NCERT Solutions for Class 7th Maths Chapter 4 Another Peek Beyond the Point
Updated on 2026-09-19
About this chapter
A decimal is a decimal fraction in disguise. 27.53 means 2 Tens + 7 Ones + 5 Tenths + 3 Hundredths, that is 2753 ÷ 100 . Dividing by 10, 100, 1000 … moves the decimal point left by as many places as there are zeroes in the divisor. Multiplying by them moves it right . To multiply two decimals: drop the points, multiply as counting numbers, then put back a point with as many decimal places as the two numbers had together . The reason is that the denominators 10 and 100 multiply to 1000. The product is not always bigger. Multiplying by a number between 0 and 1 makes a number smaller , because you are taking only a part of it. Division is ordinary long division — division using place value. When the Ones run out, regroup them as Tenths and place the decimal point in the quotient. Then Hundred
- A Quick Recap of Decimals
- Decimal Multiplication
- Is the Product Always Greater than the Numbers Multiplied?
- Decimal Division
- Division Using Place Value
- Division with a Decimal Dividend
- Division with a Decimal Divisor · Does This Ever End?
- Does This Ever End? · A Magic Number: 142857
- Dividend, Divisor, and Quotient
- the pattern box with powers of 2 and 5
Quick revision
| Idea | The rule | Why it works | Example |
|---|---|---|---|
| Decimal as a fraction | 0.254 = 254/1000 | Tenths, hundredths, thousandths are just 1/10, 1/100, 1/1000 | 0.2 + 0.05 + 0.004 |
| Divide by 1 followed by zeroes | Move the point left by the number of zeroes | Each zero shifts every digit one place down in value | 123 ÷ 10 = 12.3 |
| Multiply by 1 followed by zeroes | Move the point right by the number of zeroes | Each zero shifts every digit one place up in value | 0.306 × 100 = 30.6 |
| Multiply two decimals | Multiply without points, then count the decimal places and add them | 10 × 100 = 1000, so the denominators' zeroes add up | 5.96 × 24.8 = 147.808 |
| Both numbers greater than 1 | Product is greater than both | Taking more than one whole copy | 3.4 × 6.5 = 22.1 |
| Both numbers between 0 and 1 | Product is less than both | Taking a part of a part | 0.75 × 0.4 = 0.3 |
| One greater than 1, one between 0 and 1 | Product lies between the two numbers | A part of the bigger number | 0.75 × 5 = 3.75 |
| Fraction → decimal | Make the denominator 10, 100, 1000 … | Only then can the digits be read off place by place | 29/4 = 725/100 = 7.25 |
| Long division past the Ones | Regroup 1 One as 10 Tenths and put a point in the quotient | The point marks where whole ones end | 237 ÷ 8 = 29.625 |
| Decimal divisor | Multiply dividend and divisor by the same 10, 100 … | An equivalent fraction has the same value | 4.68 ÷ 0.13 = 468 ÷ 13 = 36 |
| Divisor between 0 and 1 | Quotient is greater than the dividend | You are asking how many small pieces fit in | 128 ÷ 0.4 = 320 |
| Never-ending quotient | A remainder keeps coming back | The same remainder forces the same digit again | 1 ÷ 7 = 0.142857… |
Exercises
- In-text Questions — A Quick Recap of Decimals Page 67 – 68
- In-text Questions — Decimal Multiplication Page 69
- In-text Questions — Decimal Multiplication Page 70 – 71
- In-text Questions — Decimal Multiplication Page 71
- In-text Questions — Is the Product Always Greater than the Numbers Multiplied? Page 72
- Figure it Out — Decimal Multiplication Page 73 – 74
- In-text Questions — Decimal Division Page 74 – 75
- In-text Questions — Division Using Place Value Page 76
- In-text Questions — Division Using Place Value · Division with a Decimal Quotient Page 77 – 80
- In-text Questions — Division with a Decimal Dividend Page 81 – 83
- Figure it Out — Decimal Division Page 83
- In-text Questions — Division with a Decimal Divisor · Does This Ever End? Page 84 – 85
- In-text Questions — Does This Ever End? · A Magic Number: 142857 Page 85 – 86
- In-text Question — Dividend, Divisor, and Quotient Page 86
- Figure it Out — Decimal Division Page 86 – 87
- In-text Question — the pattern box with powers of 2 and 5 Page 87
- In-text Questions — Look Before You Leap! Page 89 – 90
- Try This — Making Yet Another Adjustment Page 92
- In-text Questions — how calendars were worked out Page 93
- End-of-chapter question set — Figure it Out Page 93 – 95
- Puzzle Time