Decimals
Ordering decimals
The longest decimal is not the biggest. Compare column by column and the order falls out.
Different whole-number parts
To order decimals, write them smallest to largest. Start by comparing the WHOLE-NUMBER part. 8.9, 14.639, 6.45 → the whole parts are 8, 14 and 6. 14 is biggest and 6 is smallest, so the order is: 6.45, 8.9, 14.639
Same whole-number part
When the whole parts match, compare the TENTHS, then the HUNDREDTHS, and so on. 2.82, 2.6, 2.816 → all have whole part 2. Tenths: 8, 6, 8. So 2.6 is smallest. The other two both have 8 tenths, so compare hundredths: 2 and 1. So 2.816 is smaller than 2.82. Order: 2.6, 2.816, 2.82
The trap
2.816 has more digits than 2.82 — but it is SMALLER. Length tells you nothing. Only the value in each column counts. If it helps, pad the shorter number with zeros so the columns line up: 2.820 against 2.816. Now it is obvious.
Worked examples
Order 8.9, 14.639 and 6.45
- Compare the whole-number parts: 8, 14 and 6.
- 6 is smallest, 14 is biggest.
Answer: 6.45, 8.9, 14.639
Order 2.82, 2.6 and 2.816
- All have whole part 2, so compare tenths: 8, 6, 8.
- 2.6 is smallest.
- For the other two, compare hundredths: 2 against 1.
Answer: 2.6, 2.816, 2.82
Which is bigger, 2.816 or 2.82?
- 2.816 has more digits, but that means nothing.
- Pad it out: 2.820 against 2.816.
Answer: 2.82 is bigger
Comparing 0.5 and 0.45
- Pad the shorter one: 0.50 against 0.45.
- Compare tenths: 5 against 4.
Answer: 0.5 is bigger
Why padding with zeros helps
- It makes every column complete.
- Then you compare like with like.
Answer: The value never changes, but the comparison gets easy
Which is smallest: 3.07, 3.7 or 3.007?
- Pad them: 3.070, 3.700, 3.007.
- Compare tenths: 0, 7, 0. Then hundredths: 7 against 0.
Answer: 3.007
Where you see this in real life
- In a race, 10.85 s beats 10.9 s — the longer-looking time is actually the faster one.
- Comparing prices of £2.5 and £2.45: padding to £2.50 makes it clear which is cheaper.
Key words
- Tenths
- the first column after the decimal point
- Hundredths
- the second column after the decimal point
- Whole-number part
- the digits before the decimal point
- Order
- arrange from smallest to largest
- Thousandths
- the third place after the decimal point
- Place value
- the value a digit has because of its position
- Compare
- decide which of two numbers is larger