Ordering Decimals & Place Value — KS3 Maths

Comparing decimals works one place at a time, from the left. Tenths decide it first; only if those tie do the hundredths get a say. Line the points up, fill any gaps with zeros so every column is complete, and the order falls out — including the ties that look hardest.

What does each decimal place mean?

Every position after the point is worth ten times less than the one before it. That is the whole reason comparing works from the left — a single tenth outweighs everything to its right combined.

So $0.3$ is 3 tenths and $0.25$ is 2 tenths and 5 hundredths. 3 tenths beats 2 tenths, so $0.3$ is the bigger number — the extra digit in $0.25$ buys hundredths, and hundredths never outrank tenths.

Worked example

Order 0.3, 0.25, 0.7 (smallest to biggest)

Line up the points and fill the gaps, so $0.3$ becomes $0.30$:

$0.30 \qquad 0.25 \qquad 0.70$

Compare the tenths: $3$, $2$ and $7$. That's enough to order them:

$0.25 < 0.3 < 0.7$

Notice $0.3$ lands above $0.25$: three tenths beats two tenths, and the tenths column settles it before anything further right gets a vote.

Worked example

Order 1.4, 1.35, 1.6

The whole numbers are all $1$, so compare after the point. Fill the gaps ($1.4 \to 1.40$, $1.6 \to 1.60$) and compare the tenths: $4$, $3$ and $6$:

$1.35 < 1.4 < 1.6$

Worked example

Order 0.5, 0.45, 0.409 (breaking a tie)

Fill the gaps so all three have three decimal places:

$0.500 \qquad 0.450 \qquad 0.409$

Compare the tenths: $5$, $4$, $4$. So $0.5$ is the biggest — but two numbers tie on $4$ tenths. Break the tie in the next place, the hundredths: $5$ beats $0$, so $0.45 > 0.409$:

$0.409 < 0.45 < 0.5$

Going further

Negative decimals reverse the order. With negatives, the number further from zero is the smaller one — so while $0.3 > 0.25$, it's the other way round for $-0.3 < -0.25$. Compare the digits exactly as above, then flip the result. There's more on this in the adding and subtracting negative numbers lesson.

Some decimals never stop. Write $\tfrac{1}{3}$ as a decimal and you get $0.333\ldots$ going on forever. Comparing still works the same way — take enough places that one of them differs.

Where you'll use this next

• Rounding to decimal places uses the same place-value columns to decide which digit is the "decider".
• Money and measures are decimal comparisons in disguise — which is cheaper, £0.85 or £0.9?
• Converting between fractions, decimals and percentages relies on reading place value fluently.

Practice questions

Line up the points, fill the gaps with zeros, and compare from the left. Then click to check.