Large Numbers

Large Numbers

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 103.

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

3.44 x 103

= 3.44 x 1000 (103 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 = 105

The standard form of 295,000 is 2.95 x 105.

Examples

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

Answer: 9.296 x 107

92,960,000 = 9.296 x 10,000,000, therefore 9.296 x 107.

2. The moon is 3.84 x 105 kilometres from the earth. Write that as a normal number.

Answer: 384,000 km

3.84 x 105

= 3.84 x 100,000

= 384,000 km