The number system
Place value
Every digit has a value that depends on its place. In Stage 6 we work with numbers that have up to 3 decimal places — tenths, hundredths and thousandths.
Tenths, hundredths and thousandths
Each place is worth ten times the place to its right. After the decimal point come tenths, then hundredths, then thousandths. Example: in 213.807 the digit 7 is in the thousandths place, so it is worth 0.007.
Multiplying and dividing by 10, 100 and 1000
• Multiplying makes a number bigger, so the digits move LEFT (1 place for 10, 2 for 100, 3 for 1000). • Dividing makes it smaller, so the digits move RIGHT. The decimal point stays still.
Compose, decompose and regroup
You can build a number from its parts (compose), split it into parts (decompose), or swap parts of equal value (regroup), such as 5 tenths for 50 hundredths.
Worked examples
Value of a digit to thousandths
- Look at 213.807 and find the digit 7.
- It is the third place after the decimal point — the thousandths.
Answer: The value of the 7 is 0.007.
Multiplying and dividing by powers of 10
- Work out 7.2 × 1000. Multiplying by 1000 moves the digits 3 places left.
- Work out 670 ÷ 100. Dividing by 100 moves the digits 2 places right.
Answer: 7.2 × 1000 = 7200 and 670 ÷ 100 = 6.7
Composing a decimal number
- Add the parts, largest place value first: 10 + 3 + 0.1 + 0.03 + 0.006.
- Put each digit in its place: tens, ones, tenths, hundredths, thousandths.
Answer: 10 + 3 + 0.1 + 0.03 + 0.006 = 13.136
Regrouping a decimal number
- Regroup 0.546 as 0.4 + ? + 0.006.
- 5 tenths is the same as 4 tenths and 14 hundredths, so the middle part is 0.14.
Answer: 0.546 = 0.4 + 0.14 + 0.006
Where you see this in real life
- Measuring a butterfly's wingspan as 0.375 inches.
- Changing millimetres to metres by dividing by 1000.
- Reading prices and amounts of money to the nearest hundredth.
Key words
- Thousandth
- The third place after the decimal point — one part out of a thousand.
- Place value
- The value of a digit because of its position in the number.
- Compose
- To build a number by combining its parts.
- Decompose
- To break a number into the value of each digit.
- Regroup
- To swap parts of equal value, e.g. 1 tenth for 10 hundredths.