What a Decimal Is
“A decimal just keeps the place values going past the dot.”
The hook
1.5 metres tall, 1.5 litres of juice — a decimal is how we write the values between whole numbers.
In plain words
A number that adds places to the right of a dot (the decimal point) to write parts smaller than one.
The intuition
Keep the place values going to the right. The spot right after the dot is the tenths place, so 0.1 is 1/10 and 0.5 is 5/10 = 1/2. One more place gives 0.01 = 1/100.
How it's built
Left of the dot: ones, tens, hundreds as usual. Right of the dot: tenths, hundredths, each 10 times smaller. A decimal is really just a short way to write fractions with 10 or 100 on the bottom.
Example
0.3 has a 3 in the first place after the dot (the tenths place), so it equals 3/10.
Common mistake
More digits after the dot does not mean a bigger number. 0.7 is bigger than 0.07, because 0.7 is 7 tenths while 0.07 is 7 hundredths.
Where it's used
Money, length, weight, temperature — we use decimals almost any time we measure something exactly.
Where it came from
Writing small parts in line using a decimal point was made popular by Simon Stevin in the 1500s.
Prerequisites
Quick check
Which decimal is equal to 1/2?
- 0.2
- 0.5✓
- 0.05
- 0.12
Practice
Write 0.3 as a fraction.
Answer: undefined
- The 3 is in the tenths place.
- → 0.3 = 3/10
Takeaway: The first place after the dot is tenths.
Which is larger, 0.7 or 0.07?
Answer: 0
- 0.7 = 7/10
- 0.07 = 7/100
- 7 tenths beats 7 hundredths → 0.7
Takeaway: Look at the place value, not the number of digits.
Write 3/10 as a decimal.
Answer: 0.3
- Bottom is 10 → put 3 in the tenths place
- → 0.3
Takeaway: A tenths fraction becomes a one-place decimal.