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

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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 a × 10n. Where a is a number which must be between 1 and 10, and n is the amount of times you multiply a 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 a and n.

a = 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.

If you are have trouble working out how many times you have to multiply the number by 10, count the amount of places from where you have put the decimal between the 8 and 6 to where the decimal was originally at (at the end of the number).

Example 2

Write down 72 400 in standard form.

a = 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

Like example 1, If you are have trouble working out how many times you have to multiply the number by 10, count the amount of places from where you have put the decimal between the 7 and 2 to where the decimal was originally at (at the end of the number).

Example 3

Write 8 million in standard form.

First write down 8 million in digit format as 8 000 000.

Now a = 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.

Like examples 2 and 3, If you are have trouble working out how many times you have to multiply the number by 10, count the amount of places from where you have put the decimal (after the first 8) to where the decimal was originally at (at the end of the number).

Example 4

Write down 27 800 000 in standard form.

a = 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.

Just like the previous examples, If you are have trouble working out how many times you have to multiply the number by 10, count the amount of places from where you have put the decimal between the 2 and 7 to where the decimal was originally at (at the end of the number).

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 a = 8.753865974!

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

So a = 8.75 and n = 9.

So your answer will be 8.75 × 10⁹.

You may also be asked to write down a number which is in standard form back to a normal number. To do this you will need to do the above process in reverse.

So for example, if you were asked to convert 4.8 x 10^8 back to a normal number you need to mulitply the 4.8 by 10 EIGHT times, so the answer will be 480, 000, 000. Again if you are having trouble multiplying by 10, try moving the decimal instead as this can make the question easier to work out.

For more help on converting a number from standard form you may wish to look at this video.

Coverting Standard Form Numbers to Normal Numbers.

What about small numbers in standard form?

You may also use standard index form to write small numbers in (ones which are between zero and one). Again, you can apply the same method as shown in the last few examples. The only difference is that you use a negative power instead of a positive power. The negative power means you are dividing the number by 10 instead of multiplying by 10. So for example, you can write 0.0028 in stardard form as 2.8 x 10^-3. Notice that the first number is between 1 and 10, but the power is negative instead of postitive.

Comments

Mark (author) from England, UK on August 06, 2013:

Just corrected that mistake, thanks.

A. on August 04, 2013:

7.24x10^4 doesn't equal 8 600 000

Ameya Vitankar on September 20, 2011:

How do you change 30.7 in standard form?

Mark (author) from England, UK on January 07, 2011:

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 on January 06, 2011:

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