# Calculating standard form without a calculator

When adding and subtracting numbers, you have to:

1. convert the numbers from standard form into ordinary numbers
2. complete the calculation
3. convert the number back into standard form

Calculate .

## Multiplying and dividing

When multiplying and dividing you can use index laws:

1. multiply or divide the first part of the numbers
2. apply the index laws to the powers of 10
3. check whether the first part of the number is between 1 and 10
To multiply powers of 10, add the powers together, eg 106 x 104 = 106 + 4 = 1010. To divide powers of 10, subtract the powers, eg 107 ÷ 102 = 107 - 2 = 105.

### Example 1

Work out .

Multiply the first numbers – which in this case is .

Apply the index law to the powers of 10:

As 9 is between 1 and 10, this number is in standard form.

### Example 2

Work out .

Multiply the first numbers .

Apply the index law to the powers of 10

28 is not between 1 and 10, so is not in standard form. To convert this to standard form, divide 28 by 10 so that it is a number between 1 and 10. To balance out this out, multiply the second part by 10 which gives 107.

and are equivalent but only is written in standard form.

So:

Question

Calculate .

1. Divide the first part of the numbers:
2. Apply the index laws to the powers of 10
3. Check whether the first part of the number is between 1 and 10
4. So:

0.25 is not between 1 and 10, so is not in standard form. To convert this to standard form, multiply 0.25 by 10 so that it is a number between 1 and 10. To balance out that multiplication of 10, divide the second part by 10 which gives 104. So and are equivalent but only the second is written in standard form.

So: