US Conversion Steps(Dimensional Analysis)

1. Read the question to figure out what you have/know for information. The question will provide you with information that identifies your starting point and your final destination.

• Starting point = the number and unit provided by the question• Final destination = the units desired after converting

2. Using the information gathered from the question, write your starting point and your final destination.

3. Determine the means in which you will get from your starting point to your final destination (simply find “connections” or conversion factors between your starting and final unit).

4. Create a fraction by placing your starting point over one.5. Multiply between fractions.6. Write in the bottom unit of the new fraction. This should be the same as the top unit

of the previous fraction.7. Write one set of “connections” or conversion factors into the fraction. Your bottom

unit will guide you.8. Ask yourself, “Do I have the desired unit (final destination) on the top of the new

fraction?”

NO YES

9. Cancel any units that are diagonal. (This should leave you with only the units that represent your final destination)

10. Multiply the top of the fractions…multiply the bottom of the fractions…divide the top by the bottom.

(Go back to step 5) (Proceed to step 9)

Practice Conversions

1. How many seconds are in 6 minutes?

2. How many centimeters are in 27 inches?

3. If a truck weighs 15,356 pounds, how many tons is it?

4. If you had 10.5 gallons of milk, how many pints would you have?

5. Students go to school for 180 days. How many minutes is this equal to?

How many seconds are in 6 minutes?

6 minutes seconds

(6 minutes)1

( )( )

secondsminute

360 seconds

601

=360 seconds

1

=

Step 1 – Read the question and determine

what information it provides you with (starting point & final destination)

Step 2 – Write down your starting point and your final

destination1 minute = 60 secondsStep 3 –

Determine how you will

getfrom your

starting point to your final destination

(list any “connections” or conversion

factors) Step 4 – Create a fraction by placing your starting

point over one

Step 5 – Multiply between fractionsStep 6 – Write in the bottom

unit of the new fraction (this is the same as the top unit of

your previous fraction)

Step 7 – Write the appropriate conversion

factor into the fraction. Your bottom unit will guide you.

Step 8 – Determine if this top unit is the desired unit (your

final destination). In this case the answer is YES, so

we move on to step 9

Step 9 – Cancel all diagonal units. Once this is done,

your final destination should be the only unit left – in this

case seconds

Step 10 – Multiply the top of the fractions; multiply the bottom of the fractions;

divide the product of the top by the product of the bottom

Starting Point

Final Destination

How many centimeters are in 27 inches?

27 inches centimeters

(27 inches)1

( )( )

cminch

68.58 centimeters

2.541

= 68.58 cm1

=

Step 1 – Read the question and determine

what information it provides you with (starting point & final destination)

Step 2 – Write down your starting point and your final

destination1 inch = 2.54 centimetersStep 3 – Determine

how you will get

from your starting

point to your final

destination (list any

“connections” or

conversion factors)

Step 4 – Create a fraction by placing your starting

point over one

Step 5 – Multiply between fractionsStep 6 – Write in the bottom

unit of the new fraction (this is the same as the top unit of

your previous fraction)

Step 7 – Write the appropriate conversion

factor into the fraction. Your bottom unit will guide you.

Step 8 – Determine if this top unit is the desired unit (your

final destination). In this case the answer is YES, so

we move on to step 9

Step 9 – Cancel all diagonal units. Once this is done,

your final destination should be the only unit left – in this

case centimeters

Step 10 – Multiply the top of the fractions; multiply the bottom of the fractions;

divide the product of the top by the product of the bottom

Starting Point

Final Destination

If a truck weighs 15,356 pounds, how many tons is it?

15,356 pounds tons

(15,356 lbs.)1

( )( )

tonlbs.

