Numbers & the number system
Understanding place value
The value of a digit depends on its position in the number. Place value lets you read, write and work with numbers all the way up to hundred thousands.
The value of a digit
Each column in a number has a place value: ones, tens, hundreds, thousands, ten thousands, hundred thousands. The same digit is worth different amounts in different places. In 829 the 8 is worth 800; in 950 302 the 9 is worth 900 000. A place value table helps you see this.
Reading and writing big numbers
Numbers greater than 1000 are read in groups. 335 271 is 'three hundred and thirty-five thousand, two hundred and seventy-one'. A zero can be a place holder, keeping a place empty — 105 050 has a 0 in the hundreds place.
Multiplying and dividing by 10 and 100
To multiply by 10, every digit moves one place to the LEFT (67 × 10 = 670). To multiply by 100 they move two places left (35 × 100 = 3500). To divide by 10 or 100, the digits move the same number of places to the RIGHT (3600 ÷ 100 = 36). The digits themselves stay the same.
Compose and decompose
To decompose a number is to split it into the value of each digit: 805 469 = 800 000 + 5000 + 400 + 60 + 9. To compose a number is to put the parts back together. This shows exactly what each digit is worth.
Worked examples
Value of a digit
- Look at the number 829.
- Put it in a place value table: 8 hundreds, 2 tens, 9 ones.
- The 8 is in the hundreds place.
Answer: The value of the 8 is 800.
Multiplying by 10
- Calculate 67 × 10.
- Every digit moves one place to the left.
- A 0 fills the empty ones place.
Answer: 67 × 10 = 670.
Dividing by 100
- Calculate 3600 ÷ 100.
- Every digit moves two places to the right.
- 36 hundreds becomes 36.
Answer: 3600 ÷ 100 = 36.
Decomposing a number
- Take the number 805 469.
- Write the value of each digit in turn.
- 800 000 + 5000 + 400 + 60 + 9.
Answer: 805 469 = 800 000 + 5000 + 400 + 60 + 9.
Where you see this in real life
- Reading large numbers such as the population of a city.
- Using place value to work out prices when things cost ten times as much.
- Writing a game score like 1646 in an expanded way.
Key words
- Place value
- The value a digit has because of its position in a number.
- Ten thousand
- The place value column worth 10 000.
- Hundred thousand
- The place value column worth 100 000.
- Place holder
- A 0 that keeps a place empty, like the 0 in 105 050.
- Decompose
- To split a number into the value of each digit.
- Compose
- To put the parts of a number back together.