Download Skills Review: Scientific Notation Scientific Notation

Skills Review: Scientific Notation
Scientific Notation is a special way to write numbers. It is typically used to simplify very large or very small
numbers, which are common in science, such as a very large wavelength of or very small frequencies. Here are
a few examples:
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700 written in scientific notation is 7.0 X 102
4,900,000,000 written in scientific notation is 4.9 X 109
0.000000000012 written in scientific notation is 1.2 X 10-11
The number is written in two parts. First, the DIGITS that are written with the decimal point placed after the
first digit. Secondly, a “x 10 to a power” that puts the decimal place where it should be (how many places to
move the decimal place).
In this example, 5,326.6 is written as 5.3266 X 103 because 5326.6 = 5.3266 X 1000. And 1000 = 103. Another
way to look at this is to say that you had to move the decimal THREE number places to the left, so the power
of ten is “10 to the 3rd" (103).
Remember, if the number is ten or greater, the decimal point has to move to the left and the power of ten will
be positive. If the number is smaller than 1, the decimal has to move to the right, so the power of ten will be
negative.
Multiplication and Division in Scientific Notation is not very difficult once you know the basic rules.
#1 – Multiplication: To multiply to numbers written in scientific notation, you first multiply the two
number digits. Secondly, you multiply the two powers of 10. When doing so, you must ADD the
exponents of the tens. Here are two examples:
Ex #1  2.56 x 10-6 x 1.4 x 10-5
1st  multiply the two digits together:
2nd  multiply the x10s:
Ex #2  2.75 X 10-4 x 8.6 X 107
2.56 X 1.4 = 3.584
10-6 x 10-5 = 10(-6) + (-5) = 10-11
3rd  the answer is the combination:
3.584 x 10-11
1st  multiply the two digits together
2.75 X 8.6 = 23.65
2nd  multiply the x10s:
10-4 x 107 = 10(-4) + (7) = 103
3rd  the answer is the combination
23.65 X 103 = 2.365 X 104
Note: Since you typically write the digits with the decimal after the first number, you would change this
final answer to 2.365 X 104 – this is done by moving the decimal one to the left and raising the power
of ten one more number. The opposite is done when moving the decimal to the right.
#2 – Division: To divide numbers in scientific notation, you follow the same concept as when
multiplying except now you divide the two digits and when dealing with powers of ten, you SUBTRACT
the exponents.
Ex #1  6.2 x 109 ÷ 3.1 X 104
1st  divide the two digits
6.2 ÷ 3.1 = 2.0
2nd  divide the x10s
109 ÷ 104 = 109-4 = 105
3rd  the answer is the combination
Ex #2  3.55 x 10-5 ÷ 2.0 X 10-3
2.0 x 105
1st  divide the two digits
3.55 ÷ 2.0 = 1.83
2nd  divide the x10s
10-5 ÷ 10-3 = 10(-5)-(-3) = 10-2
3rd  the answer is the combination
1.83 x 10-2
Now You Try It!
(1) Write the following numbers in scientific notation:
a. 1,560,000 = ___________________
b. 0.000045 = ___________________
c. 58,000,000,000 = ____________________
d. 0.00000000000768 = ____________________
(2) Write the answers to the following problems in scientific notation:
a. 1.63 x 105 x 5.29 X 107 = _______________________
b. 2.7 x 10-9 x 4.6 X 104 = _______________________
c. 9.2 x 109 ÷ 3.15 X 106 = _______________________
d. 12.7 x 109 ÷ 8.6 X 106 = _______________________
(3) A radio wave has a frequency of 3 X 1010 Hz and a wavelength of 1.0 X 10-2 m. What is the speed of this
wave, written in scientific notation? Remember that the speed of a wave is its’ frequency times its’
wavelength! (Show your work below).