unit: dimensional analysis
\one, two, and more step problems\
directions: use dimensional analysis to perform the following calculations. show all
work and include units.
1. change 0.00765 kl into ml.
2. a chemistry student’s height is measured at 68.5 inches. how tall is the student in cm?
3. this same chemistry student has a weight of 155 lbs. what is the student’s weight in
grams? (16oz=1lb, 1 oz = 28.34 g)
4. a homerun in a baseball game was measured at 450 feet. how many meters is this equal
to?
5. mount everest is approximately 8,000 meters high. how many miles high is mount everest?

Question

Accepted Answer

### Problem 1:
# Explanation:
## Step1: Recall unit conversion for volume. $1\space kL = 1000\space L$ and $1\space L = 1000\space mL$, so $1\space kL = 1000\times1000 = 10^6\space mL$.
$0.00765\space kL\times\frac{10^6\space mL}{1\space kL}$
## Step2: Multiply the numbers. $0.00765\times10^6 = 7650$.
# Answer: $7650\space mL$

### Problem 2:
# Explanation:
## Step1: Recall the conversion factor: $1\space inch = 2.54\space cm$.
$68.5\space inches\times\frac{2.54\space cm}{1\space inch}$
## Step2: Multiply $68.5\times2.54$. $68.5\times2.54 = 174.0$ (approx, more accurately $68.5\times2.54 = 173.99\approx174.0$).
# Answer: $174.0\space cm$ (or $173.99\space cm$)

### Problem 3:
# Explanation:
## Step1: First convert pounds to ounces. $1\space lb = 16\space oz$, so $155\space lbs\times\frac{16\space oz}{1\space lb}$.
$155\times16 = 2480\space oz$
## Step2: Then convert ounces to grams. $1\space oz = 28.34\space g$, so $2480\space oz\times\frac{28.34\space g}{1\space oz}$.
$2480\times28.34 = 70283.2$
# Answer: $70283.2\space grams$

### Problem 4:
# Explanation:
## Step1: Recall the conversion factor: $1\space foot = 0.3048\space meters$.
$450\space feet\times\frac{0.3048\space meters}{1\space foot}$
## Step2: Multiply $450\times0.3048$. $450\times0.3048 = 137.16$.
# Answer: $137.16\space meters$

### Problem 5:
# Explanation:
## Step1: Recall the conversion factor: $1\space mile = 1609.34\space meters$, so we use $\frac{1\space mile}{1609.34\space meters}$.
$8000\space meters\times\frac{1\space mile}{1609.34\space meters}$
## Step2: Divide $8000\div1609.34\approx4.97$ (approx $5.0$ if rounded).
# Answer: Approximately $4.97\space miles$ (or $5.0\space miles$ when rounded)

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QUESTION IMAGE

Question

Explanation:

Problem 1:

Step1: Recall unit conversion for volume. \(1\space kL = 1000\space L\) and \(1\space L = 1000\space mL\), so \(1\space kL = 1000\times1000 = 10^6\space mL\).

Step2: Multiply the numbers. \(0.00765\times10^6 = 7650\).

Step1: Recall the conversion factor: \(1\space inch = 2.54\space cm\).

Step2: Multiply \(68.5\times2.54\). \(68.5\times2.54 = 174.0\) (approx, more accurately \(68.5\times2.54 = 173.99\approx174.0\)).

Step1: First convert pounds to ounces. \(1\space lb = 16\space oz\), so \(155\space lbs\times\frac{16\space oz}{1\space lb}\).

Step2: Then convert ounces to grams. \(1\space oz = 28.34\space g\), so \(2480\space oz\times\frac{28.34\space g}{1\space oz}\).

Answer:

Problem 2: