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NCERT Solutions for Class 7th Maths Chapter 3 A Peek Beyond the Point

Updated on 2026-09-19

About this chapter

A unit can be split into 10 equal parts (one-tenths), each tenth into 10 equal parts (one-hundredths), each hundredth into 10 one-thousandths, and so on. 10 one-tenths = 1 unit, 10 one-hundredths = 1 tenth, 100 one-hundredths = 1 unit, 1000 one-thousandths = 1 unit. The decimal point ‘.’ separates the whole-number part from the fractional part: 70.5 means 7 × 10 + 5 × 1/10, while 7.05 means 7 × 1 + 5 × 1/100. Putting zeros on the right of the last decimal digit does not change the value: 0.2 = 0.20 = 0.200. But 0.2, 0.02 and 0.002 are all different. To compare decimals, compare digits from the highest place value downwards; the first place where they differ decides. Decimals are added and subtracted exactly like whole numbers — line up the decimal points, then regroup 10 hundredths as 1 te

  • The Need for Smaller Units
  • A Tenth Part
  • A Hundredth Part
  • Decimal Place Value
  • Units of Measurement
  • Locating and Comparing Decimals / There is Zero Dilemma!
  • Locating and Comparing Decimals
  • Addition and Subtraction of Decimals
  • Decimal Sequences / Estimating Sums and Differences
  • More on the Decimal System
Quick revision
IdeaIn fraction formIn decimal formRead as
One-tenth1/100.1zero point one
One-hundredth1/1000.01zero point zero one
One-thousandth1/10000.001zero point zero zero one
Four and eight-tenths4 8/10 = 48/104.8four point eight
One and fourteen-hundredths1 14/100 = 114/1001.14one point one four
1 mm in cm1/10 cm0.1 cmone-tenth of a centimetre
1 cm in m1/100 m0.01 mone-hundredth of a metre
1 g in kg1/1000 kg0.001 kgone-thousandth of a kilogram
1 paisa in rupees1/100 rupee₹0.01one-hundredth of a rupee
Comparing6.456 vs 6.4656.465 is greater5 hundredths < 6 hundredths
Adding2.7 + 3.56.212 tenths = 1 unit + 2 tenths
Subtracting3.5 – 2.70.8borrow 1 unit as 10 tenths
Read the chapter

Exercises

  1. In-text Questions — The Need for Smaller Units Page 46–47
  2. In-text Questions — A Tenth Part Page 49
  3. In-text Questions — A Tenth Part Page 50
  4. In-text Questions — A Tenth Part Page 51
  5. In-text Questions — A Tenth Part Page 52
  6. In-text Questions — A Hundredth Part Page 53
  7. In-text Questions — A Hundredth Part Page 54–55
  8. In-text Questions — A Hundredth Part Page 55–56
  9. In-text Questions — A Hundredth Part Page 56
  10. In-text Questions — A Hundredth Part Page 57
  11. In-text Questions — A Hundredth Part Page 58
  12. Figure it Out — A Hundredth Part Page 58
  13. In-text Questions — Decimal Place Value Page 59
  14. In-text Questions — Decimal Place Value Page 60
  15. In-text Questions — Decimal Place Value Page 61
  16. In-text Questions — Decimal Place Value Page 63
  17. In-text Questions — Units of Measurement Page 64
  18. In-text Questions — Units of Measurement Page 65
  19. In-text Questions — Units of Measurement Page 66
  20. In-text Questions — Units of Measurement Page 67–68
  21. In-text Questions — Units of Measurement Page 69
  22. In-text Questions — Locating and Comparing Decimals / There is Zero Dilemma! Page 70
  23. In-text Questions — Locating and Comparing Decimals Page 71
  24. In-text Questions — Locating and Comparing Decimals Page 72
  25. In-text Questions — Locating and Comparing Decimals Page 73
  26. In-text Questions — Addition and Subtraction of Decimals Page 74
  27. In-text Questions — Addition and Subtraction of Decimals Page 75
  28. Figure it Out — Addition and Subtraction of Decimals Page 75
  29. In-text Questions — Decimal Sequences / Estimating Sums and Differences Page 75–76
  30. In-text Questions — More on the Decimal System Page 78
  31. Chapter-end exercise — Figure it Out Page 78–80
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