Calculating in standard form
Introduction
When adding or subtracting numbers written in standard form the key is first write the numbers as ordinary number. Then add or subtract them using a standard column method.
To multiply or divide numbers in standard form rearrange the sum so the numbers and powers of 10 are dealt with separately.
Before learning this topic you should first make sure you know how to convert numbers to and from standard form.
How to add, subtract, multiply and divide with numbers written in standard form
Example 1 - Adding numbers in standard form
Calculate \((3.4 × 10^{3}) + (4.65 × 10^{4})\). Give your answer in standard form.
First write the two numbers as ordinary numbers.
\((3.4 × 10^{3}) = 3400\)
\((4.65 × 10^{4}) = 46500\)
Now \(3400 + 46500 = 49900\). Which written in standard form is \(4.99 × 10^{4}\).
Example 2 - Subtracting numbers in standard form
Calculate \((2.3 × 10^{-2}) - (9.1 × 10^{-3})\). Give your answer in standard form.
Again, first write the two numbers are ordinary number.
\((2.3 × 10^{-2}) = 0.023\)
\((9.1 × 10^{-3}) = 0.0091\)
Now \(0.023 - 0.0091 = 0.0139\). Which written in standard form is \(1.39 × 10^{-2}\).
Example 3 - Multiplying numbers in standard form
Calculate \((6 × 10^{3}) × (4 × 10^{6})\). Give your answer in standard form.
First rearrange the sum to multiply the leading numbers together followed by the powers of ten.
\(\begin{aligned} (6 × 10^{3}) × (4 × 10^{6}) & = (6 × 4) × (10^{3} × 10^{6})\\ & = 24 × 10^{(3 + 6)}\\ & = 24 × 10^{9}\\ & = 2.4 × 10^{10}\\ \end{aligned}\)
Example 4 - Dividing numbers in standard form
Calculate \((4.2 × 10^{-4}) ÷ (7 × 10^{2})\). Give your answer in standard form.
When dividing, rearrange the sum to divide the leading numbers together followed by the powers of ten.
\(\begin{aligned} (4.2 × 10^{-4}) ÷ (7 × 10^{2}) & = (4.2 ÷ 7) × (10^{-4} ÷ 10^{2})\\ & = 0.6 × 10^{(-4 - 2)}\\ & = 0.6 × 10^{-6}\\ & = 6 × 10^{-7}\\ \end{aligned}\)
Worksheets to practise calculating with numbers written in standard form
Try these worksheets to practise your skills.