A bottle of juice says 1.5 litres, a runner is timed at 9.8 seconds, and a chocolate bar costs £0.75. All of these use numbers with a little dot in them — decimals — because whole numbers alone are too clumsy for measuring and money. Decimals let us write the bits in between the whole numbers.

Place value tells us that each digit is worth ten times the one to its right: hundreds, tens, ones. Every step left makes a column ten times bigger; every step right makes it ten times smaller. Decimals just keep that same pattern going past the ones — we mark where the whole part ends with a decimal point, and the digits after it count smaller and smaller pieces of one.

The first digit after the point is tenths — one of ten equal slices of a whole, which is exactly a fraction:

So 0.3 means three of those slices — three tenths:

See it: a strip of ten

Picture one whole as a long bar cut into ten equal parts. Each little part is one tenth, 0.1. Shade three of them and you have shaded 0.3 — three tenths of the whole bar:

We can see a tenth as a step on a number line. Cut the gap from 0 to 1 into ten equal steps; each little step is one tenth. Press play, then replay it: each time the marker hops along to a new tenth and reads the decimal aloud.

Reading a decimal like 3.7

The point is a fence: whole part on the left, part of one on the right. In 3.7 the 3 is three whole ones, and the 7 is seven tenths — seven of those little slices:

We say it "three point seven" — read the whole number, say "point", then read the digits after it one at a time. So 3.7 sits seven tenths of the way between 3 and 4 on the number line.

Take one more step right and each tenth splits into ten again. The second digit after the point is hundredths — one of a hundred equal pieces of a whole:

Reading left to right, the places after the point go tenths, then hundredths. So 0.27 is two tenths and seven hundredths:

A handy way to see hundredths is a hundred grid: one whole square cut into a 10 by 10 grid of 100 little squares. One little square is one hundredth, 0.01; one whole row of ten is one tenth, 0.1.

See it: shade a hundred grid

Each shaded little square is one hundredth. Count the squares and read the decimal. Press Refresh to shade a new amount.

Money is decimals you use every day

A pound is split into 100 pennies — just like a whole split into a hundred hundredths. So a price like \pounds 3.70 means 3 whole pounds and 70 pennies. The 7 is seven tenths of a pound, which is 70p, and the 0 after it says "no extra pennies".

Three worked examples

• 0.6 — six tenths. Six of the ten slices of one whole: 0.6 = \frac{6}{10}. More than a half, since a half is five tenths.
• 2.4 — two whole ones and four tenths: 2.4 = 2 + \frac{4}{10}. It sits between 2 and 3, closer to 2.
• 0.05 — no tenths and five hundredths: 0.05 = \frac{5}{100}. The 0 in the tenths place is a real worker — it keeps the 5 in the hundredths place, so this is much smaller than 0.5.

Khan Academy introduces decimals here: