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— 10^{7}) by (6.3 Ã— 10^{4}).
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— 10^{11 } 
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— 10^{11}) by (2.4 Ã— 10^{4}).
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— 10^{7} 
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— 10^{11}) Ã· (2.4 Ã— 10^{4}) = 5.125 Ã— 10^{6}
