Decimals explained | Primary Maths

01 The columns keep going

Each column to the left is ten times the one before it. Each column to the right is a tenth of it. The decimal point is not a barrier; it is a marker showing where the ones column stops.

So in 3.25, the 2 is two tenths (0.2) and the 5 is five hundredths (0.05). Read them as columns, not as the number twenty-five.

3.25. The 5 sits in the hundredths, so it is worth 0.05 — not 5, and not 0.5.

02 Why 0.5 is bigger than 0.25

This is the error that outlives all the others, because 25 is bigger than 5 and the eye believes it.

But 0.5 is five tenths and 0.25 is twenty-five hundredths — and five tenths is fifty hundredths. Put them in the same columns and 0.50 against 0.25 settles it immediately.

Line the decimal points up and compare from the left, exactly as with whole numbers. Adding noughts on the right changes nothing: 0.5, 0.50 and 0.500 are the same number.

On the line there is no argument: 0.5 sits further along than 0.25.

03 Adding, subtracting, multiplying and dividing

Adding and subtracting need one habit and nothing else: line the points up, so tenths sit under tenths. Fill the short number with noughts if it helps.

Adding and subtracting: points lined up, then work as usual. 3.25 + 0.7 is 3.25 + 0.70 = 3.95, not 3.32.
Multiplying by 10, 100, 1000: the digits move left — 3.25 × 10 = 32.5. It is the digits that move; the point stays put.
Dividing by 10, 100, 1000: the digits move right — 3.25 ÷ 10 = 0.325.
Multiplying two decimals: ignore the points, multiply as whole numbers, then put back as many decimal places as both numbers had together. 0.3 × 0.4 has two places altogether, so it is 0.12, not 1.2.

04 Decimals, fractions and percentages

They are three notations for one idea, and a question may hand you any of them and want another.

0.25 = 25/100 = 25%, which simplifies to 1/4. Reading a decimal aloud gives you the fraction for free: twenty-five hundredths is 25/100.

Worth knowing by sight: 0.5 = 1/2, 0.25 = 1/4, 0.75 = 3/4, 0.2 = 1/5, 0.1 = 1/10.

05 How to say them

These are words most children have never said out loud, and a word you cannot say is a word you avoid using. Capitals mark the syllable you lean on. Tap the speaker to hear it.

decimalsayDESS-i-muhlmore than onedecimals
A number written with a decimal point, using columns smaller than one.
tenths
The first column after the point. One tenth is 0.1, and ten of them make one whole.
hundredths
The second column after the point. One hundredth is 0.01.
decimal placemore than onedecimal places
How many digits come after the point. 3.25 has two decimal places; “round to 1 decimal place” means leave one.
equivalentsayi-KWIV-uh-luhnt
Equal in value though written differently. 0.5, 0.50 and 1/2 are all equivalent.

06 What each level is tested on

The same topic, asked differently as it goes up. The percentage is the share of papers at that level in which it appears.

P4
Tenths and hundredths, reading and writing decimals, and comparing them.
Practise P4 Decimals — 10 questions →
52% of P4 papers
P5
Thousandths, the four operations with decimals, and rounding to a given number of places.
Practise P5 Decimals — 10 questions →
61% of P5 papers
P6
Decimals inside measurement, money, rate and multi-step word problems.
Practise P6 Decimals — 10 questions →
78% of P6 papers

07 Mistakes worth knowing about

Each of these is wrong. Decide why before you open it.

“0.25 is bigger than 0.5 because 25 is bigger than 5.”
Read the columns. 0.5 is five tenths, which is fifty hundredths; 0.25 is twenty-five hundredths. Writing 0.5 as 0.50 makes it obvious.
“3.25 + 0.7 = 3.32.”
The 7 is seven tenths, so it lines up under the 2, not the 5. 3.25 + 0.70 = 3.95.
“0.3 × 0.4 = 1.2.”
Three tenths of four tenths is small, not bigger than either. 3 × 4 = 12, and the two numbers had two decimal places between them, so the answer is 0.12.
“3.25 × 10 = 3.250.”
Adding a nought on the end of a decimal changes nothing. Multiplying by 10 moves the digits one place left: 32.5.
“The 5 in 3.25 is worth 5.”
It is in the hundredths column, so it is worth 0.05. The columns after the point get smaller, not bigger.

Now try it

30 questions across 3 levels, marked as you go with the working shown.

P410 questions P510 questions P610 questions