Place value and rounding · KS3 Maths

Place value

The value of a digit depends on its position: thousands, hundreds, tens, ones, then tenths, hundredths and thousandths after the decimal point.
In 4 572.36, the 5 is worth 500 and the 3 is worth 3 tenths (0.3).
Multiplying by 10, 100 or 1000 moves the digits 1, 2 or 3 places to the left: 3.4 × 100 = 340. Dividing moves them to the right: 56 ÷ 1000 = 0.056.

To order decimals, compare the digits from the left: 0.45 is bigger than 0.405, because 5 hundredths is more than 0 hundredths.
It can help to give every number the same number of decimal places: 0.450, 0.405, 0.500.

To round, look at the next digit: 5 or more rounds up; 4 or less rounds down.
3 847 to the nearest 100 is 3 800. 2.764 to 1 decimal place is 2.8.
Significant figures start at the first non-zero digit: 48 372 to 1 significant figure is 50 000, and 0.004 57 to 2 significant figures is 0.0046.

Estimate by rounding each number to 1 significant figure: 49 × 21 ≈ 50 × 20 = 1000.
Estimates help you check whether a calculator answer is sensible.

Place value: The value of a digit because of its position in a number.
Digit: One of the symbols 0 to 9 used to write numbers.
Decimal place: A position after the decimal point.
Tenth: One part in ten: 0.1.
Hundredth: One part in a hundred: 0.01.
Rounding: Making a number simpler while keeping it close to its value.
Significant figure: A digit that counts, starting from the first non-zero digit.
Estimate: A rough answer found by rounding the numbers first.