# How to write small numbers using standard form notation (negative exponents)

Just to recap, a number in standard form takes the form:

**a × 10 ^{n}**

If you are writing small numbers in standard form n is a negative exponent (power) as this means you are actually dividing **a** by 10 to give you the original number. Also, remember that **a** must take a value between 1 and 10. Let’s take a look at a few examples of converting small numbers into standard form:

**Example 1**

Write 0.0056 in standard form.

Since **a** must be number between 1 and 10, **a** must be 5.6.

Now, to get 0.0056, 5.6 must be divided by 1000 (the same as 10³).

So 0.0056 in standard form is 5.6 × 10⁻³.

**Example 2**

Write 0.0005 in standard form.

Since **a** must be number between 1 and 10, **a** must be 5 (or 5.0)

Now, to get 0.0005, 5 must be divided by 10,000 (the same as 10⁴).

So 0.0005 in standard form is 5 × 10⁻⁴.

**Example 3**

Write 0.000000924 in standard form.

Since **a** must be number between 1 and 10, **a** must be 9.24.

Now, to get 0.000000924, 9.24 must be divided by 10,000,000 (the same as 10⁷).

So 0.000000924 in standard form is 9.24 × 10⁻⁷.

**Example 4 **

A cell has a length of 0.081mm. Write this value in standard form.

Since **a** must be number between 1 and 10, **a** must be 8.1.

Now, to get 0.081, 8.1 must be divided by 100 (the same as 10²).

So the length of the cell in standard form is 8.1 × 10⁻².

**Example 5**

Write 0.0089648364 in standard form (to 3 significant figure)

First round the number off to 3 significant figures:

0.0089648364 = 0.00896 rounded to 3 significant figures.

Since **a** must be number between 1 and 10, **a** must be 8.96.

Now, to get 0.00896, 8.96 must be divided by 1000 (the same as 10³).

So 0.00896 in standard form is 8.96 × 10⁻³.

## Other math links

- 2011 GCSE Maths Foundation Exam. 5 top topics to rev...
- Standard form help. How to convert large numbers to ...

Before I show you how to change a normal number into standard index form let me explain the definition of standard index form. Standard index form is a mathematical system of writing down small and large...

## More by this Author

- 0
The density, mass and volume triangle is as follows: So if you wanted to work out the density, you would cover up density in the magic triangle to give: Density = Mass/Volume (since mass is above volume) So if...

- 12
Find the nth term of a quadratic number sequence.

- 0
The surface area of a triangular prism can be found in the same way as any other type of prism. All you need to do is calculate the total area of all of the faces. A triangular prism has 5 faces, 3 being rectangular and...

## Comments

No comments yet.