Measurement and Problem Solving
1) Circle the letter of each sentence that is
true about numbers expressed in
scientific notation.
a. A number expressed in scientific
notation is written as the product of a
coefficient and a power of 10.
b. The power of 10 is called the
exponent
c. The coefficient is always a number
greater than or equal to one and less
than ten.
d. For numbers less than one, the
exponent is positive
2) Circle the letter of each sentence that is
true about significant figures.
a. All nonzero digits in a measurement
are assumed to be significant
b. Zeros appearing between nonzero
digits are never significant
c. Final zeros to the right of the decimal
point are always significant
d. Zeros acting as placeholders in front
of nonzero digits to the right of the
decimal are not significant.
e. Zeros to the left of the decimal point
that act as placeholders are not
significant.
3) Use the following equation to answer a- 4) Use the following equation below to
d.
answer a-d:
0.00076 = 7.6 x 10?
76 000 000 =7.6 x 10?
a. How many places did the decimal
a. What direction did the decimal point
point move? 4 In which direction? right
move? left
b. To make the equation true, does 7.6
b. To make a true equation, does 7.6
need to be multiplied by a number
need to be multiplied by a number
greater than one?no, less than 1
greater than one or less than one?
c. Is the exponent for 10 positive or
greater
negative? negative
c. Is the exponent for 10 positive or
d. What exponent makes the equation
negative? positive
true? -4
d. What exponent makes the equation
true? +7
5) What is the meaning of “accepted
6) The accepted value of a length
value” with respect to an experimental
measurement is 200cm, and the
measurement? Value that can be looked
experimental value is 198cm. Circle
up or verified; i.e. the “right” answer
the letter of the value that shows the
percent error of this measurement.
a. 2% b. –2% c. 1% d. –1%
7) In the measurement 43.52 cm, which
8) How many significant figures are in the
digit is the most uncertain?
measurement 6.80 m?
a. 4
b. 3
c. 5
d. 2
a. 2
b. 3
c. 4
d. 5
Measurement and Problem Solving
9) Circle the letter of the answer in which
503,000,000 is written correctly in
scientific notation
a. 5.03 x 10-8
b. 503 x 106
c. 5.03 x 108
d. 503 million
10) Round the following as indicated.
a. 65.145 m to 4 significant digits 65.15
b. 100.1 C to 1 significant digit 100 C
c. 155 cm to 2 significant digits 160
d. 0.000718 to 2 significant digits
0.00072
e. 65.145 m to 3 significant digits 65.1
11) Is the following sentence true or false?
An answer is as precise as the most
precise measurement from which it was
calculated False, it is as precise as the
least precise from which it was
calculated
12) All metric units are based on multiples
of what number? 10
13) What is a derived unit? Unit that
requires two directly measured units to
be manipulated Give an example mph
14) List SI Base unit, the Symbol and the Commonly used Lab unit for the following
measurements:
Length meter
Mass kg
Temperature K
Time s
Volume L (liquid) cm3 (solid)
Density g/ml or g/cm3
Using Significant Figures
Identify the number of significant digits in the following quantities.
