A longer decimal is not automatically larger. 0.5 is bigger than 0.45, even though 0.45 has more digits. The trick is to give both numbers the same number of decimal places by padding with zeros at the end: 0.5 becomes 0.50. Now compare digit by digit from the left — tenths first, then hundredths. 0.50 has 5 tenths and 0.45 has only 4 tenths, so 0.50 is larger. Remember the digits after the point are tenths and hundredths, not an ordinary whole number.
Explore this idea with maths tools
Equal parts, equal wholes
2/4 = 4/8
Both bars are the same length. Find a division of the second bar that lines up exactly with the coloured edge.
Words to know
- decimal place
- a digit position after the point (tenths, hundredths)
- tenths
- the first place after the decimal point
- hundredths
- the second place after the decimal point
Worked examples
Which is larger, 0.5 or 0.45?
- 1.Pad to 0.50 and 0.45.
- 2.5 tenths beats 4 tenths, so 0.5 is larger.
= 0.5
Which is larger, 0.7 or 0.65?
- 1.Pad to 0.70 and 0.65.
- 2.7 tenths beats 6 tenths, so 0.7 is larger.
= 0.7
Which is larger, 0.4 or 0.42?
- 1.Pad to 0.40 and 0.42.
- 2.Tenths tie; 2 hundredths beats 0, so 0.42 is larger.
= 0.42
For parents
Method: Pad both decimals to the same length, then compare place by place.
What to say: Write them one above the other with the points lined up: 0.50 versus 0.45.
Common mistakes:
- Thinking more digits means larger (0.45 > 0.5).
- Reading the digits after the point as a whole number (0.65 > 0.7).