Standard index form is a shorthand way of writing a very large or a very small number.

It is written as a  number between 1 and 10 (but not equal to 10) multiplied by a power of 10, for example 2.94 × 10² or 4.8 × 10^-3.

You can probably see how much easier it is to manage numbers when they are in standard form - counting all those zeros can be quite tricky! It can be incredibly useful in science if you want to compare the magnitude of things that are very large (such as distances in space) or very small (such as the size of bacteria or cells in the body).

In this activity, we will just look at very large numbers.

Example

Change 5830000 into standard form.

First, fix the decimal point after the first digit to make a number between 1 and 10:   5.830000 or 5.83

Next, determine the power of 10 that you must multiply 5.83 by, to get back to 5830000

In this case it is 6.

So 5830000 = 5.83 × 10⁶

Other Examples

112233.92 = 1.1223392 × 10⁵

694000000 = 6.94 x 10⁸

Let's have a go at some questions now.