GCSE(F) GCSE(H)

**Standard Form** is used to handle very small and very large numbers. It is written in two parts: the first part is a decimal number between 1 and 10, and the second part is a power of 10. An example of a number written in standard form is 3.44 x 10^{3}.

To turn a number written in standard form into a normal number, multiply the two parts of the standard form together:

3.44 x 10^{3}

= 3.44 x 1000 (10^{3} is 1000)

= 3440.

To turn a normal number into standard form, determine the decimal number that will be between 1 and 10:

taking 295,000 as an example

2.95 is the decimal number between 1 and 10.

Work out what power of 10 will be needed to multiply 2.95 to make 295,000

2.95 needs to be multiplied by 100,000 = 10^{5}

The standard form of 295,000 is 2.95 x 10^{5}.

1. The sun, on average, is 92 960 000 miles away from the earth. Write this number in standard form.

Answer: 9.296 x 10^{7}

92,960,000 = 9.296 x 10,000,000, therefore 9.296 x 10^{7}.

2. The moon is 3.84 x 10^{5} kilometres from the earth. Write that as a normal number.

Answer: 384,000 km

3.84 x 10^{5}

= 3.84 x 100,000

= 384,000 km

Our iOS app has over 1,000 questions to help you practice this and many other topics.

Available to download free on the App Store.

Available to download free on the App Store.