6.472 146308

When the result of a calculation with a calculator goes beyond
the size of the calculator's display it is presented in standard
form. For example, the above result was recorded from a calculator's
display after calculating 865^{3}

This has to be interpreted as 6.472 146 3 x 10^{8} which equals 647 214
630.

A number is expressed in standard form when it is given as a number
with one non-zero digit to the left of the decimal point multiplied
by a power of 10. All numbers can be expressed in this way. For example,

329 = 3.29 x 10^{2}

46 700 = 4.67 x 10^{4}

0.0071 = 7.1 x 10^{-3}

The power of 10 required can be found by noting how many places the
decimal point has to be moved to the left or right to obtain a number
with one non-zero digit to its left.

For example,

870 235.0 = 8.702 35 x 10^{5}

0.000 276 = 2.76 x 10^{-4}

Standard form is particularly useful in dealing with very large or
very small numbers as needed in science and astronomy.

For example :

- A molecule of water has a mass of 2.99 x 10
^{-26} kg;
- The mass of the moon is 7.37 x 10
^{22}