A Tenth Part

Class 7 Maths · Chapter 3: A Peek Beyond the Point · NCERT Ganita Prakash section 3.1–3.2

Learn

Kabir is fixing a shelf with screws. Two screws look the same, but one does not fit: one is a little longer! On a ruler marked only in whole centimetres, both are "between 2 cm and 3 cm". To see the difference we need smaller units: split each centimetre into 10 equal parts.

1 cm = 10 one-tenths

Each small part is one-tenth (1/10) of a unit. A screw that reaches 2 whole cm and 7 more small parts is 2 and 7 tenths cm: 2 + 7/10. It is also 27 tenths, because the 2 whole units are 20 tenths. We read 2 7/10 as "two and seven-tenths".

2 + 7/10 = 27/10

Adding tenths: Meher's lower arm is 2 7/10 units and her upper arm 3 6/10 units. Add units and tenths separately: (2 + 3) units and (7 + 6) tenths = 5 units and 13 tenths. But 10 tenths make 1 unit, so that is 6 units and 3 tenths = 6 3/10. Or in tenths: 27/10 + 36/10 = 63/10.

2 7/10 + 3 6/10 = 6 3/10

Subtracting: 12 4/10 − 6 7/10. We can't take 7 tenths from 4 tenths, so split one unit into 10 tenths: 12 4/10 = 11 14/10. Now 14 − 7 = 7 tenths and 11 − 6 = 5 units: 5 7/10. This is just like borrowing in whole numbers.

12 4/10 − 6 7/10 = 5 7/10

Explore: tenths on the number line.

1. Put the marker at 2 7/10 (the longer screw).
2. Put the marker at 23 tenths.
3. Put the marker halfway between 2 and 3.

Remember

• Split a unit into 10 equal parts: each is one-tenth (1/10).
• 2 7/10 = 27 tenths; 10 tenths make 1 unit, so 13 tenths = 1 unit and 3 tenths.

Quick check

4 units and 3 tenths is how many tenths?

1. 43
2. 7
3. 430
4. 34

Think about it

Why do we split a unit into smaller parts when measuring?

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.