Interpreting and Converting Metric Units Answer Key (CHEM 1405)

Back to Chemistry 1405 Practice Problems

Part One

Instructions: We need to learn how to evaluate the measurements that we are given. For every measurement, there is an assigned number and unit (or symbol). Use the table below to further analyze a series of measurements.

	Number	Base unit	Base Unit Symbol	Prefix	Prefix Symbol	Type of Measurement
1)  100 km	100	meter	m	kilo-	k	distance/length
2)  14 ms	14	second	s	milli-	m	time
3)  24 cg	24	gram	g	centi-	c	mass
4)  2640 mL	2640	liter	L	milli-	m	volume
5)  215 mm	215	meter	m	milli-	m	distance/length
6)  1.25 $\mu$g	1.25	gram	g	micro-	$\mu$	mass
7)  3.4 dL	3.4	liter	L	deci-	d	volume
8)  4.65 cm	4.65	meter	m	centi-	c	distance/length
9)  213 kg	213	gram	g	kilo-	k	mass
10)  55.3 L	55.3	liter	L	none	none	volume
11)  21.4 mg	21.4	gram	g	milli-	m	mass
12)  0.04 $\mu$s	0.04	second	s	micro-	$\mu$	time
13)  14 cg	14	gram	g	centi-	c	mass
14)  14.5 mL	14.5	liter	L	milli-	m	volume
15)  24 km	24	meter	m	kilo-	k	distance/length

 

 

Part Two: Factor Label Method

1)  100 km = ________ m

1. 1. Write the given:
      100 km
   2. Multiply the given by an empty fraction:
      $100km\times(\frac{}{})$
      
   3. Write the same units in the given on the bottom of the fraction so that the units cancel. (NO NUMBERS YET!)
      $100km\times(\frac{}{km})$
      
   4. Write the conversion unit you are looking for on top of the fraction.  HOWEVER, if you are converting one prefix unit to a different prefix unit, you will first need to convert to the base unit and then use an additional conversion factor to convert to the new prefix unit.  (STILL no numbers!)
      $100km\times(\frac{m}{km})$
   5. Place a 1 by the unit with a prefix.  This unit may be either on top or bottom depending on what your given is.
      $100km\times(\frac{m}{1km})$
      
   6. Place the conversion value (the meaning of the prefix) in front of the base unit.
      $100km\times(\frac{1000m}{1km})$
   7. Multiply everything on top and divide by everything on bottom.   
      $100km\times(\frac{1000m}{1km})=100,000m$

 

 

2)  2 s = ________ ms

1. 1. Write the given:
      2 s
   2. Multiply the given by an empty fraction:
      $2s\times(\frac{}{})$
      
   3. Write the same units in the given on the bottom of the fraction so that the units cancel. (NO NUMBERS YET!)
      $2s\times(\frac{}{s})$
      
   4. Write the conversion unit you are looking for on top of the fraction.  HOWEVER, if you are converting one prefix unit to a different prefix unit, you will first need to convert to the base unit and then use an additional conversion factor to convert to the new prefix unit.  (STILL no numbers!)
      $2s\times(\frac{ms}{s})$
      
   5. Place a 1 by the unit with a prefix.  This unit may be either on top or bottom depending on what your given is.
      $2s\times(\frac{1ms}{s})$
      
   6. Place the conversion value (the meaning of the prefix) in front of the base unit.
      $2s\times(\frac{1ms}{0.001s})$
      
   7. Multiply everything on top and divide by everything on bottom.
      $2s\times(\frac{1ms}{0.001s})=2000ms$

 

 

3)  0.45 dg = ________ kg

1. 1. Write the given:
      0.45 dg
   2. Multiply the given by an empty fraction:
      $0.45dg\times(\frac{}{})$
      
   3. Write the same units in the given on the bottom of the fraction so that the units cancel. (NO NUMBERS YET!)
      $0.45dg\times(\frac{}{dg})$
      
   4. Write the conversion unit you are looking for on top of the fraction.  HOWEVER, if you are converting one prefix unit to a different prefix unit, you will first need to convert to the base unit and then use an additional conversion factor to convert to the new prefix unit.  (STILL no numbers!)
      $0.45dg\times(\frac{g}{dg})\times(\frac{kg}{g})$
      
