Åk 6–9

3.6 Base Ten Form
When you learned about natural numbers, you have hopefully even learned about how to write a number in its longer form. It could look like this:

First with words:
4,352 =  4 thousand + 3 hundred + 5 tens + 2

Then in numbers:
4,352
= 4,000 + 300 +50 + 2

Then with numbers represented as a multiplication of the place value.

 4,352 = 4 · 1,000 + 3 · 100 +5 · 10 + 2 · 1

Example A

You know from before that a decimal can also be written like this:

0.63 = 0 wholes + 6 tenths + 3 hundredths

1 tenth = 10 hundredths and 0.63 can therefore be expressed as
0 wholes and 63 hundredths. So:

63 hundredths = 6 tenths and 3 hundredths

Even this can be written in numbers:
0.63 = 0 + 0.6 + 0.03

We write this as a multiplication of the place values:
 0.63 = 0 · 1 + 6 · 0.1 + 3 · 0.01

Example B

1 whole  = 10 tenths

3.2 = 3 wholes + 2 tenths  = 32 tenths

In numbers:
 3.2 = 3 + 0.2 = 3 · 1 + 2 · 0.1

Example C

 0.586 = 586 thousandths = 5 tenth + 8 hundredths + 6 thousandths

In numbers:
 0.586 = 0 + 0.5 + 0.08 + 0.006 = 0 · 1 + 5 · 0.1 + 8 · 0.01 + 6 · 0.001