Name: ____________________________Date: ________________
Physics 20
Course Introduction
Scientific Notation:
Example: Convert 4638600000 into scientific notation
4.638600000 x 10 9
Example: Convert 0.00000475 into scientific notation
4.75 x 10 –6
Note: A positive exponent indicates a number greater than 1 and a negative exponent
indicates a number smaller than 1.
Example: Calculate the following.
a)
(4.50 x 103) (9.25 x 105) =
b)
(3.36 x 10–7) (5.50 x 104) =
c)
7.73 x 10 4
8.24 x 10 5

Significant Digits









The number 354 has 3 significant digits.
The number 35.4 has 3 significant digits.
The number 52 has ____ significant digits.
The number 3.54 x 104 has ____ significant digits.
The number 0.354 has ____ significant digits.
The number 0.00354 has ____ significant digits.
The number 35400 has ____ significant digits.
The number 0.03540 has ____ significant digits.
The number 0.00350040 has ____ significant digits.
Rules For Multiplying and Dividing

When multiplying or dividing, _________________________________________________
_____________________________________________.
Physics 20 - Introduction
1
Name: ____________________________Date: ________________
Example: 3.3 x 0.134 =

The answer is 0.4422 but since the least number of significant digits being used is “2”, the
answer must be rounded off to “2” digits.
Example:
3746 x 0.120 =

The calculator answer is 449.52, but since the least number of significant digits is “3”, the
answer is rounded off to 3 digits.
Example:



3746 x 120 =
The calculator answer is 449520, but since the least number of significant digits is “3”, the
answer is rounded off to 3 digits.
The answer must be about 450000, but that number has 6 digits.
In this case, use scientific notation.
Answer:
a)
(5.55 x 109 )(2.34 x 105 )
(2.58 x 104 )(7.27 x 105 )
b)
(3.52 x 103 )(9.11 x 105 )
(1.48 x 104 )(2.33 x 105 )

x
(7.12 x 106 )(2.34 x 105 )
(8.22 x 10 4 )(4.71 x 105 )
=
=
Rules for Adding and Subtracting
 Perform the calculation in your calculator.
 _________________________________________________________________________.
 _________________________________________________________________________.
 ____________________________________.
Example:
34.65 + 4.235 =


Calculator answer is 38.885.
The least number of place holding after the decimal is “2”.
Answer: 38.89
Example:
1356.245 + 245.33 – 0.0001 =
Note: When adding mixtures of units, _________________________________.
When calculating long series of numbers,_________________________________.
Physics 20 - Introduction
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Name: ____________________________Date: ________________
Order of Operations:
1. Algebra [ ans: a) -76 b) 18 c)-13 d) -36 e) 74 f) 4 ]
b) 6 + 4[12  2 - (-3)(-1)]
a)-27 + 6(-9) +5
c) (-6)2 – (-7)2
where x = -2, y = 3 and z = -1
d) 3 x 2 yz
e) 7 xyz  4 y 2  x 2
f)
5 x  2 y xy

