




Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Community
Ask the community for help and clear up your study doubts
Discover the best universities in your country according to Docsity users
Free resources
Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors
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.
Typology: Summaries
1 / 8
This page cannot be seen from the preview
Don't miss anything!
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.
gallons quarts pints
gallon quart
mi hr min ft
hr min s mi
mi ft in
mi ft
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.
km m hr min
hr km min sec
yr day hr min sec
yr day hr min
m km sec min hr
sec m min hr day
ft^2 in in
ft ft
mi ft ft in in
mi mi ft ft
km m cm hr min
hr km m min sec
yd ft mi min
min yd ft hr
km m cm sec min
sec km m min hr
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.
4 gallons 4 quarts 2 pints
1 gallon 1 quart
= 32 pints
60 mi 1 hr 1 min 5280 ft
1 hr 60 min 60 s 1 mi
= 88 ft/s
1 mi 5280 ft 12 in
1 mi 1 ft
= 63,360 in
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 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
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.
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.