Comparing decimal numbers

A longer write-up does not mean a bigger number

Which number is bigger: 0.5 or 0.45? Most people shoot 0.45 — “it is longer and forty-five is more than five”. And most people are wrong.

With whole numbers it is true: more digits = a bigger number. 123 is always more than 99. After the decimal point that rule does not hold. 0.5 is five tenths, so a half. 0.45 is forty-five hundredths — and that is less than a half.

Today you will learn a trick you will never mix up: pad the numbers to the same number of places after the point. From 0.5 you make 0.50 (a zero at the end changes nothing, you know that from the last lesson). And 50 hundredths against 45 hundredths — clear.

You will need to compare decimals all the time: who ran faster, what is cheaper in the shop, whose jump was longer. It is a skill for life, not a school toy.

PE, a 60-metre sprint. Adam finished in 10.9 seconds, Tereza in 10.85. “I won, nine is more than eight!” Adam calls. Tereza shakes her head: “Wait. In a race the smaller number wins — and mine IS smaller.” She takes chalk and writes on the ground: 10.90 and 10.85. “Wholes the same. Tenths: you have 9, I have 8. Eight tenths is less than nine. I was faster by five hundredths.” Adam stares at the numbers for a bit and then owns the loss. You cannot argue with padded hundredths.

Method: pad and read from the left

Comparing decimal numbers has three steps:

Step 1: Compare the wholes. The number with bigger wholes wins at once. 3.1 > 2.99 — three beats two, you do not need to look at the rest.

Step 2: Pad the places after the point. When the wholes are the same, add zeros to the end of the shorter number so both have the same number of places. From 0.5 and 0.45 you make 0.50 and 0.45. You changed nothing — you just set it up for a fair compare.

Step 3: Compare the part after the point like a whole number. 50 against 45. Fifty is more, so 0.5 > 0.45.

Why does it work? After padding, both numbers speak in the same units — in hundredths. Fifty hundredths against forty-five hundredths. It is like comparing 50 hellers and 45 hellers. Without padding you compare tenths with hundredths — and that is like comparing ten-koruna coins with korunas by how many coins you have.

When ordering more numbers, do the same: pad them all to the same number of places and order them like whole numbers.

Compare 3.2 and 3.18

Step 1: Both wholes are 3. Not decided, we go on.

Step 2: I pad: 3.2 → 3.20. Now both numbers have two places after the point.

Step 3: After the point I compare 20 and 18. Twenty hundredths is more than eighteen hundredths.

Result: 3.2 > 3.18. The longer write-up lost. If I compared only “2 against 18”, I would get it wrong — that is why we pad.

Order from smallest: 1.5 — 1.05 — 1.15

I pad all numbers to two places after the point:

• 1.5 → 1.50
• 1.05 → 1.05
• 1.15 → 1.15

The wholes are 1 everywhere, so the part after the point decides: 50, 05 and 15. Ordered: 05 < 15 < 50.

Result: 1.05 < 1.15 < 1.5. Notice that the originally “longest” write-up 1.05 is actually the smallest number — the zero right after the point pulled it down.

Who jumped further: 2.80 m, or 2.8 m?

Sofie jumped 2.80 m, Filip 2.8 m. Who won?

I pad: 2.8 → 2.80. And I see 2.80 = 2.80.

Nobody won — they jumped exactly the same. A zero at the end after the point does not change the number, it just writes it more precisely (to hundredths instead of tenths). The judges would have to measure again, maths will not split a draw.

Practice: now you do it 🎲

Now try it for real. You will see all the questions at once, like on paper. Start with ten. When it goes well, add more.

Compare decimal numbers. Tap the sign.

Practise the questions

On paper

Pencil in hand — comparing is learned with the hand, not the eyes.

1. Compare and write < or > between the numbers: 0.7 and 0.65 — 2.09 and 2.9 — 5.31 and 5.313. By each pair write the padded forms.

2. Order from smallest: 3.4 — 3.04 — 3.44 — 3.404. First pad them all to three places after the point.

3. Invent a number that sits between 1.2 and 1.3. Then invent two more. (Hint: pad to hundredths and you have lots of numbers to pick.)

4. Write three race times so that Ema is first, Adam second and Tereza third — and the gap between them is always only in the hundredths.

Now you 💪

1. I can say why 0.5 is more than 0.45 — and prove it by padding.
2. I can order three decimal numbers with the same wholes without guessing.
3. I know that between 1.2 and 1.3 more numbers sit, and I can write at least one.

What to take from this lesson

• First compare the wholes. When they are the same, pad the places after the point with zeros.
• After padding you compare the part after the point like a whole number.
• More digits after the point does not mean a bigger number: 0.5 > 0.45.
• A zero at the end after the point does not change the number: 2.8 = 2.80.
• Between any two decimal numbers more numbers sit — just add a place after the point.

© 2026 Ing. Martin Polak / AlgoRhino · Content usage terms