Decimals Explained

What you will learn

• Read and write decimals using tenths, hundredths and thousandths.
• Say the value of a digit after the decimal point.
• Link decimals to fractions and to the number line.

Before you start: you should understand place value in whole numbers and know what a fraction is. See Place Value to a Million and Fractions Explained.

The idea

In the number $352$, each column is worth ten times the column to its right: hundreds, tens, ones. Decimals keep that pattern going past the ones column. The decimal point marks where the whole numbers stop, and every column after it is worth one tenth of the column before.

The $0$ matters: it holds the $5$ in the thousandths column.

Tenths

Cut a whole into 10 equal parts. One part is one tenth, $\frac{1}{10} = 0.1$. Three parts is $\frac{3}{10} = 0.3$.

Hundredths

Cut each tenth into 10 again and the whole has 100 parts. One part is $\frac{1}{100} = 0.01$. So $0.25$ is $2$ tenths and $5$ hundredths, which is also $25$ hundredths, $\frac{25}{100}$.

On the number line

Between $0$ and $1$ there are ten steps of $0.1$. Between $0.3$ and $0.4$ there are ten more steps of $0.01$, and so on.

Fractions and decimals

A fraction is a division, so $\frac{3}{4} = 3 \div 4 = 0.75$. Fractions with $10$, $100$ or $1000$ on the bottom are quick to write as decimals, because the bottom number tells you the last column.

Worked examples

Example 1: Read a decimal

Say what each digit in $3.406$ is worth.

1. $3$ is $3$ ones.
2. $4$ is $4$ tenths, which is $0.4$.
3. $0$ is $0$ hundredths: it holds the place.
4. $6$ is $6$ thousandths, which is $0.006$.

Answer: $3 + 0.4 + 0.006 = 3.406$

Example 2: Convert a decimal to a fraction

Write $0.375$ as a fraction in its simplest form.

1. The last digit is in the thousandths column, so write it over $1000$: $\frac{375}{1000}$.
2. Both numbers divide by $125$: $375 \div 125 = 3$ and $1000 \div 125 = 8$.
3. So $\frac{375}{1000} = \frac{3}{8}$.

Answer: $\frac{3}{8}$

Example 3: Money

£$2.35$ is how many pence?

1. $2$ pounds is $200$ pence.
2. $0.35$ pounds is $35$ pence.
3. $200 + 35 = 235$.

Answer: $235$ pence.

Some fractions never stop: $\frac{1}{3} = 0.333\ldots$ repeats forever. These are called recurring decimals, written $0.\dot{3}$.

Why it matters

Money is the decimal system most people use every day: £4.75 is 4 pounds and 75 hundredths of a pound. Measurements in science and engineering are written in decimals, such as a 1.5 mm drill bit, a 37.2 °C temperature or a 9.58-second sprint, and calculators and spreadsheets work in decimals by default.

Being able to read decimals and spot a misplaced decimal point is a practical life skill. A dose of 0.5 ml is very different from 5 ml. Later lessons cover comparing, rounding and calculating with decimals.