A Peek Beyond the Point
The decimal point
Learn how the decimal point lets us write tenths and hundredths neatly.
We write 456, not 4 × 100 + 5 × 10 + 6 × 1: the position tells you the value. Can we do the same with tenths and hundredths?
There's a problem. If 4 and 2/10 were written 42, how would we know it isn't forty-two? The string 705 could mean:
- 7 hundreds, 0 tens, 5 ones = 700 + 5
- 7 tens, 0 ones, 5 tenths = 70 + 5/10
- 7 ones, 0 tenths, 5 hundredths = 7 + 5/100
So we put a dot to show where the whole part ends: the decimal point. Now the three are easy to tell apart: 705, 70.5 and 7.05.
- 70.5 = 7 × 10 + 5 × 1/10
- 7.05 = 7 × 1 + 5 × 1/100
Reading them:
| Number | Read as |
|---|---|
| 705 | seven hundred and five |
| 70.5 | seventy point five |
| 7.05 | seven point zero five |
| 0.274 | zero point two seven four |
After the point, read each digit on its own. 0.274 is not zero point two hundred seventy-four: it is 2 tenths, 7 hundredths and 4 thousandths.
Going the other way: 234 tenths = 234/10 = 20 + 3 + 4/10 = 23.4.
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