Download SCIENTIFIC NOTATION

Student Resource Sheet POW - 10
SCIENTIFIC NOTATION
In science, you will often encounter very small and very large numbers. The mass of an atom of
gold, for example is 0.000000000000000000000327 gram. A gram of hydrogen contains
602,000,000,000,000,000,000,000 hydrogen atoms. Writing and using such small or large
numbers is very cumbersome. You can work more easily with these
numbers by writing them in scientific, or exponential notation.
Objective
When you have completed this activity, you should be able to
1. utilize mathematical skills in order to compute using scientific notation.
Materials
calculator
Activity 1
Scientific notation takes the form of M x 10n. The coefficient ‘M’ is equal to or greater than one
but less than ten. The exponent ‘n’ represents the number of decimal places to be moved.
Positive ‘n’ indicates the standard form is larger than one (1x 102 = 100). A negative ‘n’ would
indicate a number smaller than one (1 x 10-2 = 0.01).
Example 1: Convert 2,300,000 to scientific notation.
You move the decimal point so that there is only one digit to its left, a total of six places.
2,300,000 = 2.3 x 106
Example 2: Convert 0.000037 to scientific notation.
For this, you move the decimal point five places to the right.
0.000037 = 3.7 x 10-5
1. Solve the following by converting the underlined numbers to scientific notation. Use the
examples to aid you.
a. There are 0.00000000000106 kilometers in a light-year.
b. The half-life of Uranium-235 is 713,000,000 years
c. The FM band on your radio has a frequency between 88,000,000 and 108,000,000
cycles per second.
d. The wavelength of a gamma ray is 0.00000000001 cm.
e. There are computer memory chips as small as 0.00000005 meters.
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Student Resource Sheet POW - 10
Activity 2
Using scientific notation makes calculating more straightforward. To multiply numbers written
in scientific notation, multiply the coefficients and add the exponents. To divide numbers
written in scientific notation, first divide the coefficients. Then subtract the exponent in the
denominator (bottom) from the exponent in the numerator (top).
Example 1: (4.0 x 104) x (2.0 x 102) = (4.0 x 2.0) x 104+2 = 8.0 x 106
Example 2:
6.0 x 106 =
2.0 x 104
6.0 x 106-4 = 3.0 x 102
2.0
2. Solve each problem, and express each answer in correct scientific notation.
a. (4.3 x 105) (0.4 x 105) = __________________
b. (4.5 x 104) (1.23 x 103) = __________________
c. (3.6 x 105) (1.3 x 10-3) = __________________
d. 4.5 x 104 = __________________
1.23 x 103
e. 4.01 x 107 = __________________
1.5 x 103
f. 4.8 x 105 = __________________
2.4 x 10-3
Activity 3
Before you add or subtract numbers written in scientific notation, you must make the exponents
the same because the exponents determine the locations of the decimal points in the original
numbers. The decimal points must be aligned before you add two numbers. For numbers in
scientific notation, making the exponents the same aligns the decimal points.
Example 1: 5.4 x 103 + 6.2 x 102 = 5.4 x 103 + 0.62 x 103 = 6.02 x 103
OR 5.4 x 102 + 6.2 x 102 = 60.2 x 102 = 6.02 x 103
Example 2: 8.9 x 107 – 3.1 x 105 = 8.9 x 107 – 0.031 x 107 = 8.869 x 107
OR 890 x 105 – 3.1 x 105 = 886.9 x 105 = 8.869 x 107
3. Solve each problem, and express each answer in correct scientific notation.
a. (4.3 x 105) + (0.4 x 106) = __________________
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b. (7.0 x 104) + (6.85 x 106) = __________________
c. (5.4 x 105) + (3.4 x 106) = __________________
d. (6.0 x 104) – (-4.5 x 104) = __________________
e. (4.6 x 103) – (1.8 x 103) = __________________
f. (7.1 x 10-2) + (1.5 x 10-2) = __________________
Analysis
1. The diameter of a human hair is 0.000000000154 meter. Write this diameter in scientific
notation.
2. Describe the process you used to perform the conversion in question 1.
3. Calculate the frequency (in Hertz) of a gamma ray by dividing its speed by its
wavelength.
Speed = 3.0 x 108 m/sec
Wavelength = 1 x 10-12 meter
S
F
4. Create a sequence chain to describe the process you followed to solve question 3.
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Student Resource Sheet POW - 10
5. Add the masses of one oxygen atom and two hydrogen atoms to find the mass of a water
molecule.
Mass of one oxygen atom = 5.34 x 10-23 grams
Mass of one hydrogen atom = 1.67 x 10-24 grams
6. Describe the process you used to calculate your answer in question 5.
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