# Converting between ordinary numbers and standard form

To convert a number into , split the number into two parts - a number multiplied by a of 10.

## Powers of 10

Standard form uses the fact that the decimal place value system is based on powers of 10:

## Large numbers

### Example

Write 50,000 in standard form.

50,000 can be written as:

So:

Question

What is 800,000 written in standard form?

800,000 can be written as .

So:

is not written in standard form as the first number is not between 1 and 10. To correct this, we need to divide 34 by 10. To balance out the division of 10, we also need to multiply the second part by 10, which gives 108.

and are equal in value, but only the second is written in standard form.

### Example

What is 87,000 in standard form?

87,000 can be written as .

So .

Question

What is 135,000 written in standard form?

135,000 can be written as .

So .

This process can be simplified by considering where the first digit is compared to the units column.

### Example

3,000,000 = because the 3 is 6 places away from the units column.

36,000 = because the 3 is 4 places away from the units column.

Question

What is 103,000,000 in standard form?

because the 1 is 8 places away from the units column.

Question

What is 1,230 in standard form?

because the 1 is 3 places away from the units column.