When adding or subtracting two numbers which are in standard form all you have to do is convert them back in to their ordinary form, calculate your answer and then once again convert it back into standard form. Look below for examples:

Addition

7.5 x 105+ 9.2 x 10=

750,000 + 920,000 = 1,670,000

1.67 x 106 = Final Answer

Subtraction

9.3 x 104- 4.52 x 104 =

93,000 - 45,200 = 47,800

4.78 x 104 = Final Answer

Multiplication

To multiply numbers in standard form, you can simply multiply together the parts in front of the x10, and then add the powers together to give you your answer. Look at the examples below:

e.g.

(3 x 105) x (5 x 103) = (3 x 5) x (105 + 103) = 15 x 108

It is important to remember that standard index form requires the number in front of x10 be equal to or greater than 1, and less than 10, so our answer above is not yet in standard form. To fix that, we divide 15 by 10, and compensate by adding 1 to the index:

15 x 108 = 1.5 x 10

1.5 x 10= Final Answer

Division

To divide numbers in standard form, you can simply divide the parts in front of the x10, and then subtract the powers after the x10 to find your answer.

(8 x 105) ÷ (2 x 103) = (8 ÷ 2) x (105 - 103)= 4 x 102

4 x 102 = Final Answer

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