Problem Solutions - Conversions

1. CHM 111 Conversions (Solutions) CH1 Math Skills Toolbox
Useful Conversions: 4 qts = 1 gal; 0.946 L = 1 qt; 1 mile = 5280 ft; 1 ft = 30.5 cm
39.4 in = 1 m; 1 lb = 0.454 kg 1 in = 2.54 cm, 1 m = 102 cm
1 m = 1012 pm; 1 m = 106 µm; 1 m = 109 nm; 1 km = 103 m
1 mL = 1 cm3; °C + 273 = K K − 273 = °C
Please note that METRIC conversions will NOT be given on exams or quizzes, including
temperature conversions between C and K.
1. a) Convert 25 ºC to Kelvin (K).
°C + 273 = K
25 °C+ 273 = 298 K
b) Convert 35 ºC to Kelvin (K).
°C + 273 = K
35 °C + 273 = 238 K
c) Convert 154 ºC to Kelvin (K).
°C + 273 = K
154 °C+ 273 = 119 K
d) Convert 500 K to degrees Celsius (ºC).
K − 273 = °C
500 K − 273 = 227 °C
e) Convert 215 K to degrees Celsius (ºC).
K − 273 = °C
215 K − 273 = 58 °C
2. a) Convert 1000 gallons to quarts
1000 gallons (
4 qts
1 gallon
) = 4000 qts
b) Convert 150. quarts to gallons
150 qts (
1 gal
4 qts
) = 37.5 gal

2. CHM 111 Conversions (Solutions) CH1 Math Skills Toolbox
c) Convert 120 miles to feet
120 miles (
5280 ft
1 mile
) = 633600 feet or 6.3 105
feet
d) Convert 753 feet to miles
753 ft (
1 mile
5280 ft
) = 0.143 miles
3. Convert the following quantities:
a) Convert 100.0 nm to m and write your answer in scientific notation.
100.0 nm(
1 m
1 × 109nm
) = 1.0 × 10−7
m
b) Convert 3.0 m to nm and write your answer in scientific notation.
3.0 m(
1 × 109
nm
1 m
) = 3.0 × 109
nm
c) Convert 356.0 m to nm and write your answer in scientific notation.
356.0 m(
1 × 109
nm
1 m
) = 3.560 × 1011
nm
d) Convert 4.36 107 m to nm and write your answer in scientific notation.
4.36 ×10
-7
m(
1 × 109
nm
1 m
) = 4.36 × 102
nm
e) Convert 233 m to cm and write your answer in scientific notation.
233 m(
1 × 102
cm
1 m
) = 2.33 × 104
cm
f) Convert 2.76 cm to m and write your answer in scientific notation.
2.76 cm(
1 m
1 × 102cm
) = 2.76 × 10−2
m

3. CHM 111 Conversions (Solutions) CH1 Math Skills Toolbox
g) Convert 2.76 pm to m and write your answer in scientific notation.
2.76 pm(
1 m
1 × 1012pm
) = 2.76 × 10−12
m
h) Convert 211 m to pm and write your answer in scientific notation.
211 m(
1 × 1012
pm
1 m
) = 2.11 × 1014
pm
i) Convert 4.34 µm to m and write your answer in scientific notation.
4.34 µm(
1 m
1 × 106µm
) = 4.34 × 10−6
m
j) Convert 364.7 µm to m and write your answer in scientific notation.
364.7 µm(
1 m
1 × 106µm
) = 3.647 × 10−4
m
k) Convert 153 m to µm and write your answer in scientific notation.
153 m (
1 × 106
µm
1 m
) = 1.53 × 108
µm
4. Use the following conversion factors to covert the quantities below. (Think about how the set
up for the problem changed based on the conversion factor used (i.e., compare to problem #3).
Compare your answers to those in problem #3.))
1  109 m = 1 nm; 1  1012 m = 1 pm; 1  102 m = 1 cm; 1  106 m = 1 µm
a) Convert 100.0 nm to m and write your answer in scientific notation.
100.0 nm(
1 × 109
m
1 nm
) = 1.000 × 10−7
m
b) Convert 356.0 m to nm and write your answer in scientific notation.
356.0 m (
1 nm
1 × 109m
) = 3.560 × 1011
nm
c) Convert 4.36 107 m to nm and write your answer in scientific notation.
4.36 × 10
-7
m(
1 nm
1 × 109
m
) = 436nm = 4.36 × 102
nm

4. CHM 111 Conversions (Solutions) CH1 Math Skills Toolbox
d) Convert 233 m to cm and write your answer in scientific notation.
233 m(
1 cm
1 × 102m
) = 2.33 × 104
cm
e) Convert 2.76 cm to m and write your answer in scientific notation.
2.76 cm(
1 × 102
m
1 cm
) = 2.76 × 10−2
m
f) Convert 2.76 pm to m and write your answer in scientific notation.
2.76 pm (
1 × 1012
m
1 pm
) = 2.76 × 10−12
m
g) Convert 211 m to pm and write your answer in scientific notation.
211 m(
1 pm
1 × 1012 m
) = 2.11 × 1014
pm
h) Convert 4.34 µm to m and write your answer in scientific notation.
4.34 µm(
1 × 106
m
1 µm
) = 4.34 × 10−6
m
5. a) Convert 125 mL to cm3.
125 mL (
1 cm3
1 mL
) = 125 cm3
b) Convert 2.45 cm3 to mL.
2.45 cm3
(
1 mL
1 cm3
) = 2.45 mL