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Cadiz 13-14
Physics
Name _________________________
Date ______________Section ______
Extra Practice Units Calculations and Math Operations
Work problems that you may have difficulty with first.
Dimension
Length
Volume
Mass
Temperature
Time
Unit
Symbol
Quantities of each unit are related by powers of 10. Prefixes tell you how the units are related. Write the
symbol and meaning of the prefixes below:
Prefix
giga
Mega
kilo
hecto
deka
deci
centi
milli
micro
nano
1.
2.
3.
4.
5.
6.
7.
8.
1.
Symbol
How many in a unit
1g=
_____ kg
1 kg = _____ g
1 m = _____ km
1 km = _____ m
1 m = _____ cm
1 cm = _____ m
1 L = _____ mL
1 mL = _____ L
If you need to multiply or divide numbers, the number of significant figures in the answer must be the same
as the number of significant figures in the measurement with the least significant figures. For example:
5.61 x 2.0 = 11. Try:
a. 35.78 / 4.4
b. 105 x 3.4
c. 6.798 x 9.25
2.
Meaning
d.
e.
f.
4.27 / 5.5
6.789 x 1.0
5.0 / 1.546
If you need to add or subtract numbers, the number of decimal places in the answer cannot be greater than
the least number of decimal places in the measurements. For example: 1.536 + 2.0 = 3.5. Try:
a.
b.
c.
d.
e.
f.
4.5 + 8.99
0.004 + 0.1
49 + 1.1
99.5 – 1.4
224.44 – 1.678
97.34 – 55.1
1.
Express the following in scientific notation:
a.
50,000 grains of sand =
b.
0.00006 mm =
c.
(7.6 x 10-4m) x (1.5 x 107m) =
d.
0.00053 / 29 =
e.
How far does light travel in 8.64 x 104 seconds (speed of light is 3.0 x 108m/s)
2.
How many significant figures are in 14.99876?
3.
4.
Calculate 43.5 + 6.779 =
Calculate 43.5 x 6.779 =
What is the density of a brick with mass 45.9 g and volume of 34.56 cubic centimeters?
5.
Convert 46 degrees Fahrenheit into Celsius.
6.
Compare the temperature of the human body in degrees Fahrenheit and Celsius.
Scientific notation presents an easier way to write very large and very small numbers. Instead of writing
67,000,000,000, we use a power notation. We write 6.7 x 10 10. 6.7 is the coefficient – always a number
between 1 and 10. 10 is the base. The superscript 10 means that the decimal point is 10 spots to the right.
Instead of writing 0.00000000056, we write 5.6 x 10 -10. The superscript -10 means that the decimal point is
10 spots to the left. Complete the following:
Number
45,000
378,000
6,890,000
0.05
0.0089
0.00071
Scientific notation
5.6 x 109
3.25 x 106
1.322 x 103
1.4 x 10-5
9.24 x 10-8
7. A mountain’s elevation above sea level is 9.8 x 10 3 m. Write the elevation in standard notation
8. The eye’s retina contains about 130 million light-sensitive cells. How many is that in scientific
notation?
9. A mulberry silkworm can spin a single thread that measures up to 1300 m in length. How long it that in
scientific notation?
Multiplying and Dividing: When you multiply in scientific notation, you multiply the coefficients and
add the exponents. For example, (1.1 x 10 3) x (5.1 x 104) = 5.6 x 107. When you divide in scientific
notation, you divide the coefficients and subtract the exponents. For example, (5.1 x 10 6) / (1.1 x 103) =
(4.6 x 103). If the coefficient of your answer is not between 1 and 10, you need to alter it to be in scientific
notation. Try the following:
1.
(4.7 x 105) x (2.1 x 104) =
2.
(3.2 x 104) x (3.2 x 107) =
3.
(5.6 x 10-4) x (1.3 x 10-5) =
4.
(8.7 x 103) x (5.1 x 104) =
5.
(6.4 x 109) / (2.0 x 104) =
6.
(9.1 x 103) / (3.2 x 106) =
7.
(8.4 x 10-3) / (9.8 x 10-2) =
8.
(1.3 x 10-9) / (3.4 x 10-11) =
9.
A rectangular lake has a width of 6000 m and a length of 1.2 x 10 4 m. What is the area of the lake in
scientific notation?
10. One surface of a cut gemstone is rectangular in shape. It is 0.0002 m wide and has an area of 0.000006
m2. How long is the surface in scientific notation?
Adding and Subtracting: When you add or subtract in scientific notation, the coefficients must be raised
to the same power of 10. If they are not, convert them first. Add the coefficients together and keep the
same exponent. If the coefficient of your answer is not between 1 and 10, you need to alter it to be in
scientific notation. Try the following:
1.
2.
3.
4.
(1.3 x 104) + (4.4 x 104) =
(6.2 x 105) – (1.5 x 105) =
(9.8 x 106) – (8.9 x 105) =
(5.6 x 107) – (4.4 x 108) =
Convert the following> You MUST use units and factor label format taught in class
1.
35dm to meters
2.
4 hours to seconds
3.
4 hours to days.
4.
4 hours to years
5.
55 miles per hour to meters per second
6.
2.5 tons per year to grams per second
7.
5 Liters per second to gallons per minute