What Are Decimals?
A decimal is another way of writing part of one. The point is not a full stop, it is the line between whole things and pieces of a thing.
What a decimal is
A decimal is a way of writing an amount that is not a whole number.
Money already works this way. A price of 3.45 dollars means 3 whole dollars and 45 cents. The cents are part of a dollar, not another whole dollar, and the point is what keeps the two apart.
Every decimal works the same way. Left of the point, whole things. Right of the point, pieces of one thing.
The columns
Each column to the right of the point is worth ten times less than the one before it.
So 3.45 is 3 wholes, plus 410, plus 5100. That is the entire idea, and almost every later mistake comes from skipping it.
The rule
The first column after the point is tenths. The second is hundredths. The third is thousandths.
A digit's position decides what it is worth. The digit itself does not.
On a number line
Between 0 and 1 there are ten equal steps, and each step is one tenth.
Ask your child where 0.7 sits and where 0.35 sits. If they place 0.35 further along, the column idea has not landed yet, and that is the thing to fix before anything else.
Saying them aloud
This one small habit prevents a lot of confusion.
- 3.45 is three point four five. Not "three point forty five".
- 0.7 is zero point seven, and it is fine to call it seven tenths.
- 0.06 is zero point zero six. The zero is doing real work, so say it.
Saying "forty five" invites the brain to treat the digits after the point as an ordinary number, which is exactly the mistake that follows.
Decimals are fractions in disguise
Every decimal can be written as a fraction, and the column name tells you the denominator.
- 0.7 is 710, because 7 sits in the tenths column.
- 0.45 is 45100, because the last digit sits in the hundredths column.
- 0.125 is 1251000, and that simplifies to 18.
Common mistakes
1. Reading the part after the point as a whole number
Deciding 0.35 is bigger than 0.7 because 35 is bigger than 7. Those digits are not 35 and 7, they are 35 hundredths and 7 tenths. Seven tenths is 70 hundredths, so it wins comfortably.
2. Thinking more digits means a bigger number
With whole numbers that is true: 1000 beats 99. After a decimal point it is not. 0.5 is bigger than 0.4999, even though the second one has more digits.
3. Dropping a zero that is holding a place
Writing three hundredths as 0.3 instead of 0.03. The zero in the tenths column is not padding, it is the reason the 3 lands in the hundredths column at all.
Practice questions
Seven questions. One attempt each, and the explanation appears once the answer is in.
Check yourself
No sign up. Nothing is sent anywhere, the score stays on this device.
For parents
Use money, because your child already believes money. Ask what 0.7 of a dollar is, then what 0.35 of a dollar is. Seventy cents against thirty five cents settles the argument in one second, and the same reasoning transfers straight back to the numbers.
What to learn next
Stuck on this topic? Get one class, free.
A tutor works through it live with your child, one on one, and sends you a short written report afterwards. No card needed.