Place Value, Rounding and Estimation

In short: Each digit's value depends on its place: in 48 362 the 8 is worth 8000. To round, look at the digit just to the right of the place you are rounding to: 5 or more rounds up, 4 or less rounds down. Estimate by rounding first, then working out the easy sum.

Before you start

• Counting in ones, tens, hundreds and thousands.
• Multiplying by 10, 100 and 1000 (see Multiplying and Dividing by 10, 100 and 1000).

Places and values

Big numbers are written in groups of three digits, with a space between groups: 1 278 356.

One million is a 1 with six zeros: 1 000 000. It is a thousand thousands, because $1000\times 1000=1000000$.

Expanded form

Expanded form breaks a number into the value of each digit.

$$352407=300000+50000+2000+400+7$$

You can also use multiplication, and powers of ten:

$$352407=(3\times 100000)+(5\times 10000)+(2\times 1000)+(4\times 100)+7$$

$$4038=(4\times 10^3)+(3\times 10^1)+(8\times 1)$$

Here $10^3$ means $10\times 10\times 10=1000$. The small number says how many tens are multiplied.

Comparing and ordering

To compare two numbers, first count the digits. More digits means bigger. If they have the same number of digits, compare from the left until two digits differ.

Rounding

Estimating

To estimate, round each number to its first digit, then work it out in your head. An estimate tells you if a real answer is sensible.

Quick summary

• A digit's value depends on its place: in 1 278 356, the 7 is worth 70 000.
• One million is 1 000 000, a thousand thousands.
• Expanded form adds the value of each digit: $3058=3000+50+8$.
• To round, look at the next digit to the right: 5 or more rounds up, 4 or less stays.
• Estimate by rounding each number first, then check that real answers are close.

Quiz