NCERT Solutions for Class 7 Maths Chapter 3: A Peek Beyond the Point – Ganita Prakash

Chapter 3 of the Class 7 NCERT Ganita Prakash textbook (Part 1) is titled “A Peek Beyond the Point” — it introduces decimals: why we need units smaller than 1 (tenths, hundredths, thousandths), place value with decimals, comparing and ordering decimals, decimals on a number line, addition/subtraction, and measurement unit conversions. These Class 7 Mathematics Chapter 3 solutions are also useful as quick revision notes before exams.

Below are original, independently verified solutions to the chapter’s key questions.

3.1–3.2 The Need for Smaller Units & A Tenth Part

Q. A honeybee’s body is divided into three parts: head = 2 3/10 units, thorax = 5 4/10 units, abdomen = 7 5/10 units. Find its total length.
Solution: 2.3 + 5.4 + 7.5 = 15.2 units.

Q. A Celestial Pearl Danio fish measures 2 4/10 cm, and a Philippine Goby measures 9/10 cm. Find the difference in their lengths.
Solution: 2.4 − 0.9 = 1.5 cm (i.e. 1 5/10 cm).

Q. Arrange in increasing order: 9/10, 1 7/10, 130/10, 13 1/10, 10 5/10, 7 6/10, 6 7/10, 4/10.
Solution: Converting all to decimals (0.9, 1.7, 13.0, 13.1, 10.5, 7.6, 6.7, 0.4) and ordering: 0.4 < 0.9 < 1.7 < 6.7 < 7.6 < 10.5 < 13.0 < 13.1.

Q. Extend the pattern: 4, 4 3/10, 4 6/10, ___, ___, ___, ___ (find the next four terms).
Solution: Each term increases by 0.3, so the pattern continues: 4.9, 5.2, 5.5, 5.8. Next four terms: 4.9, 5.2, 5.5, 5.8.

3.4 Decimal Place Value

Q. (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?
Solution: (a) 1,000 thousandths = 1 unit. (b) 100 thousandths = 1 tenth. (c) 10 thousandths = 1 hundredth. (d) 100 tenths = 1 ten. (e) 1,000 hundredths = 1 ten.

Q. Write in decimal form: (a) 234 hundredths (b) 105 tenths.
Solution: (a) 234/100 = 200/100+30/100+4/100 = 2 + 3/10 + 4/100 = 2.34. (b) 105/10 = 100/10+5/10 = 10 + 5/10 = 10.5.

3.5 Units of Measurement

Q. How many mm does 1 m have?
Solution: 1 m = 100 cm, and 1 cm = 10 mm, so 1 m = 100 × 10 = 1,000 mm.

Q. How many mm are there in 1 km?
Solution: 1 km = 1,000 m, and 1 m = 1,000 mm, so 1 km = 1,000 × 1,000 = 1,000,000 mm.

3.6 Locating and Comparing Decimals

Q. Name all the divisions between 1 and 1.1 on a number line (marked in hundredths).
Solution: 1.01, 1.02, 1.03, 1.04, 1.05, 1.06, 1.07, 1.08, 1.09 — the nine interior marks dividing the 1.00–1.10 gap into tenths of a tenth.

Q. Which of 0.2, 0.02, 0.002 is smallest and which is largest?
Solution: 0.002 is smallest and 0.2 is largest (0.002 < 0.02 < 0.2).

Q. Which of these are equal: 4.5, 4.05, 0.405, 4.050, 4.50, 4.005, 04.50?
Solution: 4.5 = 4.50 = 04.50 (trailing/leading zeros that don’t add a nonzero digit don’t change the value). 4.05 = 4.050. 0.405 and 4.005 are both different from each other and from the rest.

Q. Which is greater: (a) 1.23 or 1.32 (b) 3.81 or 13.800 (c) 1.009 or 1.090?
Solution: (a) 1.32 > 1.23 (compare tenths digit: 3>2). (b) 13.800 > 3.81 (more whole-number digits). (c) 1.090 > 1.009 (compare hundredths digit: 9>0).

Q. Which of 0.9, 1.1, 1.01, 1.11 is closest to 1.09?
Solution: Distances from 1.09: |1.09−0.9|=0.19, |1.09−1.1|=0.01, |1.09−1.01|=0.08, |1.09−1.11|=0.02. The smallest distance is 0.01, so 1.1 is closest.

Q. Using each of the digits 4, 1, 8, 2, 5 exactly once, form a decimal as close as possible to 25.
Solution: Use 2 and 5 for the whole-number part (25) and arrange the remaining digits 1, 4, 8 in ascending order after the decimal point for the smallest possible “extra” distance: 25.148 (only 0.148 away from 25 — the closest achievable arrangement using all five digits exactly once).

