Comparing decimals: 0.7 or 0.65?
Compare and order decimals to 3 decimal places, including unequal-length decimals
The idea
A decimal is a fraction of a whole, split into equal parts.
- 0.7 means 7 parts out of 10.
- 0.65 means 65 parts out of 100.
Ten parts and one hundred parts are not the same size, so we cannot compare 7 and 65 directly.
Make the parts the same size
Write 0.7 with hundredths. One tenth is ten hundredths, so:
0.7 = 0.70
Now both numbers are in hundredths, and we compare the digits:
- 0.70 has 70 hundredths
- 0.65 has 65 hundredths
70 is more than 65, so 0.7 is greater than 0.65.
The trap
0.65 looks longer, so it seems bigger. Length is not size. Line up the decimal points and pad with zeros before you compare.
Try these in your head
- Which is greater: 0.8 or 0.79?
- Which is greater: 0.5 or 0.45?
- Put these in order, smallest first: 0.6, 0.58, 0.605.
Say your reasoning out loud: "I made the parts the same size, then compared."
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