Hinglish

A Hundredth Part and Decimal Place Value

Class 7 Maths · Chapter 3: A Peek Beyond the Point · NCERT Ganita Prakash section 3.3–3.4

Learn

A strip 8 9/10 units long is folded in half. It ends between 4 4/10 and 4 5/10, so we need still smaller parts: split each tenth into 10 parts. There are 10 × 10 = 100 such parts in a unit, each 1/100 (one-hundredth). The fold is at 4 + 4/10 + 5/100, which is also 4 and 45 hundredths.

10 hundredths = 1 tenth · 100 hundredths = 1 unit

Why tens? Our place value system already works in tens: each place is 10 times the one on its right (1000, 100, 10, 1). Going on to the right we get 1/10, 1/100, 1/1000 … This is the decimal system ("decem" is Latin for ten, like Sanskrit daśha).

1000 · 100 · 10 · 1 · 1/10 · 1/100 · 1/1000

The decimal point shows where the whole part ends. 705 = 7 hundreds and 5 ones; 70.5 = 7 tens and 5 tenths; 7.05 = 7 units and 5 hundredths. We read 70.5 as "seventy point five" and 0.274 as "zero point two seven four" (not "two hundred seventy four"), digit by digit.

7.05 = 7 × 1 + 0 × 1/10 + 5 × 1/100

Converting: 234 tenths = 200/10 + 30/10 + 4/10 = 20 + 3 + 4/10 = 23.4. And 234 hundredths = 2.34; 105 tenths = 10.5. Adding hundredths works like whole numbers: 15.34 + 2.68: 4 + 8 = 12 hundredths = 1 tenth and 2 hundredths, carry 1 → 18.02.

234 tenths = 23.4 · 234 hundredths = 2.34

Explore: hundredths on the number line.

  1. Put the marker at the fold: 4 and 45 hundredths.
  2. Put the marker at 4.48.
  3. Put the marker at 4 + 4/10 + 2/100.

Remember

  • Each place is 10 times the place on its right: … 10, 1, 1/10, 1/100, 1/1000.
  • The decimal point separates the whole part: 7.05 = 7 units and 5 hundredths; read digits after the point one by one.

Quick check

How do we write 7 units and 5 hundredths?

  1. 7.05
  2. 7.5
  3. 70.5
  4. 7.005
Answer

7.05. Tenths place empty → 0; hundredths → 5.

Think about it

Can we write 4 and 2 tenths as "42", leaving out the tenths? What goes wrong?

One answer

No: 42 already means 4 tens and 2 ones. Without a point we can't tell where the whole part ends, which is why we write 4.2.

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.