Place value
- The value of a digit depends on its position: millions, hundred thousands, ten thousands, thousands, hundreds, tens, units, then tenths, hundredths and thousandths after the decimal point.
- In 4.073, the 7 is worth 7 hundredths (0.07) and the 3 is worth 3 thousandths (0.003).
- Zeros are placeholders: 406 012 is four hundred and six thousand and twelve.
Ordering numbers
- For whole numbers, the one with more digits is bigger (for positive numbers).
- For decimals, compare digits from the left. It helps to write them with the same number of decimal places: 0.5 = 0.50, which is bigger than 0.45.
- A longer decimal is not always bigger: 0.405 is less than 0.5.
Multiplying and dividing by powers of 10
- Multiplying by 10, 100 or 1000 moves the digits 1, 2 or 3 places to the left: 3.6 × 100 = 360.
- Dividing by 10, 100 or 1000 moves the digits 1, 2 or 3 places to the right: 45 ÷ 1000 = 0.045.
Inequality symbols
- < means 'is less than' and > means 'is greater than': 0.7 > 0.65.
- ≤ means 'is less than or equal to' and ≥ means 'is greater than or equal to'.
- The symbol always points to the smaller number.
Using a known fact
- If you know 23 × 47 = 1081, then 2.3 × 4.7 = 10.81, because each number has been divided by 10, so the answer is divided by 100.
- Check the size of the answer with an estimate: 2 × 5 = 10.
Key terms
- 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.
- Placeholder
- A zero used to keep the other digits in the right place.
- Decimal point
- The dot separating whole numbers from parts of a whole.
- Tenth
- One part in ten: 0.1.
- Hundredth
- One part in a hundred: 0.01.
- Inequality
- A statement that one value is greater or less than another.