   5. Place a 1 by the unit with a prefix.  This unit may be either on top or bottom depending on what your given is.
      $0.45dg\times(\frac{g}{1dg})\times(\frac{1kg}{g})$
      
   6. Place the conversion value (the meaning of the prefix) in front of the base unit.
      $0.45dg\times(\frac{0.1g}{1dg})\times(\frac{1kg}{1000g})$
      
   7. Multiply everything on top and divide by everything on bottom.
      $0.45dg\times(\frac{0.1g}{1dg})\times(\frac{1kg}{1000g})=0.000045\operatorname{kg}$

 

 

4)  25 L = ________ mL

1. 1. Write the given:
      25 L
   2. Multiply the given by an empty fraction:
      $25L\times(\frac{}{})$
      
   3. Write the same units in the given on the bottom of the fraction so that the units cancel. (NO NUMBERS YET!)
      $25L\times(\frac{}{L})$
      
   4. Write the conversion unit you are looking for on top of the fraction.  HOWEVER, if you are converting one prefix unit to a different prefix unit, you will first need to convert to the base unit and then use an additional conversion factor to convert to the new prefix unit.  (STILL no numbers!)
      $25L\times(\frac{mL}{L})$
      
   5. Place a 1 by the unit with a prefix.  This unit may be either on top or bottom depending on what your given is.
      $25L\times(\frac{1mL}{L})$
      
   6. Place the conversion value (the meaning of the prefix) in front of the base unit.
      $25L\times(\frac{1mL}{0.001L})$
      
   7. Multiply everything on top and divide by everything on bottom.
      $25L\times(\frac{1mL}{0.001L})=25,000mL$
      

 

 

5)  225 cm = ________ mm

1. 1. Write the given:
      225 cm
   2. Multiply the given by an empty fraction:
      $225cm\times(\frac{}{})$
      
   3. Write the same units in the given on the bottom of the fraction so that the units cancel. (NO NUMBERS YET!)
      $225cm\times(\frac{}{cm})$
      
   4. Write the conversion unit you are looking for on top of the fraction.  HOWEVER, if you are converting one prefix unit to a different prefix unit, you will first need to convert to the base unit and then use an additional conversion factor to convert to the new prefix unit.  (STILL no numbers!)
      $225cm\times(\frac{m}{cm})\times(\frac{mm}{m})$
   5. Place a 1 by the unit with a prefix.  This unit may be either on top or bottom depending on what your given is.
      $225cm\times(\frac{m}{1cm})\times(\frac{1mm}{m})$
      
   6. Place the conversion value (the meaning of the prefix) in front of the base unit.
      $225cm\times(\frac{0.01m}{1cm})\times(\frac{1mm}{0.001m})$
      
   7. Multiply everything on top and divide by everything on bottom.
      $225cm\times(\frac{0.01m}{1cm})\times(\frac{1mm}{0.001m})=2250\operatorname{mm}$
      

 

 

For some extra practice, try the following!

6)  625 mL =  _____ L

$625mL\times(\frac{0.001L}{1mL})=0.625L$

 

7)  384 g =     _____ kg

$384g\times(\frac{1kg}{1000g})=0.384\operatorname{kg}$

 

8)  12 cm =    _____ $\mu$m

$12cm\times(\frac{0.01m}{1cm})\times(\frac{1\mu m}{0.000001m})=120,000\mu m$

 

9)  21.4 kg =  _____ g

$21.4kg\times(\frac{1000g}{1kg})=21,400g$

 

10)  10 ms =  _____ s

$10ms\times(\frac{0.001s}{1ms})=0.01s$

 

11)  14 L =     _____ $\mu$L

$14L\times(\frac{1\mu L}{0.000001L})=14,000,000\mu L$

 

12)  55.4 L =  _____ mL

$55.4L\times(\frac{1mL}{0.001L})=55,400mL$

 

13)  4.2 dm = _____ km

$4.2dm\times(\frac{0.1m}{1dm})\times(\frac{1km}{1000m})=0.00042\operatorname{km}$

 

14)  21 g =     _____ mg

$21g\times(\frac{1mg}{0.001g})=21,000mg$