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# Multiplying and Dividing in Scientific Notation

## Part 1: Multiplying in Scientific Notation

PROCEDURE: To multiply numbers in scientific notation, multiply the decimal numbers. Then add the exponents of the powers of 10. Place the new power of 10 with the decimal in scientific notation form. If your decimal number is greater than 10, count the number of times the decimal moves to the left, and add this number to the exponent.

SAMPLE PROBLEM: Multiply (2.6 Ã— 107) by (6.3 Ã— 104).

 Step 1: Multiply the decimal numbers. 2.6 Ã— 6.3 = 16.38 Step 2: Add the exponents. 7 + 4 = 11 Step 3: Put the new decimal number with the new exponent in scientific notation form. 16.38 Ã— 1011 Step 4: Because the new decimal number is greater than 10, count the number of places the decimal moves to put the number between 1 and 10. Add this number to the exponent. In this case, the decimal point moves one place, so add 1 to the exponent. ## Part 2: Dividing in Scientific Notation

PROCEDURE: To divide numbers in scientific notation, first divide the decimal numbers. Then subtract the exponents of your power of 10. Place the new power of 10 with the decimal in scientific notation form. If the resulting decimal number is less than 1, move the decimal point to the right and decrease the exponent by the number of places that the decimal point moved.

SAMPLE PROBLEM: Divide (1.23 Ã— 1011) by (2.4 Ã— 104).

 Step 1: Divide the decimal numbers. 1.23 Ã· 2.4 = 0.5125 Step 2: Subtract the exponents of the powers of 10. 11 - 4 = 7 Step 3: Place the new power of 10 with the new decimal in scientific notation form. 0.5125 Ã— 107 Step 4: Because the decimal number is not between 1 and 10, move the decimal point one place to the right and decrease the exponent by 1. (1.23 Ã— 1011) Ã· (2.4 Ã— 104) = 5.125 Ã— 106