Tenths and the Decimal Point

A child is measured with a tape: 1 metre and a bit. A shop sign says a loaf costs 2.50. A running race is won in 9.58 seconds. These numbers all have a dot in them. What does the dot mean?

Past the ones

In the Ones, Tens and Hundreds lesson, each place was worth ten times the place to its right: ones, tens, hundreds. Now go the other way. To the right of the ones is a place worth ten times less than one: tenths. To the right of that are hundredths.

To show where the ones end, we put a dot after them, the decimal point:

• 2.7 means 2 ones and 7 tenths, two and seven tenths;
• 0.5 means no ones and 5 tenths, which is 5/10.

A number written with a decimal point is called a decimal. In some countries people write a comma instead of a dot, 2,7, and say the same thing.

Tenths on the number line

Cut the step from 2 to 3 into ten equal parts. Each part is one tenth. The seventh mark is 2.7: two and seven tenths. A ruler does this for you: each centimetre is cut into ten millimetres, so 2.7 centimetres is 2 centimetres and 7 millimetres.

Tenths and hundredths are fractions with a bottom number of 10 or 100. So some fractions are easy to write as decimals:

• 1/2 = 5/10 = 0.5;
• 1/4 = 25/100 = 0.25;
• 3/4 = 75/100 = 0.75.

Money works this way too: 2.50 is 2 whole coins and 50 hundredths of a coin.

Which is bigger?

Is 0.25 bigger than 0.5, because it has more digits? No. With whole numbers, more digits meant bigger. After the decimal point, that rule breaks. Compare place by place from the left, as in the Bigger and Smaller lesson:

• both have 0 ones;
• in the tenths, 0.5 has 5 and 0.25 has only 2.

So 0.5 is bigger. You can check it with fractions: 0.5 is a half, 0.25 a quarter. A trick that helps: write 0.5 as 0.50. A zero at the end of a decimal changes nothing, and now both have hundredths: 50 hundredths beats 25 hundredths.

Try it at home

1. Find a ruler. Point to 3.5 centimetres, then 0.8 centimetres.
2. Find three prices with a decimal point on food packets or a receipt. Which is the biggest?
3. Which is bigger: 0.7 or 0.65? Answer below.

Answer to 3: 0.7, because it has 7 tenths and 0.65 has only 6.

Words to know

• tenth - one of ten equal parts of one, 1/10
• hundredth - one of a hundred equal parts of one, 1/100
• decimal point - the dot after the ones place
• decimal - a number written with a decimal point, like 2.7

Big idea

Place value carries on past the ones: tenths, then hundredths, each ten times smaller. The decimal point marks where the ones end. 0.5 is 5/10, a half. Compare decimals place by place from the left, not by how many digits they have.