2.2: Answer Key

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1) No, it is not a proper answer; you do not know whether the professor meant homework problem number 20 or 20 homework problems. Twenty is a quantity and does not make sense without a unit

Middle Zeros: Zeros that appear between other nonzero digits are ALWAYS significant.

Leading Zero: Zeros that appear in front of all nonzero digits are NEVER significant.

Trailing Zero with a decimal point: Trailing zeros in a number with a decimal point are significant.

Trailing Zero without a decimal point: Trailing zero in a number without a decimal points are ambiguous.

5) A conversion factor is a fraction whose numerator and denominator. The system is set up will result in the units in numerator and denominator cancels leaving behind the desire unit.

Scientific Notation

7) a)1.0000 x 10⁸ b) 4.970 x 10^-4 c)3.001 x 10¹ d) 2.500 x 10³

9) a) 7.36350 x 10⁵b)3.9 x 10^-3 c) 2.500 x 10³ d) 4.78 x 10^-1

11) a) 86200 b) 0.0055 c) 0.00000102 d) 0.000000000603

13) a) 4700 b) 7.410 x 10³ c) 0.00093 d) 4.5 x 10^-3

15) a) 840,000 b) 5.13 x 10² c) 0.00000630 d) 2.50 x 10^-1

Significant Figures

17) a) 6.46 cm b) 33.5 mL c) 6.28 mL

19) a) 6 SF all non-zeros are significant

all leading zeros are not significant

all middle zeros are significant

all trailing zeros with a decimal point are significant

b) 6 SF all non-zeros are significant

all middle zeros are significant

c) 6 SF all non-zeros are significant

all trailing zeros with a decimal point are significant

d) 3 SF all non-zeros are significant

all leading zeros are not significant

21) a) 6 SF all non-zeros are significant

all leading zeros are not significant

all middle zeros are significant

all trailing zeros with a decimal point are significant

b) 6 SF all non-zeros are significant

all middle zeros are significant

c) 6 SF all non-zeros are significant

all trailing zeros with a decimal point are significant

d) 3 SF all non-zeros are significant

all leading zeros are not significant

23) a) 5 SF b) 4 SF c) 4 SF d) 4 SF

Rounding

25) a) 24.6 b) 0.342 c) 4.35 x 10⁴ d) 7.00 x 10³

27) a) 5.65 x 10¹ b) 8.90 x 10⁸ c) 1.00 x 10⁶ d) 0.984

29) a) incorrect; 4.56 x 10³ b) incorrect; 8.51 x 10³ c) correct d) incorrect; 0.0531

31) b) 216.4, 2.2 x 10², 2 x 10²

c) 0.3668, 0.37, 0.4

d) 0.008889, 0.0089, 0.009

33) b) 654.9, 6.5 x 10², 7 x 10²

c) 0.7513, 0.75, 0.8

d) 0.007778, 0.0078, 0.008

Significant Figures in Calculations

35) a) 4986.2 b) 1.1 c) correct d) 0.154

37) a) 55 b) correct c) 0.86 d) 0.001

39) a) 48 b) 2597 c) correct d) 0.009

41) a) correct b) 6.220 x 10³ c) 136 d) 4.5315

Unit Conversion

43) a) 1.000 x 10⁶ mg b) 6.981 x 10^-6 m c) 1.5 x 10^-2 L d) 3.45 x 10³ mm

45) a) 3.4 x 10⁴g b) 7.53934 x 10^-6 m c) 3.6 x 10³ cL d) 1.09 x 10³ mm

47) a) 4.76 x 10⁴ mm b) 6.71 kg c) 0.248 mi d) 30.5 cm

49)

m	km	mm	nm	pm
6.02 x10^-5 m	6.02 x 10^-8 km	6.02 x 10^-2 mm	6.02 x 10⁴nm	6.02 x 10⁷ pm
2.53 x 10^-11 m	2.53 x 10^-14 km	2.53 x 10^-8 mm	0.0253 nm	25.3 pm
2.25 x 10^-7 m	2.25 x 10^-10 km	0.000225 mm	225 nm	2.25 x 10⁵ pm
8.22 m	8.22 x 10^-3 km	8.22 x 10³ mm	8.22 x 10⁹ nm	8.22 x 10¹² pm
4.20 x 10² m	0.42	4.2 x 10⁵ mm	4.2 x 10¹¹ nm	4.2 x 10¹⁴ pm

51)

m	km	mm	nm	pm
1.88 x10^-5 s	1.88 x 10^-8 km	1.88 x 10^-2 mm	1.88 x 10⁴nm	1.88 x 10⁷ pm
1.43 x 10^-11 m	1.43 x 10^-14 km	1.43 x 10^-8 mm	0.0143 nm	14.3 pm
3.65 x 10^-7 m	3.65 x 10^-10 km	0.000365 mm	365 nm	6.65 x 10⁶ pm
6.34 m	6.34 x 10^-3 km	6.34 x 10³ mm	6.34 x 10⁹ nm	6.34 x 10⁹ pm
6.9 x 10² m	6.9 km	6.9 x 10⁵ mm	6.9 x 10⁸ nm	6.9 x 10¹¹ pm

Unit Raised to a Power

53) a) 3.5 x 10² in² b) 2.2 x 10¹ ft² c) 3.1 yd³

55) a) 5.33 x 10³ in² b) 3.44 x 10⁶ mm c) 3.44 x 10^-6 km

57) a) 2.09 x 10⁴ in² b) 1.35 x 10⁷ mm² c) 1.35 x 10^-5 km

Density

59) 11.33 g/mL, yes

61) a) 2.34 x 10³ g b) 69.1 cm³

63) a) 6.894 x 10³ g b) 70.76 cm³

Cumulative Problems

65) $63.54

67) 6.52 x 10³ h

69) 32.5 lb of apples