Decimals

Tenths

Cut a whole bar into 10 equal pieces. Each piece is one tenth of the bar, written $\frac{1}{10}$1/10. Color 3 of the pieces, and $\frac{3}{10}$3/10 of the bar is colored: three tenths.

The bar is cut into 10 equal pieces, and 3 of them are colored.

Another way to write tenths

Tenths can also be written as a decimal. Three tenths is written 0.3. The dot is called the decimal point. The 0 in front of it says there are no whole bars, and the 3 just after it counts tenths. 0.3 is read "zero point three", and it is the same amount as $\frac{3}{10}$3/10.

In the same way, $\frac{1}{10}$1/10 is 0.1, $\frac{7}{10}$7/10 is 0.7 and $\frac{9}{10}$9/10 is 0.9.

The bar opens at 3 tenths, $\frac{3}{10}$3/10, which is 0.3. Shade tenths until exactly half the bar is colored. That takes 5 of the 10 pieces, so a half is $\frac{5}{10}$5/10, written 0.5.

The place after the point

A decimal carries on the place value of whole numbers. Each place is worth ten times the place to its right: a hundred is ten tens, and a ten is ten ones. Going the other way, one whole is ten tenths, so the place just to the right of the ones is the tenths place. The decimal point marks where the ones end and the tenths begin.

2.3 has a 2 in the ones place and a 3 in the tenths place. It is two wholes and three tenths: $2+\frac{3}{10}$2 + 3/10. On a number line it lies between 2 and 3, three tenths of the way along.

The space from 2 to 3 is cut into 10 tenths, and 2.3 is 3 tenths past 2.

Ten tenths make a whole

Count on in tenths: 0.7, 0.8, 0.9. The next tenth makes ten tenths, and ten tenths are one whole, so the count goes on to 1, then 1.1 and 1.2. After 0.9 comes 1, not 0.10.

One more tenth takes 0.9 to 1, and the next takes 1 to 1.1.

One place, one digit

Three tenths is 0.3: the 3 goes in the first place after the point. 3.0 would put the 3 before the point, in the ones place, and that is 3 whole bars, ten times too much. 0.03 would push the 3 one place further right, where every piece is ten times smaller again.

The first place after the point counts tenths, not tens. The tens place is two to the left of the point; the tenths place is one to the right of it.