# Standard form help. How to convert large numbers to standard index form.

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 numbers. A number in standard index form will take the form **m × 10 ^{n}**.

**m**is a number which must be between 1 and 10 and

**n**is the amount of times you multiply

**m**by to give you the original number. Let’s take a look at a few examples of writing down large numbers in standard form.

**Example 1 **

Write down 8 600 000 in standard form.

All you need to do is find the values of m and n.

m = 8.6 as m must be between 1 and 10.

n = 6 because you have to multiply 8.6 by 10 six times to give you 8 600 000.

So your answer is 8.6 × 10⁶.

**Example 2**

Write down 72 400 in standard form.

m = 7.24 as m must be between 1 and 10.

n = 4 because you have to multiply 7.24 four times to give you 72,400

So your answer is 7.24 × 10⁴

**Example 3**

Write 8 million in standard form.

First write down 8 million as 8 000 000.

Now m = 8 (or 8.0 if you prefer) as m must be between 1 and 10.

n = 6 because you have to multiply 8 six times to give 8 000 000.

So your answer is 8 × 10⁶.

**Example 4 **

Write down 27 800 000 in standard form.

m = 2.78 as m must be between 1 and 10.

n = 7 because you have to multiply 2.78 seven times to give 27 800 000.

So your answer is 2.78 × 10⁷.

**Example 5**

Write down 8 753 865 974 in standard form.

Now in this case since there are several non zero digits so it will be appropriate to round your number to 3 significant figures before you put the number in standard index form. You do this because standard form is meant to be a quick way of writing down large numbers and it will be defeating the point if you make m = 8.753865974!

8 753 865 974 = 8 750 000 000 (3 s.f)

So m = 8.75 and n = 9.

So your answer will be 8.75 × 10⁹.

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