Place value and ordering
Every column is worth ten of the next
In 4,372.18 the 3 is worth 300, because it sits in the hundreds column.
Moving one column left multiplies a digit's value by 10. Moving one column right divides it by 10.
| thousands | hundreds | tens | ones | . | tenths | hundredths |
|---|---|---|---|---|---|---|
| 4 | 3 | 7 | 2 | . | 1 | 8 |
Multiplying by 100 moves every digit two places left: 3.47 × 100 = 347. Dividing by 1000 moves them three places right: 52 ÷ 1000 = 0.052.
Multiplying by 0.1 is the same as dividing by 10, and dividing by 0.01 is the same as multiplying by 100. So 52 × 0.1 = 5.2, and 0.3 ÷ 0.01 = 30.
Ordering decimals: line up the points
Which is bigger, 0.6 or 0.59? The second has more digits, but that does not matter. Line up the decimal points and fill gaps with zeros:
- 0.600
- 0.590
- compare the tenths first: 6 is more than 5
- so 0.6 is bigger than 0.59
With negative numbers, the further from zero, the smaller: −7 is less than −4. A number line helps: left is smaller.
The symbols
- = equals, ≠ does not equal
- < less than, > greater than (the wide end faces the bigger number)
- ≤ less than or equal to, ≥ greater than or equal to
So −2 ≤ n < 3 includes −2 but not 3. For whole numbers n, that is −2, −1, 0, 1, 2.
The most common slip in ordering: treating 0.125 as bigger than 0.5 because 125 is bigger than 5. Always compare column by column.
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