Multiplying and dividing standard form

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Here is an example of a sum that involves multiplying standard form:

(4.2 x 10^-4) x (5 x 10^2)

To solve this, you begin by multiplying the numbers, to get

21 x 10^-4 x 10^2

Then add the powers of the 10s, because you are multiplying.

21 x 10^-2

Now all you have to do is change it to standard form (because the multiplier has to be between 1 and 10.)

2.1 x 10^-1

REMEMBER:

If you move the decimal place to the left, you add to the power

If you move the decimal place to the right, you subtract from it.

Here is an example of a sum that involves dividing standard form:

(67.5 x 10^4) ÷ (5 x 10^3)

First, you divide the numbers, to get:

13.5 x 10^4 ÷ 10^3

Then you subtract the powers of 10, because you are dividing

13.5 x 10^1

Now just change it into standard form, because the multiplier has to be between 1 and 10

1.35 x 10^2

REMEMBER

If you move the decimal point to the left, add the power

If you move the decimal point to the right, minus the power

Multiplying

Dividing