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Unit Conversions, Summaries of Science education

hr km min sec. = 6. How many seconds are there in a year? yr day hr min sec yr day hr min. = 7. Convert the speed of light, 3.0 × 108 m/s to km/day m km sec.

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Unit Conversions
When you are dealing with data that has units, you must be aware of how the units change when arithmetic operations
are performed on them.
 When you multiply 3 ft by 4 ft to find area the units are ft × ft which are ft
2
.
 When you divide m
2
by m the units are
2
m
m
which are
m
.
To use multiple units that are not the same, you must
convert the units into a common unit
. For example, you
cannot use feet/second and miles/hour in the same calculation. You must make them both the same.
An example of disastrous consequences: NASA has crash-landed spacecraft onto Mars twice because some
calculations were done in metrics and some were done in Imperial units!

The process for doing this is to set up a fraction chart so that the units you are trying to get rid of reduce out and
are replaced by the units you want.

Then multiply the top numbers together and multiply the bottom numbers together.

Divide the resulting numbers.

EXAMPLE: To convert 10 ft/sec to mi/hr, the problem is set up like this:
10 ft
1 mi
60 sec
60
min
1
sec
5280 ft
1
min
1 hr
=
36000
6.818
5280
=
==
=
mi/hr
In these problems, the units have been placed in the right spot. You only need to place numbers.
1. Convert 4 gallons to pints
gallons
quarts
pints
gallon
quart
=
2. Convert 60 mi/hr to ft/s
mi
hr
min
ft
hr
min
s
mi
=
3. Convert 1 mile to inches
mi
ft
in
mi
ft
=
4. Convert 44 ft/s to mi/hr
ft
sec
min
mi
sec
min
hr
ft
=
Notice
that the unwanted units
are placed one on top and one
on bottom so they reduce to 1.
pf3
pf4
pf5
pf8

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Unit Conversions

When you are dealing with data that has units, you must be aware of how the units change when arithmetic operations are performed on them.

 When you multiply 3 ft by 4 ft to find area the units are ft × ft which are ft^2_._

 When you divide m^2 by m the units are

m^2 m

which are m_._

To use multiple units that are not the same, you must convert the units into a common unit. For example, you cannot use feet/second and miles/hour in the same calculation. You must make them both the same.

An example of disastrous consequences: NASA has crash-landed spacecraft onto Mars twice because some calculations were done in metrics and some were done in Imperial units!

 The process for doing this is to set up a fraction chart so that the units you are trying to get rid of reduce out and are replaced by the units you want.

 Then multiply the top numbers together and multiply the bottom numbers together.

 Divide the resulting numbers.

 EXAMPLE: To convert 10 ft/sec to mi/hr, the problem is set up like this:

10 ft 1 mi 60 sec 60 min

1 sec 5280 ft 1 min 1 hr

====^ mi/hr

In these problems, the units have been placed in the right spot. You only need to place numbers.

  1. Convert 4 gallons to pints

gallons quarts pints

gallon quart

  1. Convert 60 mi/hr to ft/s

mi hr min ft

hr min s mi

  1. Convert 1 mile to inches

mi ft in

mi ft

  1. Convert 44 ft/s to mi/hr

ft sec min mi

sec min hr ft

Notice that the unwanted units are placed one on top and one on bottom so they reduce to 1.

  1. Convert 25 km/hr to m/s

km m hr min

hr km min sec

  1. How many seconds are there in a year?

yr day hr min sec

yr day hr min

  1. Convert the speed of light, 3.0 × 108 m/s to km/day

m km sec min hr

sec m min hr day

  1. Convert 3 ft^2 to in^2

ft^2 in in

ft ft

  1. Convert 2 mi^2 to in^2

mi ft ft in in

mi mi ft ft

  1. Convert 12 km/hr to cm/s

km m cm hr min

hr km m min sec

  1. Convert 3.2 yd/min to mi/hr

yd ft mi min

min yd ft hr

  1. Convert the speed of an electron in a hydrogen atom (2,200 km/s) to cm/hr

km m cm sec min

sec km m min hr

CONVERSION FACTORS

1 meter (m) = 100 centimeters (cm) = 1,000 millimeters (mm)

1 kilometer (km) = 1,000 meters (m)

1 kilogram (kg) = 1,000 grams (g)

1 mile (mi) = 5280 feet (ft)

3 feet (ft) = 1 yard (yd)

4 quarts (qt) = 1 gallon (gal)

2 pints (pt) = 1 quart (qt)

CONVERSION FACTORS

1 meter (m) = 100 centimeters (cm) = 1,000 millimeters (mm)

1 kilometer (km) = 1,000 meters (m)

1 kilogram (kg) = 1,000 grams (g)

1 mile (mi) = 5280 feet (ft)

3 feet (ft) = 1 yard (yd)

4 quarts (qt) = 1 gallon (gal)

2 pints (pt) = 1 quart (qt)

Unit Conversions

When you are dealing with data that has units, you must be aware of how the units change when arithmetic operations are performed on them.

