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 × 10n. 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.

More by this Author


Comments 5 comments

catman3000 profile image

catman3000 3 years ago from England, UK Author

Just corrected that mistake, thanks.


A. 3 years ago

7.24x10^4 doesn't equal 8 600 000


Ameya Vitankar 5 years ago

How do you change 30.7 in standard form?


catman3000 profile image

catman3000 5 years ago from England, UK Author

First round the number to 3 significant figures:

12,831,970 = 12,800,000 as you don't want all the non zero digits in the answer.

Now, write this is standard form:

= 1.28 x 10^7


neiko 5 years ago

how do you write twelve million eight hundred thirty one thousand nine hundred seventy in standard form

    0 of 8192 characters used
    Post Comment

    No HTML is allowed in comments, but URLs will be hyperlinked. Comments are not for promoting your articles or other sites.


    Click to Rate This Article
    working