Question

1. convert 10 m to mm, using one of the conversion factors from question 4 above. show all your work. (4 points)

use the following equalities to derive conversion factors for the next two problems
2.54 cm = 1 inch
10 mm = 1 cm
100 cm = 1 m
1000 m = 1 km

1. how many mm are in 5 km? hint: use must use three of the equalities to make conversion factors to solve this problem. (5 points) show all your work! if conversion factors are not used, the correct answer is only worth 2 points.
2. larry needs to make as many 12 inch strips as possible from a 125 m roll of wire. how many can he make? hint: start with what you know... do you know how many strips, or how much wire you have? second: use dimensional analysis and conversion factors to arrive at your answer. (7 points) you must show all your work to receive full credit.

exam has 30 points possible: 7 = 1 15 = 2 20 = 3 25 = 3.7 >25 = 4
your score___________

Explanation:

Problem 7: Convert 10 m to mm

Step1: Convert meters to centimeters

We know that \( 100 \, \text{cm} = 1 \, \text{m} \), so to convert meters to centimeters, we multiply by 100.
\( 10 \, \text{m} \times \frac{100 \, \text{cm}}{1 \, \text{m}} = 1000 \, \text{cm} \)

Step2: Convert centimeters to millimeters

We know that \( 10 \, \text{mm} = 1 \, \text{cm} \), so to convert centimeters to millimeters, we multiply by 10.
\( 1000 \, \text{cm} \times \frac{10 \, \text{mm}}{1 \, \text{cm}} = 10000 \, \text{mm} \)

Step1: Convert kilometers to meters

We know that \( 1000 \, \text{m} = 1 \, \text{km} \), so to convert kilometers to meters, we multiply by 1000.
\( 5 \, \text{km} \times \frac{1000 \, \text{m}}{1 \, \text{km}} = 5000 \, \text{m} \)

Step2: Convert meters to centimeters

We know that \( 100 \, \text{cm} = 1 \, \text{m} \), so to convert meters to centimeters, we multiply by 100.
\( 5000 \, \text{m} \times \frac{100 \, \text{cm}}{1 \, \text{m}} = 500000 \, \text{cm} \)

Step3: Convert centimeters to millimeters

We know that \( 10 \, \text{mm} = 1 \, \text{cm} \), so to convert centimeters to millimeters, we multiply by 10.
\( 500000 \, \text{cm} \times \frac{10 \, \text{mm}}{1 \, \text{cm}} = 5000000 \, \text{mm} \)

Step1: Convert meters to centimeters

We know that \( 100 \, \text{cm} = 1 \, \text{m} \), so to convert meters to centimeters, we multiply by 100.
\( 125 \, \text{m} \times \frac{100 \, \text{cm}}{1 \, \text{m}} = 12500 \, \text{cm} \)

Step2: Convert centimeters to inches

We know that \( 2.54 \, \text{cm} = 1 \, \text{inch} \), so to convert centimeters to inches, we divide by 2.54 (or multiply by \( \frac{1 \, \text{inch}}{2.54 \, \text{cm}} \)).
\( 12500 \, \text{cm} \times \frac{1 \, \text{inch}}{2.54 \, \text{cm}} \approx 4921.26 \, \text{inches} \)

Step3: Find the number of 12 - inch strips

To find the number of 12 - inch strips, we divide the total length in inches by 12.
\( \frac{4921.26 \, \text{inches}}{12 \, \text{inches per strip}} \approx 410.105 \)

Since we can't have a fraction of a strip, we take the whole number part.

Answer:

\( 10000 \, \text{mm} \)

Problem 8: How many mm are in 5 km?