Learn · Numeracy · 4 min

Decimals & place value, from scratch

The decimal point marks where the whole numbers end and the parts-of-a-whole begin. Each place to the right is ten times smallerthan the one before it:

Tenths1st place after the point — 110 = 0.1
Hundredths2nd place — 1100 = 0.01
Thousandths3rd place — 11000 = 0.001

Play with it — set each place

Ones

value 1

Tenths

value 110

Hundredths

value 1100

Thousandths

value 11000

3.472

3 + 4 tenths + 7 hundredths + 2 thousandths
= 3 + 0.4 + 0.07 + 0.002

Every step to the right is 10× smaller. The decimal point just marks where the whole numbers end.

A decimal is just a fraction over 10, 100, 1000…

0.7 = 710 (seven tenths)
0.07 = 7100 (seven hundredths — ten times smaller)
0.25 = 25100 = ¼ (a quarter)
2.5 = 2 + 510 = 2½

Comparing decimals — line up the places

To compare, don't count digits — compare place by place, starting at the tenths. This is where almost everyone slips up, so play with it:

Which is bigger?

00.51

0.5

0.45

0.5 > 0.45

Compare the tenths first: 5 tenths beats 4 tenths. The number of digits doesn't decide it.

⚠ The trap most people fall for

“A decimal with more digits is bigger.” No. 0.45 looks longer than 0.5, but 0.5 = 5 tenths and 0.45 = 4 tenthsand a bit. 5 tenths > 4 tenths, so 0.5 > 0.45. A handy trick: give them the same number of places — 0.50 vs 0.45 — now it's obvious.

Tips & tricks

Adding or subtracting? Line up the points

Stack them so the decimal points are in a column (3.4 + 0.75 → line up), then add as normal.

Add zeros on the end freely

0.5 = 0.50 = 0.500. Trailing zeros after the point change nothing — handy for lining decimals up.

×10 moves the point one place right

0.42 × 10 = 4.2 · ÷10 moves it one place left: 0.42 ÷ 10 = 0.042.

Turn it into a fraction to sanity-check

0.75 = 75100 = ¾. If you know the fraction, you know the decimal.

Now you try — 0/3

1. Which is the largest number?

2. What is the value of the 7 in 3.472? (Write it as a decimal.)

3. Add: 3.5 + 0.25

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