Calculations with standard index form

• Adding and subtracting numbers written in standard form can be carried out by converting to an ordinary (decimal) number format before completing the calculation. The numbers are then changed back into standard form.
• Multiplication and division of numbers written in standard form is processed wholly within standard form.

Knowledge of converting numbers into and from standard form will be useful before looking at calculations with standard index form.

Adding and subtracting numbers in standard form can be done by working with ordinary (decimal) numbers:

1. Write the standard form numbers as ordinary numbers.
2. Do the addition or subtraction.
3. Write the answer in standard form.

A good understanding of standard form is needed for this method.

To multiply numbers in standard form:

1. Multiply the values of A. These are the numbers that are between 1 and 10.
2. Multiply the powers of 10 by adding the indices.
3. Write the answer in standard form.

To divide numbers in standard form:

1. Write the calculation as a fraction.
2. Divide the values of A.
3. Divide the powers of ten by subtracting the indices.
4. Write the answer in standard form.

After multiplying or dividing, the answer may not be in standard form. To adjust the number so it is in standard form:

1. First, write the value A in standard form multiplied by the given power of ten.
2. Simplify the powers of ten by adding the indices.

It may be useful to review the laws of indices and how to write a number in standard form.

Practise what you've learned about calculations with standard index form in this quiz. You might need a pen and paper to help with your working out.

Calculations in standard form are most often used by scientists working with very small and very large numbers. For example, Earth is 1∙5 × 10⁸ km from the Sun. Neptune is 4∙5 × 10⁹ km from the Sun.

To find the difference in these distances a subtraction in standard form is used. 4∙5 × 10⁹ – 1∙5 × 10⁸ is 4∙35 × 10⁹ km.

Calculating the time that it takes for light to travel from the Sun to the Earth involves a division. The distance of the Earth from the Sun (1∙5 × 10¹¹ metres) divided by the speed of light (3 × 10⁸ metres/second) gives 500 seconds (8 minutes and 20 seconds). The time that light takes to travel distances is used as a measure of distance when looking at far distant galaxies.