Decimal Division

Class 7 Maths · Chapter 12: Another Peek Beyond the Point · NCERT Ganita Prakash section P2 4.3

Learn

Meher cuts a 3.9 m ribbon into 10 equal pieces: 3.9 ÷ 10 = 39/10 × 1/10 = 39/100 = 0.39 m; into 100 pieces, 0.039 m. Shared between two, 29 m gives 14 m each and 1 m left, which is 1/2 = 5/10 = 0.5 m more: 14.5 m. Among four: 29/4 = (29 × 25)/100 = 7.25 m.

29 ÷ 4 = 725/100 = 7.25

Long division continues past the point. 1325 ÷ 4: 331 with 1 one left. Regroup 1 one as 10 tenths (write the decimal point in the quotient): 10 tenths ÷ 4 = 2 tenths, 2 left; 20 hundredths ÷ 4 = 5 hundredths. So 1325 ÷ 4 = 331.25. In the same way 237 ÷ 8 = 29.625 and 0.06 ÷ 5 = 0.012.

1325 ÷ 4 = 331.25

Decimal divisor: make it a counting number by multiplying both numbers by 10, 100 …. Ishaan rides 126 km in 2.5 hours: 126 ÷ 2.5 = 1260 ÷ 25 = 50.4 km per hour. And 4.68 ÷ 0.13 = 468 ÷ 13 = 36. Dividing by a number below 1 gives more: 128 ÷ 0.4 = 320.

126 ÷ 2.5 = 1260 ÷ 25 = 50.4

Does it ever end? 10 ÷ 3 leaves remainder 1 at every step: 3.333… forever. 1 ÷ 7 = 0.142857142857…: the remainders 1, 3, 2, 6, 4, 5 go round in a cycle, so the digits do too. 142857 × 2, × 3 … × 6 give the same digits rotated! A decimal ends only when the denominator (in lowest form) has just 2s and 5s, like 1/8 = 0.125.

1 ÷ 7 = 0.142857 142857 …

Explore: does it end?

1. Sort the divisions.

Remember

• Long division keeps going: regroup ones into tenths, tenths into hundredths, and put the point in the quotient.
• For a decimal divisor, multiply both numbers by 10, 100 … first. Some divisions never end.

Quick check

3 litres of juice is shared equally by 8 friends. How much does each get?

1. 0.375 litre = 375 mL
2. 0.38 litre
3. 2.67 litres
4. 0.83 litre

Think about it

Is 24.6 ÷ 1.5 the same as 2.46 ÷ 0.15?

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.