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## Worksheets and How To Multiply/Divide in Scientific Notation

(Start with How to Do Scientific Notation or go to worksheets)

To multiply two numbers in scientific notation:

- Re-arrange the expression so you can multiply the coefficients and powers-of-ten separately.
- Resolve the two multiplication expressions. Multiply the powers-of-ten expressions by adding their exponents.
- Multiply the separated expressions back together.
- Reformat the result so it has only one non-zero digit to the left of the decimal point.

Example 1: Multiply numbers in superscript format 1.3x10 ^{2}x 4.5x10^{-3}

= (1.3 x 4.5) x (10^{2}x 10^{-3})

= 5.85x10^{-1}Example 2: Multiply numbers in E format 9.9E-3 x 2.2E+5

= (9.9 x 2.2) x (E-3 x E+5)

= 21.78E+2

= 2.178E+3To divide two numbers in scientific notation:

- Re-arrange the expression so you can divide the coefficients and powers-of-ten separately.
- Resolve the two division expressions. Divide the powers-of-ten expressions by subtracting the divisor's exponent from the dividend's exponent.
- Multiply the separated expressions back together.
- Reformat the result so it has only one non-zero digit to the left of the decimal point.

Example 1: Divide numbers in superscript format 1.2x10 ^{2}/ 4.0x10^{-3}

= (1.2 / 4.0) x (10^{2}/ 10^{-3})

= 0.3x10^{5}

= 3.0x10^{4}Example 2: Divide numbers in E format 1.32E-3 / 1.2E+1

= (1.32 / 1.2) x (E-3 / E+1)

= 1.1E-4