1. 2 Metric and English

2. ( ) ( ) ( ) ( ) ( ) ( ) 2.54 cm 1 in 1 in 2.54 cm 1 m 102 cm 102 cm
The fundamental conversion factor for length is 2.54 cm = 1 inch
How many inches are in exactly one meter?
What is the second step?
And the final answer is?
What is the third step?
What is the fourth step?
What is the first step?
What is the fifth step?
What are the unit factors for this conversion?
Write the units of the desired quantity on the right of the future equation.
That’s the one, insert it in the equation next.
That’s the one, insert it to the right of the 1 m.
Pick the unit factor that has m in the denominator and cm in the numerator.
Write the given quantity on the left of the future equation.
Write the other relevant unit factors.
1 x  =
Pick the unit factor that has cm in the denominator and
inches in the numerator.
( )
2.54 cm
1 in
( )
1 in
2.54 cm
( )
1 m
102 cm
( )
102 cm
1 m
( )
102 cm
1 m
( )
1 in
2.54 cm
1 m
= in
39.37

3. ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 103 m 1 km 1 ft 12 in 1 in 2.54 cm
Here’s another relevant question, how many feet are in
exactly one kilometer?
Can you guess it? Realize that now we are converting metric to English.
Is that the best place for it?
What are we left with?
What are the needed unit factors?
Is that it?
What is the first step for solving this problem?
The placement of those factors was pretty obvious,
but what of the metric to English unit factor?
Are these all of the needed unit factors?
And the final answer is?
Where are the clues for the remaining unit factors?
Do we have a unit factor which has meters in the denominator
and centimeters in the numerator?
Why the change in strategy?
And where does it go?
What is the third step?
What is the second step?
These clues are in the numerator of the left unit factor,
and the denominator of the middle unit factor.
Let’s divide out the units and see.
No, it looks like it belongs next to the unit factor with
inches in the denominator.
It goes somewhere in the middle.
We do!
We are left with units of feet, which is the unit of the desired quantity,
so we are finished.
We must have the unit factor for converting centimeter into inches.
And that factor is a definition, and so has infinite sig. figs.
1 x x   12 =.
Write the units of the desired quantity at the right of the future equation.
Because this time it is not obvious which unit factors we need.
Writing down the given and desired units will help us decide.
A bit different this time, write down the given quantity at the left
of the future equation.
No, but let’s put those that we have into the equation to see if the partially
completed equation gives us some clues for what else is needed
Now we write down the needed unit factors.
We need a unit factor for converting kilometers to meters.
There’s another unit factor we know we must have.
We need a unit factor for converting something into feet.
Let’s try inches
( )
103 m
1 km
( )
1 ft
12 in
( )
1 in
2.54 cm
( )
100 cm
1 m
( )
103 m
1 km
( )
102 cm
1 m
( )
1 in
2.54 cm
( )
1 in
2.54 cm
( )
1 ft
12 in
1 km
= ft
3281

4. ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 5280 ft
Let’s try a more complicated problem.
How many millimeters are in 2.50 miles?
What is the fourth step?
What is the third step?
What is the fifth step?
What is the first step?
What is the second step?
What is the sixth step?
( )
5280 ft
1 mi
( )
12 in
1 ft
( )
1 in
2.54 cm
( )
1 m
102 cm
( )
1 m
103 mm
( )
1 mi
5280 ft
( )
1 ft
12 in
( )
2.54 cm
1 in
( )
102 cm
1 m
( )
103 mm
1 m
( )
5280 ft
1 mi
( )
12 in
1 ft
( )
2.54 cm
1 in
( )
1 m
102 cm
( )
103 mm
1 m
2.50 mi
= mm
2.5 x x 12 x  x =
4.02 x 106 mm