Question

metrics and measurement
in the chemistry classroom and lab, the metric system of measurement is used, so it is
important to be able to convert from one unit to another.
factor label method

1. write the given number and unit.
2. set up a conversion factor (fraction used to convert one unit to another).

a. place the given unit as denominator of conversion factor.
b. place desired unit as numerator.
c. place a 1 in front of the larger unit.
d. determine the number of smaller units needed to make 1 of the larger unit.

1. cancel units, solve the problem.

the factor label method can be used to solve virtually any problem including changes in
units. it is especially useful in making complex conversions dealing with concentrations
and derived units.
convert the following.

1. 36 ml = ______ dl
2. 950 g = ______ kg
3. 275 mm = ______ cm
4. 1,000 l = ______ kl
5. 1,000 ml = ______ l
6. 4,500 mg = ______ g
7. 26 cm = ______ mm
8. 0.005 kg = ______ dag
9. 0.075 m = ______ cm
10. 16 g = ______ mg

chemistry 18766

Explanation:

Step1: Convert 36 mL to dL

• First, convert mL to L: \(36\space mL\times\frac{1\space L}{1000\space mL}\)
• Then convert L to dL: \(36\space mL\times\frac{1\space L}{1000\space mL}\times\frac{10\space dL}{1\space L}= 0.36\space dL\)

Step2: Convert 950 g to kg

• Use the conversion factor \(\frac{1\space kg}{1000\space g}\)
• \(950\space g\times\frac{1\space kg}{1000\space g}=0.95\space kg\)

Step3: Convert 275 mm to cm

• Use the conversion factor \(\frac{1\space cm}{10\space mm}\)
• \(275\space mm\times\frac{1\space cm}{10\space mm}=27.5\space cm\)

Step4: Convert 1000 L to kL

• Use the conversion factor \(\frac{1\space kL}{1000\space L}\)
• \(1000\space L\times\frac{1\space kL}{1000\space L}=1\space kL\)

Step5: Convert 1000 mL to L

• Use the conversion factor \(\frac{1\space L}{1000\space mL}\)
• \(1000\space mL\times\frac{1\space L}{1000\space mL}=1\space L\)

Step6: Convert 4500 mg to g

• Use the conversion factor \(\frac{1\space g}{1000\space mg}\)
• \(4500\space mg\times\frac{1\space g}{1000\space mg}=4.5\space g\)

Step7: Convert 25 cm to mm

• Use the conversion factor \(\frac{10\space mm}{1\space cm}\)
• \(25\space cm\times\frac{10\space mm}{1\space cm}=250\space mm\)

Step8: Convert 0.005 kg to dag

• First convert kg to g: \(0.005\space kg\times\frac{1000\space g}{1\space kg}\)
• Then convert g to dag: \(0.005\space kg\times\frac{1000\space g}{1\space kg}\times\frac{1\space dag}{10\space g}=0.5\space dag\)

Step9: Convert 0.075 m to cm

• Use the conversion factor \(\frac{100\space cm}{1\space m}\)
• \(0.075\space m\times\frac{100\space cm}{1\space m}=7.5\space cm\)

Step10: Convert 16 g to mg

• Use the conversion factor \(\frac{1000\space mg}{1\space g}\)
• \(16\space g\times\frac{1000\space mg}{1\space g}=16000\space mg\)

Answer:

1. \(0.36\space dL\)
2. \(0.95\space kg\)
3. \(27.5\space cm\)
4. \(1\space kL\)
5. \(1\space L\)
6. \(4.5\space g\)
7. \(250\space mm\)
8. \(0.5\space dag\)
9. \(7.5\space cm\)
10. \(16000\space mg\)