1. 3.58 g 3
2. 804.58 kg 5
3. 14.809 cm 4
4. 0.007832 cg 4
5. 107.334 km 6
6. 130 004.5 mm 7
7. 0.0004898 mm 4
8. 250.0 km 4
9. 3000 cm 1
10. 14.380 s 5
11. 307 cm 3
12. 0.00450 cm 3
Measurement and Problem Solving
Solve each of the following and express the answer in the correct number of
significant digits (when appropriate, use scientific notation)
13. 4.52 g + 13.8 g + 7.9483 g
14. (48.4398 m)(1.52 m) 73.6 m2
26.3g
15. 82.5 cm + 13.56 cm 96.1 cm
16. 13.80 cm – 6.0741 cm 7.73 cm
17. 16.8892 km + 3.5 km 20.4 km
18. 8.472 cg – 1.440 cg 7.032 cg
19. 45.456 g + 3.56 g 49.02 g
20. 30 s – 1.442 s 28 s
21. 106.22 mm + 80.0 mm 186.2
mm
23. 30.44 kg + 3.9422 kg 34.38 kg
22. 54.00 g – 30.220 g 23.78 g
25. (8.4 cm)(3.58 cm) 3.0 x 101
26. 35.068 km3 ÷ 5.7 km
5.2 km2
28. 85.0869 m2 ÷ 9.0049 m
9.4490m
27. (1.075m)(2.0m) 2.2 m2
24. 1.45050 kg – 0.00667 kg
1.44383 kg
29. (3.0899 mm)(22.4 mm) 69.2
mm2
30. 0.00826 cm2 ÷ 0.00033 cm
25cm
31. (0.00457 cm)(0.18 cm) 8.2 x
10-4 cm2
32. 0.005600 mm2 ÷ 0.200 m
0.0280 m
33. (10.00 m)(84.767 m) 847.7 m2
34. 3.4500 cm2 ÷ 460 cm
0.0075cm
Scientific Calculations
Express the following in Scientific Notation
1. 700
7.0 x 102
6. 27 906
2.7906 x 104
2. 3 958
3.958 x 103
7. 1.56
1.56 x 100
6
3. 2 245 000
2.245 x 10
8. 0.0235
2.35 x 10-2
4. 98 000 000 000
9.8 x 1010
9. 0.000 79
7.9 x 10-4
-2
5. 0.097
9.7 x 10
10. 1 900
1.9 x 103
Express the following in Standard Form
11. 2.7 x 102
12. 5.9 x 10-3
15. 1.00 x 10-4
0.000100
16. 6.998714 x
0.0000006998714
10-7
13. 9.78 x 100
9.78
17. 1.9 z 101
19
14. 4.771 x 105
477100
18. 2.7 x 10-6
0.0000027
Calculate the following and express in the correct number of significant digits
19. 2.9 x 103
.097
20. (5.5 x102)(1.58x105)(0.0209) 1.7 x 106
3 x 104
21. 189 x 901
2,36 x
22. (7.654 x 10-10)(21)(987)
8,9 x 10-31
7.21 x 10-4
108
(29.5)(6.02 x 1023)
270
0.0059
Measurement and Problem Solving
23. (28.0)(0.082)
770
24. (976.5)(5.98)(123.45)
5.8 x 106
0.003
(0.047) (2.66)
25.
2.3 x
26. 4.2 x 109
4.3 x 107
5
11
19
(7.2x10 )(8.92x10 ) 10
98
(4.33 x10-2)(6.0
x10-1)
27. (0.002)(1.90)(24)
9.2 x 10- 28. 23 x 19
440
5
(987.20)
29. 159 x 1.9
3.0 x 102 30. (1.4 x 104)(2 x 10-6)
0.03
0.7
0.062
31. 6.54  9
32. .00278  .045
33. 39.8 – 1.297
38.5
34. 89 x 0.020
1.8
35. 2.3 + 129 + 57
188
2.6 x 103
36. 238  .091
Determine the number of significant digits
37. 6.021 g 4
38. 40.07 cm 4
39. 49.0 in 3
40. 0.024 in 2
41. 120 m 2
42. 0.0027 g 2
43. 20.00 g 4
44. 8000 in 1
45. 3.900 m 4
46. 7500.0 cg 5 47. .070 km 2
48. 139 cm 3
3
-4
49. 1.68 x 10 3
50. 2.0 x 10 2
51. 2000 L 1
52. 0.01001 m 4
Round each of the following to 3 significant digits
53. 8.838
54. 1997 2.00 x 55. 0.02345
56. 1000 1.00 x 103
103
.0235
23
57. 6.024 x 10
58. 1995.6 2. X 59. 29.4949
60. .00479 .00479
6.02 x 1023
103
29.5
61. 25.051 25.1
62. 973.44 973
63. 1.3449
64. 1.204 x 102 1,20 x
1.34
102