David Lauren
Izabela Wisniewska
Solution Set
1) A. 0.6 bones = 0.6 bones × 54.6 cm = 32.76 cm = 3.276 cm × 10 to the 1st
1 bone
B. 600 cm = 600 cm × 1 bone ≈10.9 bones = 1.09 × 10 to the 1st
54.6 cm
C. First we should convert 10 bones into centimeters. Then we will convert the equivalent of
10 bones inches and then into sticks.
First conversion:
10 bones = 10 bones × 54.6 cm = 546 cm
1 bone
Second conversion:
546 cm = 546 cm × 1 in
≈ 215 in
2.54 cm
Third conversion:
215 in = 215 in × 1 stick ≈ 9.4 sticks × 10 to the 0th
22.875 in
D. From the previous conclusion: 10 bones = 9.4 sticks
10 sticks = 10 sticks × 10 bones ≈ 10.6 bones = 1.06 × 10 to the 1st
9.4 sticks
E. First we should convert 5,280 ft into cm. Then convert cm into inches.
5,280 ft = 5,280 ft × 30.5 cm = 161,040 cm
1 ft
161,040 cm = 161,040 cm × 1 km = 1.6104 km × 10 to the 0th
100,000 cm
2) 220 mm = 220 mm × 1 cm = 22 cm
10 mm
220 mm = 220 mm × 1 meter = 0.22 meters × 10 to the 0th
1,000 mm
3) Volume A = 6” * 6” * 6” in inches cubed.
= 216 in³
Volume B = 6 cm * 6 cm * 6 cm
=216 cm³
Volume A has a larger volume.
The ratio of Volume A to Volume B is 16.4 to 1. This ratio is not equal to 2.54 because we are
dealing with volume. 2.54 only applies to the rule that you are converting from 1 inch to 1
centimeter. Dealing with volume automatically changes 2.54 to cubing the original ratio (2.54)
which makes it 16.387 which rounds up to 16.4 or just 16.
4) First, we have to establish a factor label between ft squared and cm squared.
1 ft squared = 30.5 cm × 30.5 cm × 30.50 cm = 930.25 cm squared.
1,200 ft squared = 1,200 ft squared × 930.25 cm squared = 1,116,300 cm squared
1 ft squared
1 m = 100 cm, 1 m squared = 100 cm × 100 cm = 10,000 cm squared.
1,200 ft squared =
111.63 cm squared = 111.63 cm squared × 1m squared
= 0.011163 m squared =
10,000 cm squared
1.1163m squared × 10 to the negative 2nd
5) 1 in cubed = 1 in × 1 in × 1 in
1 in cubed = 2.54 cm × 2.54 cm × 2.54 cm = 16.387 cm cubed
3000 in cubed = 3000 in cubed × 16.387 cm cubed = 49,161cm cubed
1 in cubed
1 in cubed = 0.0254 m × 0.0254 m × 0.0254 m = 0.000016 m cubed
3000 in cubed = 3000in cubed × 0.000016 m cubed = 0.048 m cubed = 4.8 m cubed × 10 to
1 in cubed
the negative 2nd
6) 6000 ft³ = 23 × 10 ֿ¹ in³ 1ft³ = 2568 in
3.0 × 10³ = 2.307
2.6 ×10³
The ratio is 2,586 inches³ to 1 ft³. This ratio is 2568 rather than 12 because it is cubed. Cubing
12 makes it to ft³. Cubing is used for volume so instead of 12 it would be 2586.
7) Every minute the message appears 10 times
Every hour it appears 600 times
Every day it appears (600 × 24) 14,400 times
In the week the message appears (14,400 × 7) 100,800 times