3.7 Addition and Subtraction of Decimals

Q. Find the sums: (a) 5.3+2.6 (b) 18+8.8 (c) 2.15+5.26 (d) 9.01+9.10
Solution: (a) 7.9 (b) 26.8 (c) 7.41 (d) 18.11

Q. Find the differences: (a) 5.6−2.3 (b) 18−8.8 (c) 10.4−4.5 (d) 17−16.198
Solution: (a) 3.3 (b) 9.2 (c) 5.9 (d) 0.802

Q (Sonu’s estimation claim). Sonu claims that the sum of two decimals always lies strictly between (sum of their whole-number parts) and (that sum + 2). Test this with 25.936 + 8.202.
Solution: Whole-number parts sum = 25+8 = 33. Exact sum: 25.936+8.202 = 34.138. Check: 33 < 34.138 < 35. ✓ The claim holds, because each decimal part is less than 1, so their sum is less than 2.

Q. Extend the alternating pattern: 5.5, 6.4, 6.39, 7.29, 7.28, 8.18, 8.17, ___, ___.
Solution: The pattern alternates +0.9 then −0.01: 8.17+0.9 = 9.07, then 9.07−0.01 = 9.06. Next two terms: 9.07, 9.06.

Q (Mahi’s shopping). Mahi buys 0.25 kg beans, 0.3 kg carrots, 0.5 kg potatoes, 0.2 kg capsicums, and 0.05 kg ginger. Find the total weight.
Solution: 0.25+0.3+0.5+0.2+0.05 = 1.3 kg.

Q (Pinto’s milk supply). Pinto supplies 3.79 L, 4.2 L, and 4.25 L on the first three days of a week, totalling 25 L over 6 days. Find the total supplied over the remaining 3 days.
Solution: First 3 days = 3.79+4.2+4.25 = 12.24 L. Remaining = 25−12.24 = 12.76 L.

Q (Tinku’s weight). Tinku weighed 35.75 kg in January and 34.50 kg in February. Did he gain or lose weight, and by how much?
Solution: Since 35.75 > 34.50, Tinku lost weight. Change = 35.75−34.50 = 1.25 kg.

3.8 More on the Decimal System

Q. Arrange in descending order: 11.01, 1.011, 1.101, 11.10, 1.01.
Solution: 11.10 > 11.01 > 1.101 > 1.011 > 1.01.

Q. Using digits 1, 4, 0, 8, 6 (each exactly once): (a) form a decimal as close as possible to 30 (b) form the smallest possible decimal between 100 and 1,000.
Solution: (a) Best whole-number part using two of the digits is 40 (using 4, 0) — closer to 30 than 10, 60, or 80. Remaining digits 1, 6, 8 arranged ascending: 40.168. (b) Smallest 3-digit whole part without a leading zero: 104 (using 1, 0, 4). Remaining digits 6, 8 ascending: 104.68.

Q. Does a decimal number with more digits always represent a greater value?
Solution: No. For example, 0.9 > 0.123456789, even though the second number has far more digits — what matters is the value of each place, starting from the leftmost (most significant) digit, not the total digit count.

Q. Convert 45 paise to rupees and find the cost of travel insurance for 1,00,000 (1 lakh) passengers at 45 paise each.
Solution: 45 paise = ₹0.45. Total cost = 0.45 × 1,00,000 = ₹45,000.

Q. 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 = 0.01, 1/10 = 0.1 ⇒ 1/10 is greater. (b) 1/100 = 0.01, 90/1000 = 0.09 ⇒ 90 thousandths is greater. (c) 1/1000 = 0.001, 90/100 = 0.9 ⇒ 90 hundredths is greater.

Q. Write as decimals: (a) 87 ones, 5 tenths, 60 hundredths (b) 12 tens and 12 tenths (c) 10 tens, 10 ones, 10 tenths, 10 hundredths.
Solution: (a) 87 + 0.5 + 0.60 = 88.10. (b) (12×10) + (12×0.1) = 120 + 1.2 = 121.2. (c) (10×10)+(10×1)+(10×0.1)+(10×0.01) = 100+10+1.0+0.10 = 111.10.

Q. Write as decimals: (a) 1/2 (b) 3/2 (c) 1/4 (d) 3/4 (e) 1/5 (f) 4/5.
Solution: (a) 0.5 (b) 1.5 (c) 0.25 (d) 0.75 (e) 0.2 (f) 0.8.

Why This Chapter Matters (for Boards)

Decimal fluency here (place value, comparison, addition/subtraction, unit conversion) underpins nearly every later Class 7-10 topic involving measurement, money, percentages, and data.

More on This Chapter

See also: Class 7 Maths Part 1 NCERT Book and the Class 7 Maths Formulas Handbook.

Related pages: Extra Questions: Class 7 Maths Chapter 3 | Revision Notes: Class 7 Maths Chapter 3

Frequently Asked Questions

Q: How do I compare two decimals with different numbers of digits after the point?
A: Compare place by place starting from the leftmost digit after the decimal point (tenths, then hundredths, then thousandths); pad the shorter number with trailing zeros if it helps to compare digit-by-digit at each place.

Q: Why doesn’t adding a zero after a decimal point change its value?
A: Because that zero represents “0 of the next smaller place value,” contributing nothing new — e.g. 4.5 and 4.50 both mean 4 + 5/10, since the extra 0/100 adds nothing.