As well as very large numbers, standard form also deals with very small numbers:

4.56 x 10^{-3} is 4.56 ÷ 1000 = 0.00456.

To turn a small number written in standard form into a normal number, divide the number by the power of 10:

8.45 x 10^{-4}

= 8.45 ÷ 10 000

= 0.000845 (note that the 8 is the 4^{th} digit after the decimal point

To turn a small number into standard form, identify the number that will be between 1 and 10. For example, 0.00406:

4.06 is the number between 1 and 10

it needs to be divided by 1000

therefore 4.06 x 10^{-3} (note there are three decimal places to get to 4 in 0.00406)

A white blood cell has a diameter of 1.2 x 10^{-5}m. Write this as a normal number.

1.2 x 10^{-5}

= 1.2 ÷ 100,000

= 0.000012

Answer: 0.000012m

Write -0.056 in standard form.

-0.056

= -5.6 ÷ 100

= -5.6 x 10^{-2}

Answer: -5.6 x 10^{-2}

See also Calculating with Negative Indices

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