xz
z
2. Solve the following using calculators, using correct number of significant digits and
convert to scientific notation.
a) 0.003 × 2157 = ___________________ =_____________________
b) 1.5  0.2 = ___________________ =___________________
c)
147.5× 2.9×0.3000 = ___________________ =_____________________
d) 3.56+8.3+5.0+0.300 = _______________= ______________
e)
(3.75 105 )( 4.255 10 1 )
= _______________= ______________
(4.110 7 )(0.160000888)
f)
(4.13 105  6.14 105 )(8.13 10 11 )
= _______________= ______________
(7.14 10 4 )(6.3110 2 )
g)
(1.83  106 ) 2 (8.13  10 4  6.14  10 4 )
= _______________= ______________
1.31 103
3. Convert to scientific notation with correct significant digits.
a) 401.000 = ______________
b)603.4 = ____________________
c) 4.1 cm + 5.2 mm +0.43 cm = ________________________ = ______________
d) 5.6 m + 3.8 cm + 5.72 cm = _________________________ = ______________
Physics 20 - Introduction
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Name: ____________________________Date: ________________
e) 6.31 L + 3.4 L + 5.73 mL = __________________________ = ______________
f) 4.7 cm +5.3 mm + 2.1 m = __________________________ = ______________
g) 5.63×103 + 2.1×103 = _____________________ = _______________
4. Unit Conversion: Some the more common conversions (refer to appendix SR 7)
1 mile = 1.6 km
1 m = 3.281 ft
1 m = 1.094 yd
1 m = 39.37 in
1 cm = 0.3937 in
1 ft = 0.333 yd
1 N = 0.2248 lb
Complete the following conversions. Show your work.
a) 225 cm = _______________________m
b) 55.7 m = _______________________ cm
c) 325 mm = _______________________ km
d) 200 mm =_______________________ cm
e) 20 s =_______________________ min
f) 450 min = _______________________ h
Physics 20 - Introduction
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Name: ____________________________Date: ________________
g) 35 h = _______________________s
l) 25 m/s = _______________________km/h
n) 125 kg/m3 =_______________________ g/cm3
o) 225 cm =_______________________ m
q) 325 mi =_______________________ km
s) 20 a =_______________________s
Compute, expressing your answer in scientific notation to the correct number of significant digits:
a) 10.41 g + 12 g + 27.8 g + 253 g = ___________________ g
b) (23.6 m/s) (26 s) = ______________________m
c) 459 g – 0.24 kg = ____________________ kg
d)
3.7456 N
= _______________________N/m2
2.15 m2
Physics 20 - Introduction
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Name: ____________________________Date: ________________
e)
3.51 x 104 m
= ____________________ m/s2
(2.19 x 102 s)(5.62 x 104 s)
f) (6.49 x 10-5 km/h) (2.48 x 10-4 h) = _____________________ km
Using your calculator, solve for the following:
a)
245 x 543 x 2435 = ______________________________
b)
0.345 x 0.003284 x 12.4 = ____________________________
Express the answer to each calculation in properly rounded form.
1. Find the area of a rectangular region 4.125 m long and 3.1 m wide.
2. What is the perimeter of a triangle with sides 2.1 cm, 3.04 cm, and 5 cm?
3. A piggy bank contains 31 quarters. What is the total value of the money in the bank?
4. A car travels 143.6 km in 1.05 hours. At this rate, how far will the car travel in 3 .4 hours?
5. An opened box of candy is marked “net weight 65 9.” The mass of candy in the box is
measured as 57.265 g. How much candy has been eaten?
Physics 20 - Introduction
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Name: ____________________________Date: ________________
6. Density is found from the formula, density 
mass
. What is the density of a cube of
volume
platinum with mass 9.070 g, if it measures 0.75 cm on a side?
7. Perform the following mathematical operations, expressing the answers to the correct number
of significant digits.
(a) 463.66 + 29.2 + 0.17= ____________________
(b) 426.66 – 39.2 = ____________________
(c) (2.6)(42.2) = ____________________
(d) (65)(0.041)(325) = ____________________
(e) (0.0060)(26)(55.1) = ____________________
(f) 3.265/2.35 = ____________________
(g)
= ____________________
(h) 5.6 + 2.34 + 5.698 – 8.23 = ____________________
8. If a gold atom is considered to be a cube with sides 2.5 x 10-9 m, in how many gold atoms
could stack on top of one another in gold foil with a thickness of 1.0 x 10-7 m?
9. On the average, 1.0 kg of aluminum consists of 2.2 x 102 atoms. How many atoms would
there be in a block of aluminum 10 cm by 1.2 cm by 15.6 cm, if the density of aluminum is 2.7
g/cm3.
Physics 20 - Introduction
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Name: ____________________________Date: ________________
Transposition of Formulae:
Rearrange each of the formulae given below so that the variable in parenthesis is the subject of
the equation.
e.g. F  ma (m)
answer m 
F
a
EA
, (d)
d
1.
F  ma , (a)
2.
C
3.
P1 P2
, (A2)

A1 A2
4.
P  A  hpg , (g)
5.
V2  V1  at , (V1)
6.
V2  V1  at , (a)
7.
F
8.
V  r 2 , (ω)
9.
T  2
10.
V2  V1  2as , (V1)
GmM
, (r)
r2
L
, (L)
g
Physics 20 - Introduction
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2
2