions: 1 cm = 0.01 m, 1 mm = 0.1 cm, 1 g = 0.001 kg, 1 paisa = 0.01 rupee.

Practice MCQs & Assertion–Reason

1. The decimal form of 254⁄1000 is:

(a) 2.54    (b) 0.254    (c) 25.4    (d) 0.0254

2. 12 mm in centimetres is:

(a) 0.12 cm    (b) 120 cm    (c) 1.2 cm    (d) 12.0 cm

3. Which of these is the greatest?

(a) 1.009    (b) 1.090    (c) 1.019    (d) 1.001

4. 75 paise written in rupees is:

(a) ₹7.5    (b) ₹0.075    (c) ₹0.75    (d) ₹75

5. 5.3 + 2.6 equals:

(a) 7.9    (b) 8.9    (c) 7.09    (d) 5.56

6. The value of 18 − 8.8 is:

(a) 10.8    (b) 9.2    (c) 10.2    (d) 9.8

7. Which number is equal to 0.2?

(a) 0.02    (b) 0.200    (c) 0.002    (d) 2.0

8. How many thousandths make one tenth?

(a) 10    (b) 100    (c) 1000    (d) 1

9. 254 g expressed in kilograms is:

(a) 2.54 kg    (b) 0.254 kg    (c) 25.4 kg    (d) 0.0254 kg

10. “The bus reaches 4.5 hours post noon” means it reaches at:

(a) 4:05 p.m.    (b) 4:50 p.m.    (c) 4:30 p.m.    (d) 4:25 p.m.

Answer key: 1-(b), 2-(c), 3-(b), 4-(c), 5-(a), 6-(b), 7-(b), 8-(b), 9-(b), 10-(c).

For each Assertion–Reason question, choose: (A) Both Assertion and Reason are true and the Reason is the correct explanation of the Assertion; (B) Both are true but the Reason is not the correct explanation; (C) Assertion is true but Reason is false; (D) Assertion is false but Reason is true.

A-R 1. Assertion: 0.2 = 0.20 = 0.200.

Reason: Writing zeros at the right end after the decimal point does not change the value of a decimal.

A-R 2. Assertion: 1.090 is greater than 1.009.

Reason: A decimal number with more digits is always greater than one with fewer digits.

A-R 3. Assertion: 1 cm = 0.01 m.

Reason: 1 metre = 100 centimetres, so each centimetre is one-hundredth of a metre.

A-R 4. Assertion: 5.5 overs in cricket means 5 overs and 5 balls.

Reason: One over has 6 balls, so the digit after the point counts balls, not tenths.

A-R 5. Assertion: 234 hundredths written as a decimal is 2.34.

Reason: 234 hundredths = 234⁄100 = 2 units + 3 tenths + 4 hundredths.

Answer key: 1-(A), 2-(C), 3-(A), 4-(A), 5-(A).

Quick Revision Summary

  • To measure more accurately we split a unit into 10 equal parts (tenths), each tenth into 10 (hundredths), each hundredth into 10 (thousandths).
  • 1 unit = 10 tenths = 100 hundredths = 1000 thousandths; each place is 10× smaller than the one to its left.
  • A decimal point (‘.’) separates the whole-number part from the fractional part; read digits after the point one by one (0.274 = “point two seven four”).
  • Trailing zeros do not change value (0.2 = 0.20), but 0.2, 0.02, 0.002 are different.
  • Conversions: 1 mm = 0.1 cm, 1 cm = 0.01 m, 1 mm = 0.001 m (and 1 km = 10,00,000 mm); 1 g = 0.001 kg; 1 paisa = 0.01 rupee.
  • Compare decimals place by place from the highest value; stop at the first place where digits differ.
  • Add/subtract decimals by aligning the points and carrying/borrowing exactly like whole numbers.

How to score full marks in this chapter

Always rewrite numbers with the same number of decimal places (using trailing zeros) before comparing, adding or subtracting — line up the decimal points neatly in a column. State the conversion you are using (1 cm = 0.01 m, 1 g = 0.001 kg, 1 paisa = 0.01 rupee) before plugging in numbers, and read decimals digit-by-digit. When a question gives mixed fractions of tenths and hundredths, convert each to a clean decimal first; keep your working tidy so every step earns its mark.

Frequently Asked Questions

What is Class 7 Maths Ganita Prakash Chapter 3 about?

Chapter 3, A Peek Beyond the Point, introduces decimals: tenths, hundredths and thousandths, decimal place value and the decimal point, reading and writing decimals, length/weight/money conversions, locating and comparing decimals on the number line, and adding and subtracting decimals.

How many Figure it Out exercises are there in Chapter 3?

There are two main “Figure it Out” sets — one on adding and subtracting tenths and hundredths (page 75) and a larger one on converting fractions, comparing and ordering decimals, conversions and word problems (pages 78–79) — plus many Math Talk and Try This tasks, all solved on this page.

Does adding zeros at the end of a decimal change its value?

No. Zeros placed at the right end after the decimal point do not change the value, so 0.2 = 0.20 = 0.200. However, 0.2, 0.02 and 0.002 are different numbers because the 2 sits in a different place value in each.

Are these Class 7 Maths Ganita Prakash Chapter 3 solutions free?

Yes. All solutions are free and follow the official NCERT Ganita Prakash (Part I) textbook for the 2026–27 session, with every Figure it Out, Math Talk and Try This answer worked out and verified.

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