 When you multiply 3 ft by 4 ft to find area the units are ft × ft which are ft^2_._

 When you divide m^2 by m the units are

m^2 m

which are m_._

To use multiple units that are not the same, you must convert the units into a common unit. For example, you cannot use feet/second and miles/hour in the same calculation. You must make them both the same.

An example of disastrous consequences: NASA has crash-landed spacecraft onto Mars twice because some calculations were done in metrics and some were done in Imperial units!

 The process for doing this is to set up a fraction chart so that the units you are trying to get rid of reduce out and are replaced by the units you want.

 Then multiply the top numbers together and multiply the bottom numbers together.

 Divide the resulting numbers.

 EXAMPLE: To convert 10 ft/sec to mi/hr, the problem is set up like this:

10 ft 1 mi 60 sec 60 min

1 sec 5280 ft 1 min 1 hr

====^ mi/hr

In these problems, the units have been placed in the right spot. You only need to place numbers.

  1. Convert 4 gallons to pints

4 gallons 4 quarts 2 pints

1 gallon 1 quart

= 32 pints

  1. Convert 60 mi/hr to ft/s

60 mi 1 hr 1 min 5280 ft

1 hr 60 min 60 s 1 mi

= 88 ft/s

  1. Convert 1 mile to inches

1 mi 5280 ft 12 in

1 mi 1 ft

= 63,360 in

  1. Convert 44 ft/s to mi/hr

44 ft 60 sec 60 min 1 mi

1 sec 1 min 1 hr 5280 ft

= 30 mi/hr

Notice that the unwanted units are placed one on top and one on bottom so they reduce to 1.

In addition to metric prefixes, here are some equalities that may prove useful for the following unit conversions:

1 ft = 0.30 m 1 in = 2.54 cm 1 mile = 1609 m 2.21 lb = 1 kg

  1. Convert 62.4 lb into g 14. Convert 1 mile into km
  2. Convert the 1 week into seconds 16. Convert 34 km into cm
  3. Convert 75 ft^2 into m^2 18. Convert 3 feet to cm
  4. Convert 6.3 ft^2 to m^2 20. Convert 28 km to mm.
  5. Convert 45 g to lb. 22. Convert the speed 25 m/s into km/h
  6. Convert the speed 90 mi/h into m/s 24. Convert the speed 9.8 m^3 into ft^3
  7. Convert 170 cm/min to mm/s 26. Convert 450 m/s to m/h.
  8. Convert 85 cm/min to m/s. 28. Change 25 km/h to m/s

1 mi 1609 m 1 km 1.609 km 1 1 mi 1000 m

62.4 lb 1 kg 1000 g 28, 235.3 g 1 2.21 lb 1 kg

1 wk 7 day 24 hr 3600 s 604,800 s 1 1 wk 1 day 1 hr

34 km 1000 m 100 cm 3,400,000 cm 1 1 km 1 m

2 75 ft 0.3m 0.3m (^) 6.75 m 2 1 1ft 1ft

3 ft 0.3 m 100 cm 90 cm 1 1 ft 1 m

2 6.3 ft 0.3 m 0.3 m (^) 0.567 m 2 1 1 ft 1 ft

28 km 1000 m 1000 mm 28,000,000 mm 1 1 km 1 m

45 g 1 kg 2.21 lb 0.09945 lb 1 1000 g 1 kg

25 m 3600 s 1 km 90 km / h s 1 hr 1000 m

90 mi 1 hr 1609 m 40.2 m / s hr 3600 s 1 mi

3 3 m 1 ft 1 ft 1 ft (^) 111.1 ft 3 1 0.3 m 0.3 m 0.3 m

170 cm 1 min 10 mm 28.3 mm / s min 60 s 1 cm

450 m 3600 s 1,620,000 m / h s 1 hr

85 cm 1 min 1 m 0.0014 m / s min 60 s 100 cm

25 km 1 hr 1000 m 6.9 m / s hr 3600 s 1 km

Unit Conversions

Some students find this difficult at first, but once it is demonstrated enough times they catch on.

Some students may not clearly understand that square and cubic units are not the same as first-degree units. You might have to draw a line, square and cube with the same length on the board and show that the have dimensions.

It is recommended that you project the first two pages onto a whiteboard and go through at least a third of them as a class. Make sure to emphasize why the units are placed where they are placed (this is the key to the whole process). It may take students a number of problems before everyone gets the idea.

Problems 13-28 may be used as practice problems once students get the idea. Some students may, at first, need guidance in placing units correctly in these problems.

NOTE:

Depending on how well versed your students are in metric and Imperial units of measure, you may need to print the conversion factors on fourth page and provide each group with a copy. To save for future use, print them on cardstock or laminate them.