FRAME 5-20.
Solution to
Multiplying Using Scientific Notation
Frame 5-19.
Scientific notation can make multiplication a little easier (or at least look
a. 0.00045
neater).
b. 0.000007
Consider the problem: 32,000 x 10,200,000,000.
By using scientific notation, you can change the appearance of the
problem to 3.2 x 10 4 times 1.02 x 10 10.
To solve the problem, you
(1) Multiply the coefficients (numbers in front).
(2) Add the exponents (the powers of 10). The sum will be
your new power of 10.
(3) Rewrite the answer so it is in scientific notation format,
if needed.
3.2 x 10 4 X 1.02 x 10
10
= 3.2 x 1.02 x 10 4+10 = 3.264 x 10 14
Solve this problem:
3 x 10 5 X 7 x 10 6
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FRAME 5-21.
Solution to
NOTE: When you multiplied the coefficients to the problem in Frame 5-
Frame 5-20.
20, you got a new coefficient that was above 10 (21 x 10 11). However,
21 x 10 11
Frame 5-15 states that the coefficient should be between 1 and 10. That
(or 2.1 x 10 12)
is, the number to the left of the decimal point is to be a single digit.
Since 21 = 2.1 x 10 1
Then 21 x 10 11 = 2.1 x 10 1. x 10 11 = 2.1 x 10 1+11 = 2.1 x 10 12.
Solve these two problems:
4
3
a. 3 x 10
times 2 x 10
= __________________
4
6
b. 5 x 10
times 2 x 10
= __________________
NOTE: Positive and negative exponents are added using the same rules
for adding positive and negative numbers.
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MD0900
5-12