Decimals
A decimal is a fraction of ten, a hundred or a thousand, written on one line instead of two. The point separates the whole numbers from the parts, and every digit after it has a place of its own.
The decimals tool
Hundredths on a line
Drag the marker: every step is one hundredth
0.37 37
Zero is at the left end, one at the right.
How decimals works
-
Read the digits after the point by place
The first digit after the point counts tenths, the second counts hundredths, the third thousandths. So 0.3 is three tenths and 0.37 is thirty-seven hundredths. Each place is ten times smaller than the one before it, exactly as whole number places are ten times bigger.
-
Line the places up to compare
Decimals are compared place by place, starting straight after the point. Writing 0.5 as 0.50 makes the comparison plain: fifty hundredths against forty-five hundredths, so 0.5 is bigger. Never compare the digits as though the point were not there.
-
Remember where they came from
Every decimal has a fraction inside it: 0.5 is 5/10, which is 1/2, and 0.25 is 25/100, which is 1/4. Zeros written on the end do not change the value — 0.50 and 0.5 are the same amount — but zeros added on the left of a whole number would change it: 0.05 is five hundredths.
Worked examples
0.37
Thirty-seven hundredths. The 3 is in the tenths place, worth 0.3, and the 7 is in the hundredths place, worth 0.07, so 0.3 + 0.07 = 0.37, which is the fraction 37/100.
0.5 or 0.45 — which is bigger?
0.5. Written with the same number of places, 0.5 is 0.50, which is fifty hundredths, and fifty is more than forty-five. The longer decimal is not the bigger one; the place values decide.
0.25
Twenty-five hundredths, which is 25/100, which simplifies to 1/4. A quarter of a metre, a quarter of a litre, twenty-five pence in a pound — all of them are 0.25 written in decimal form.
Where it goes wrong
- Judging by the number of digits It is easy to read 0.45 as bigger than 0.5 because 45 is bigger than 5, but the digits are in different places. Lining the decimals up with the same number of places — 0.50 against 0.45 — settles it every time.
- Ignoring the point Read 2.5 as 25 and every answer that follows is a factor of ten out. The point is the whole meaning of a decimal: it marks where the whole numbers stop and the parts begin.
- Adding a zero in the wrong place 0.50 is the same as 0.5, because a trailing zero in the hundredths place adds nothing. Putting the zero after the point but in front of the 5 is a different number entirely: 0.05 is five hundredths, ten times smaller.
Questions
What does the decimal point actually mean?
It marks the boundary between whole numbers and parts of a whole. Everything to the left is counted in ones, tens and hundreds; everything to the right is counted in tenths, hundredths and thousandths, with each place ten times smaller than the last.
Why is 0.5 bigger than 0.45?
Because the places decide, not the digits. Write both with two decimal places and you are comparing 0.50 with 0.45: fifty hundredths is more than forty-five hundredths. Reading 0.45 as "forty-five" is reading a number that is not on the page.
Where do decimals come from?
From fractions with ten on the bottom, or a hundred, or a thousand. 3/10 is 0.3, 37/100 is 0.37. Decimals exist so that measurements can be written on one line and worked with using the same columns and carrying that whole numbers use.
Why are decimals used for money and measures?
Because money is already divided into hundreds and measures into tens and thousands. A pound splits into a hundred pence and a metre into ten decimetres or a thousand millimetres, so one hundredth of a pound is 0.01 and one tenth of a metre is 0.1. The decimal simply records the part you have.
Is 0.50 the same as 0.5?
Yes. A zero written at the end of a decimal adds nothing, because there are no hundredths to count: 0.50 is fifty hundredths and 0.5 is five tenths, and five tenths is exactly fifty hundredths. Zeros at the end are useful for lining up columns, not for changing amounts.