Locating and Comparing Decimals

Class 7 Maths · Chapter 3: A Peek Beyond the Point · NCERT Ganita Prakash section 3.6

Learn

On the number line: 1.4 is 1 unit and 4 tenths, so split the gap from 1 to 2 into 10 parts and take 4. To find 4.185, zoom in step by step: between 4 and 5 → between 4.1 and 4.2 → between 4.18 and 4.19 → halfway, at 4.185.

4 < 4.1 < 4.18 < 4.185 < 4.19

The zero dilemma: is 0.2 the same as 0.20 and 0.200? Yes! All three mean 2 tenths; zeros at the end add nothing. But 0.02 (2 hundredths) and 0.002 (2 thousandths) are different, because the 2 is in a different place. So 4.5 = 4.50 = 04.50, but 4.05 and 4.005 are smaller.

0.2 = 0.20 = 0.200 but 0.02 ≠ 0.2

Comparing: which is larger, 6.456 or 6.465? Compare digit by digit from the left: both have 6 units, both have 4 tenths; then 5 hundredths < 6 hundredths, so 6.456 < 6.465. We can stop there: the later digits are worth less than one hundredth. Note: more digits does not mean bigger: 3.81 < 13.8.

6.456 < 6.465

Closest decimal: which of 0.9, 1.1, 1.01 and 1.11 is closest to 1? Order them: 0.9 < 1 < 1.01 < 1.1 < 1.11. 1.01 is only 1/100 away, while 0.9 and 1.1 are 1/10 away, so 1.01 is closest.

|1.01 − 1| = 0.01 < 0.1

Explore: order the decimals.

1. Put the numbers in increasing order.

Remember

• Zeros at the end of a decimal don't change it (0.2 = 0.20); zeros right after the point do (0.02).
• Compare place by place from the left; stop at the first place where the digits differ.

Quick check

Which is greater: 1.009 or 1.090?

1. 1.090
2. 1.009
3. They are equal
4. Can't tell

Think about it

Using the digits 4, 1, 8, 2 and 5 once each, make a decimal number as close as possible to 25.

Practice

Practise with fresh questions at three levels (easy, medium, hard), some answered hands-on, with hints and worked answers. Get 4 of your last 5 right to finish the topic.