Question

dimensional analysis problems #1
convert the following problems. show all your work! box your final answer.
english to metric conversions:
1.) how many inches are there in 13 centimeters? ( \frac{13,\text{cm} \times 1,\text{inch}}{2.54,\text{cm}} = 5.1,\text{inches} )
2.) how many pounds are there in 2300 grams? ( \frac{2300,\text{g} \times 1,\text{lb}}{454,\text{g}} = 5.1 \times 10^0,\text{lb} )
3.) how many quarts are there in 18.7 liters? ( \frac{18.7,\text{l} \times 1.06,\text{qt}}{1,\text{l}} = 1.9 \times 10^1,\text{qt} )
4.) how many miles are there in 25 kilometers? ( \frac{25,\text{km} \times \text{m}}{\text{km}} ) (incomplete)
5.) how many meters are there in 1500 inches? ( \frac{1500,\text{inch} \times 2.54,\text{cm}}{1,\text{inch}} \times \frac{1,\text{m}}{100,\text{cm}} = 3.8 \times 10^1,\text{m} )
6.) how many mg are there in 240 pounds? ( \frac{240,\text{lb} \times \text{mg}}{\text{lb}} ) (incomplete)
7.) how many ml are there in 17.2 quarts? ( \frac{17.2,\text{qt} \times \text{ml}}{\text{qt}} ) (incomplete)
8.) how many meters are there in 13.1 miles? ( \frac{13.1,\text{mi} \times \text{meters}}{\text{miles}} ) (incomplete)

Explanation:

Problem 1: How many inches are there in 13 centimeters?

Step1: Recall the conversion factor

We know that 1 inch = 2.54 centimeters. So to convert centimeters to inches, we use the formula: inches = centimeters / 2.54.

Step2: Substitute the value

We have 13 centimeters. So inches = \( \frac{13}{2.54} \approx 5.12 \)

Step1: Recall the conversion factor

1 pound = 453.592 grams (more accurately, but often 454 g is used for approximation). The formula to convert grams to pounds is: pounds = grams / 453.592.

Step2: Substitute the value

For 2300 grams, pounds = \( \frac{2300}{453.592}\approx5.07 \)

Step1: Recall the conversion factor

1 liter = 1.05668821 quarts. The formula to convert liters to quarts is: quarts = liters × 1.05668821.

Step2: Substitute the value

For 18.7 liters, quarts = \( 18.7\times1.05668821\approx19.76 \)

Answer:

\boxed{5.12} (approximate value, more precisely \( \frac{13}{2.54}\approx5.118 \))

Problem 2: How many pounds are there in 2300 grams?