Decimals — introduction

Up to now, every number you wrote was a whole number — 1, 7, 84, 3 472. In Year 4 you meet decimals, which let you write numbers between the whole numbers.

A new place to the right

In a whole number, the rightmost digit is the ones. Decimals add new places to the right of a point: tenths, hundredths and (later) thousandths.

So 3.47 means three ones, four tenths and seven hundredths.

The little dot is the decimal point. In many European countries (including SK, CS, DE, ES) people write a comma instead — for example 3,47. The maths is identical.

What a tenth is

Take 1 whole. Split it into ten equal parts. Each part is one tenth, written as 0.1.

0.1 = $\frac{1}{10}$

0.2 = $\frac{2}{10}$

…

0.9 = $\frac{9}{10}$

1.0 = $\frac{10}{10}$ = one whole

You can see the tenths on a number line: ten equal jumps from 0 to 1.

What a hundredth is

Now split one tenth into ten equal parts. Each part is one hundredth, written as 0.01.

0.01 = $\frac{1}{100}$

0.10 = $\frac{10}{100}$ = $\frac{1}{10}$ = 0.1

0.47 = $\frac{47}{100}$

It takes a hundred hundredths to make one whole.

Where decimals show up in real life

• Money. £3.47 means 3 pounds and 47 hundredths of a pound (47 pence).
• Length. 1.75 m is a metre and 75 hundredths of a metre.
• Temperature. 36.6 °C is 36 degrees and 6 tenths.
• Sports. A runner's 100 m time of 12.04 seconds is 12 seconds and 4 hundredths.

What you'll learn

• Tenths, hundredths and place value — read any decimal carefully
• Decimals on a number line — see where they sit
• Comparing decimals — which is bigger?
• Decimals as fractions — the bridge to fractions
• Adding and subtracting decimals — line up the decimal points
• For parents — tips for grown-ups

Try it out

• 🔢 Decimal place value — which digit is in the tenths or hundredths place?
• 📏 Decimal on a number line — read a tenth from a 0..1 line
• ⚖️ Compare decimals — pick <, > or =
• 🔄 Decimal ↔ fraction
• ➕➖ Add and subtract decimals — column method