7.678 tons

12000

=15,356 ton

2000

=

Step 1 – Read the question and determine

what information it provides you with (starting point & final destination)

Step 2 – Write down your starting point and your final

destination2000 pounds = 1 tonStep 3 – Determine

how you will get

from your starting point to your final destination

(list any “connections” or conversion

factors) Step 4 – Create a fraction by placing your starting

point over one

Step 5 – Multiply between fractionsStep 6 – Write in the bottom

unit of the new fraction (this is the same as the top unit of

your previous fraction)

Step 7 – Write the appropriate conversion

factor into the fraction. Your bottom unit will guide you.

Step 8 – Determine if this top unit is the desired unit (your

final destination). In this case the answer is YES, so

we move on to step 9

Step 9 – Cancel all diagonal units. Once this is done,

your final destination should be the only unit left – in this

case tons

Step 10 – Multiply the top of the fractions; multiply the bottom of the fractions;

divide the product of the top by the product of the bottom

Starting Point

Final Destination

If you had 10.5 gallons of milk, how many pints would you have?

10.5 gallons pints

(10.5 gallons)1

( )( )

quartsgallon

84 pints

41

=(10.5)(4)(2 pints)

(1)(1)(1) =

Step 1 – Read the question and determine

what information it provides you with (starting point & final destination)

Step 2 – Write down your starting point and your final

destination

1 gallon = 4 quarts1 quart = 2 pintsStep 3 –

Determine how you will

getfrom your

starting point to your final destination

(list any “connections” or conversion

factors) Step 4 – Create a fraction by placing your starting

point over one

Step 5 – Multiply between fractions

Step 6 – Write in the bottom unit of the new fraction (this is the same as the top unit of

your previous fraction)

Step 7 – Write the appropriate conversion

factor into the fraction. Your bottom unit will guide you.

Step 8 – Determine if this top unit is the desired unit (your

final destination). In this case the answer is NO, so we

move back to step 5

Step 9 – Cancel all diagonal units. Once this is done,

your final destination should be the only unit left – in this

case pints

Step 10 – Multiply the top of the fractions; multiply the bottom of the fractions;

divide the product of the top by the product of the

bottom

Starting Point

Final Destination

( )( )

pintsquart

21

Step 5 – Multiply between fractionsStep 6 – Write in the bottom

unit of the new fraction (this is the same as the top unit of

your previous fraction)

Step 7 – Write the appropriate conversion

factor into the fraction. Your bottom unit will guide you.

Step 8 – Determine if this top unit is the desired unit (your

final destination). In this case the answer is YES, so

we move on to step 9

Students go to school for 180 days. How many minutes is this equal to?

180 days minutes

(180 days)1

( )( )

hoursday

259,200 minutes

241

=(180)(24)(60 minutes)

(1)(1)(1) =

Step 1 – Read the question and determine

what information it provides you with (starting point & final destination)

Step 2 – Write down your starting point and your final

destination

1 day = 24 hours1 hour = 60 minutesStep 3 –

Determine how you will

getfrom your

starting point to your final destination

(list any “connections” or conversion

factors) Step 4 – Create a fraction by placing your starting

point over one

Step 5 – Multiply between fractions

Step 6 – Write in the bottom unit of the new fraction (this is the same as the top unit of

your previous fraction)

Step 7 – Write the appropriate conversion

factor into the fraction. Your bottom unit will guide you.

Step 8 – Determine if this top unit is the desired unit (your

final destination). In this case the answer is NO, so we

move back to step 5

Step 9 – Cancel all diagonal units. Once this is done, your final destination should be the

only unit left – in this case minutes

Step 10 – Multiply the top of the fractions;

multiply the bottom of the fractions; divide the product of the top by the

product of the bottom

Starting Point

Final Destination

( )( )

minuteshour

601

Step 5 – Multiply between fractions

Step 6 – Write in the bottom unit of the new fraction (this is the same as the top unit of

your previous fraction)

Step 7 – Write the appropriate conversion

factor into the fraction. Your bottom unit will guide you.

Step 8 – Determine if this top unit is the desired unit (your

final destination). In this case the answer is YES, so

we move on to step 9