Standard form math help. How to write large numbers in standard index form.

A number in standard form (or standard index form) has the following formula:

a × 10ⁿ

where a is a number between 1 and 10, and n is the amount of times you have to multiply a to give you the original number.

Standard form is a way of writing down very large numbers or very small number in a shorter way, so that we can save time when writing down numbers.

In the following examples we are only looking at large numbers. Check out my other articles for writing very small numbers (numbers between 0 and 1) in standard form.

Example 1

Write down 4000 in standard form.

a has to be between 1 and 10 so make a 4.0 (or 4)

Now to make 4000 we have to multiply 4.0 by 10 three times. So n is equal to 3.

Therefore our answer is 4.0 × 10³

Example 2

Write down 370,000 in standard form.

a has to be between 1 and 10 so make a 3.7

Now to make 370000 we have to multiply 3.7 by 10 five times (count the amount of places you move the decimal point if you are finding this tough). So n is equal to 5.

Therefore our answer is 3.7 × 10⁵

Example 3

Write down 87,500,000 in standard form.

a has to be between 1 and 10 so make a equal to 8.75

Now to make 87500000 we have to multiply 8.75 by 10 seven times (count the amount of places you move the decimal point if you are finding this tough) Therefore n is equal to 7.

So our final answer is 8.75 × 10⁷.

Example 4

Write 7,984,566 in standard index form.

Again we need to write a as a number between 1 and 10. Now it will be a bit pointless writing a as 7.984566 as we are still writing down the original number. Remember, standard form is meant to be shorter way of writing down your number. Therefore, round the original number off to 3 significant figures as 7,980,000. Now we can make a as 7.98.

Now to make 7,980,000 we have to multiply 7.98 by 10 six times (count the amount of places you move the decimal point if you are finding this tough) Therefore n is equal to 6.

So our final answer is 7.98 × 10⁶ (3 significant figures)