1.02 Multiplication and Division using Scientific Notation.

Multiplication.

To multiply two numbers that are expressed using scientific notation, you simply multiply the first part of each number, then add the powers, (taking into account their signs). We may then have to move the decimal point in the answer, until there is only one digit before it and "adjust" the power as required. (i.e. for each position you move the decimal point to the left, add 1 to the power, for each position you move it to the right, subtract 1 from the power.)

Examples.

6 x 10² x 2 x 10³ = 1.2 x 10⁶ .
(6 x 2 = 12) (2 + 3 = 5) .
(12 x 10⁵ = 1.2 x 10⁶) .

3 x 10^-2 x 2 x 10⁶ = 6 x 10⁴ .
(3 x 2 = 6) (-2 + 6 = 4) .

-4.5 x 10^-2 x 3 x 10^-6 = -1.35 x 10^-11 .
((-4.5) x 3 = -13.5) ((-2) + (-6) = -10) .
(-13.5 x 10^-10 = -1.35 x 10^-9) .

If the addition or multiplication of positive and negative numbers above is unclear, please refer to adding positive and negative numbers and multiplying and dividing positive and negative numbers .

Division.

To divide two numbers that are expressed using scientific notation, you simply divide the first part of the first number, by the first part of the second number and then subtract the second power from the first. Again we may then have to move the decimal point in the answer until there is only one digit before it and "adjust" the power as before.

Examples .

8 x 10⁴ ÷ 2 x 10² = 4 x 10² .
(8 ÷ 2 = 4) (4 - 2 = 2) .

-4 x 10^-2 ÷ 8 x 10⁶ = -5 x 10^-9 .
((-4) ÷ 8 = -0.5 ) (-2 - 6 = -8) .
(-0.5 x 10^-8 = 5 x 10^-9) .

-1.5 x 10² ÷ -6 x 10^-6 = 2.5 x 10⁷ .
((-1.5) ÷ -6 = 0.25) (2 - (-6) = 8).
(0.25 x 10⁸ = 2.5 x 10⁷).