Question

conversions and dimensional analysis quiz

1. a runner completes a distance of 1.5 kilometers (km). how many meters (m) is this distance?

a. 0.0015 m
b. 1500 m
c. 150 m
d. 15 m

1. a scientist measures a mass of 450 milligrams (mg). express this mass in grams (g) using dimensional analysis. show your work.

a. 450,000 g
b. 4.50 g
c. 0.450 g
d. 45 g

1. which conversion factor should be placed in the parentheses to correctly convert 75.0 ml to liters (l) using dimensional analysis?

75.0 ml×( )=l
a. 1000 ml / 1l
b. 1l / 100ml
c. 1ml / 1000l
d. 1l / 1000ml

1. the dimensional analysis setup for converting 5.0 hours to seconds is shown. write out the missing conversion factor from the blank parentheses in the setup.

5.0 hours × (60 minutes / 1 hour) × ( ) = seconds

1. which of the following masses is the largest?

a. 0.0000015 micrograms (μg)
b. 1.8 grams (g)
c. 1200 milligrams (mg)
d. 0.001 kilograms (kg)

Explanation:

Step1: Recall distance conversion

We know that 1 km = 1000 m. To convert 1.5 km to m, we multiply by 1000. So, $1.5\times1000 = 1500$ m.

Step2: Recall mass conversion

Since 1 g = 1000 mg, to convert 450 mg to g, we divide by 1000. So, $\frac{450}{1000}=0.450$ g.

Step3: Recall volume conversion

We know that 1 L = 1000 mL. To convert from mL to L, the conversion - factor is $\frac{1L}{1000mL}$.

Step4: Recall time conversion

We know that 1 minute = 60 seconds. So the missing conversion factor is $\frac{60\text{ seconds}}{1\text{ minute}}$.

Step5: Convert all masses to grams

• For a: 0.0000015 $\mu$g. Since 1 $\mu$g=$10^{- 6}$g, then $0.0000015\times10^{-6}=1.5\times10^{-12}$g.
• For b: 1.8 g.
• For c: 1200 mg. Since 1 g = 1000 mg, then $\frac{1200}{1000}=1.2$g.
• For d: 0.001 kg. Since 1 kg = 1000 g, then $0.001\times1000 = 1$g. So 1.8 g is the largest.

Answer:

1. B. 1500 m
2. C. 0.450 g
3. D. $1L/1000mL$
4. $\frac{60\text{ seconds}}{1\text{ minute}}$
5. B. 1.8 grams (g)