A Quick Recap of Decimals

Class 7 Maths · Chapter 12: Another Peek Beyond the Point · NCERT Ganita Prakash section P2 4.1

Learn

Decimals extend our place value system past the ones: 27.53 is 2 tens, 7 ones, 5 tenths and 3 hundredths. A fraction with denominator 10, 100, 1000 … is easy to write as a decimal: 254/1000 = 2/10 + 5/100 + 4/1000 = 0.254.

254/1000 = 0.254

Zoya buys spices: 50 g of cinnamon is 50/1000 kg = 0.05 kg, and 250 g of pepper is 0.25 kg. Kabir writes 173/100 = 1.73 and 23/1000 = 0.023: when there are not enough digits, put zeros in front.

173/100 = 1.73 · 23/1000 = 0.023

A rule for ÷ 10, 100, 1000: write the number with a decimal point at the end, count the zeros in the divisor, and move the point left that many places, adding zeros in front if needed. 123 ÷ 10 = 12.3, 24 ÷ 100 = 0.24, 12 ÷ 1000 = 0.012.

12 ÷ 1000 = 0.012

Multiplying by 10, 100, 1000 moves the point right: 5.7 × 100 = 570, 0.306 × 1000 = 306. Each place to the left is ten times smaller; each place to the right ten times bigger.

0.306 × 1000 = 306

Explore: place a decimal.

1. Put the marker at 173/100.
2. Now at 1786/1000, to the nearest hundredth on this line.

Remember

• A fraction over 10, 100, 1000 … is written as a decimal by moving the point left.
• × 10ⁿ moves the point right, ÷ 10ⁿ moves it left by n places.

Quick check

What is 847/10000 as a decimal?

1. 0.0847
2. 0.847
3. 8.47
4. 0.00847

Think about it

Write 2 kg 25 g in kilograms as a decimal.

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.