experiment & report 2 dimensional analysis
chem 110 lab
name
(last) (first)
instructor’s initials
purpose: the purpose of this laboratory exercise it to develop and practice the skill of dimensional analysis which is used in most chemistry calculations.
a. metric-metric conversions
solve each of the following metric-metric conversions using dimensional analysis and going through the basic unit. give complete setups, including all units. be sure your answers are rounded to the correct number of significant figures. (assume all numbers given are measured numbers)
1. convert 4.2 microliters to liters
1.
2. convert 2.2 centimeters to millimeters
2.
3. convert 5.99 kilograms to decigrams
3.
4. convert 111 cubic centimeters to liters
4.
5. convert 8 square meters to square kilometers
5.
6. convert 33 square centimeters to square nanometers.
6.
7. convert 8.5 × 10³ square millimeters to square decimeters.
7.

Question

Accepted Answer

### Problem 1: Convert 4.2 microliters to liters
# Explanation:
## Step1: Recall metric prefixes. 1 microliter ($\mu$L) = $10^{-6}$ liters (L), or 1 L = $10^{6}$ $\mu$L. So the conversion factor is $\frac{1\ L}{10^{6}\ \mu L}$.
$4.2\ \mu L	imes\frac{1\ L}{10^{6}\ \mu L}$
## Step2: Multiply the values. $4.2	imes10^{-6}\ L$ (since $\frac{4.2}{10^{6}} = 4.2	imes10^{-6}$)
# Answer: $4.2	imes10^{-6}\ L$

### Problem 2: Convert 2.2 centimeters to millimeters
# Explanation:
## Step1: Recall that 1 centimeter (cm) = 10 millimeters (mm). So the conversion factor is $\frac{10\ mm}{1\ cm}$.
$2.2\ cm	imes\frac{10\ mm}{1\ cm}$
## Step2: Multiply 2.2 by 10. $22\ mm$
# Answer: $22\ mm$

### Problem 3: Convert 5.99 kilograms to decigrams
# Explanation:
## Step1: First, convert kilograms (kg) to grams (g). 1 kg = 1000 g, so conversion factor $\frac{1000\ g}{1\ kg}$. Then convert grams to decigrams (dg). 1 g = 10 dg, so conversion factor $\frac{10\ dg}{1\ g}$.
$5.99\ kg	imes\frac{1000\ g}{1\ kg}	imes\frac{10\ dg}{1\ g}$
## Step2: Multiply the values. $5.99	imes1000	imes10\ dg = 5.99	imes10^{4}\ dg = 59900\ dg$
# Answer: $59900\ dg$ (or $5.99	imes10^{4}\ dg$)

### Problem 4: Convert 111 cubic centimeters to liters
# Explanation:
## Step1: Recall that 1 cubic centimeter ($cm^3$) = 1 milliliter (mL), and 1 liter (L) = 1000 mL. So 1 $cm^3$ = $10^{-3}$ L, or conversion factor $\frac{1\ L}{1000\ cm^3}$.
$111\ cm^3	imes\frac{1\ L}{1000\ cm^3}$
## Step2: Divide 111 by 1000. $0.111\ L$
# Answer: $0.111\ L$

### Problem 5: Convert 8 square meters to square kilometers
# Explanation:
## Step1: Recall that 1 kilometer (km) = 1000 meters (m), so 1 square kilometer ($km^2$) = $(1000\ m)^2 = 10^{6}\ m^2$. Conversion factor $\frac{1\ km^2}{10^{6}\ m^2}$.
$8\ m^2	imes\frac{1\ km^2}{10^{6}\ m^2}$
## Step2: Calculate $8	imes10^{-6}\ km^2$ (since $\frac{8}{10^{6}} = 8	imes10^{-6}$)
# Answer: $8	imes10^{-6}\ km^2$

### Problem 6: Convert 33 square centimeters to square nanometers
# Explanation:
## Step1: First, convert centimeters (cm) to nanometers (nm). 1 cm = $10^{7}$ nm (since 1 m = $10^{2}$ cm and 1 m = $10^{9}$ nm, so 1 cm = $10^{9}/10^{2} = 10^{7}$ nm). For square units, $(1\ cm)^2 = (10^{7}\ nm)^2 = 10^{14}\ nm^2$. So conversion factor $\frac{10^{14}\ nm^2}{1\ cm^2}$.
$33\ cm^2	imes\frac{10^{14}\ nm^2}{1\ cm^2}$
## Step2: Multiply 33 by $10^{14}$. $3.3	imes10^{15}\ nm^2$ (since 33 = $3.3	imes10^{1}$, so $3.3	imes10^{1}	imes10^{14} = 3.3	imes10^{15}$)
# Answer: $3.3	imes10^{15}\ nm^2$

### Problem 7: Convert $8.5	imes10^{3}$ square millimeters to square decimeters
# Explanation:
## Step1: Recall that 1 decimeter (dm) = 100 millimeters (mm), so 1 square decimeter ($dm^2$) = $(100\ mm)^2 = 10^{4}\ mm^2$. Conversion factor $\frac{1\ dm^2}{10^{4}\ mm^2}$.
$8.5	imes10^{3}\ mm^2	imes\frac{1\ dm^2}{10^{4}\ mm^2}$
## Step2: Divide $8.5	imes10^{3}$ by $10^{4}$. $0.85\ dm^2$ (since $\frac{8.5	imes10^{3}}{10^{4}} = 8.5	imes10^{-1} = 0.85$)
# Answer: $0.85\ dm^2$

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Question

Explanation:

Problem 1: Convert 4.2 microliters to liters

Step1: Recall metric prefixes. 1 microliter ($\mu$L) = $10^{-6}$ liters (L), or 1 L = $10^{6}$ $\mu$L. So the conversion factor is $\frac{1\ L}{10^{6}\ \mu L}$.

Step2: Multiply the values. $4.2\times10^{-6}\ L$ (since $\frac{4.2}{10^{6}} = 4.2\times10^{-6}$)

Step1: Recall that 1 centimeter (cm) = 10 millimeters (mm). So the conversion factor is $\frac{10\ mm}{1\ cm}$.

Step2: Multiply 2.2 by 10. $22\ mm$

Step1: First, convert kilograms (kg) to grams (g). 1 kg = 1000 g, so conversion factor $\frac{1000\ g}{1\ kg}$. Then convert grams to decigrams (dg). 1 g = 10 dg, so conversion factor $\frac{10\ dg}{1\ g}$.

Step2: Multiply the values. $5.99\times1000\times10\ dg = 5.99\times10^{4}\ dg = 59900\ dg$

Answer:

Problem 2: Convert 2.2 centimeters to millimeters