# Unit Conversions

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Example 1
Convert 4.294 feet to feet and inches (to the nearest 16th of an inch)
4 feet + .294 of a foot
4 feet + .294 ft * 12in/ft
4 feet + 3.528 inches
4 feet + 3 inches + .528 of an inch
We look at the decimal .528 and find the boundaries in 16ths of an inch.
8/16 = .500
.528
9/16 = .5625
The decimal is closer to 8/16 so SketchUp will round down to 8/16.
The fraction 8/16 simplifies to ½ of an inch.
ANSWER: 4 feet 3 ½ inches

Example 2
Convert 4.528 feet to feet and inches (to the nearest 16th of an inch)
4 feet + .528 of a foot
4 feet + .528 ft * 12 in/ft
4 feet + 6.336 inches
4 feet + 6 inches + .336 of an inch
We look at the decimal .336 and find the boundaries in 16ths of an inch.
5/16 = .3125
.336
6/16 = .375
The decimal is closer to 5/16 so SketchUp will round down to 5/16.
ANSWER: 4 feet 6 5/16 inches

Example 3
Convert 0.5 feet to inches.
0.5 of a foot
0.5 ft * 12 in/foot = 6 inches
This one comes out even, but some students will say the answer is 5 inches, why?
ANSWER: 6 inches

Example 4
Write 2.892 feet as feet and inches (to the nearest 4th of an inch)
2 feet + .892 of a foot
2 feet + .892 ft * 12 in/ft
2 feet + 10.704 inches
2 feet + 10 inches + .704 of an inch
We look at the decimal .704 and find the boundaries in 4ths of an inch.
2/4 = .500
.704
3/4 = .750
The decimal is closer to 3/4 so SketchUp will round up.
Answer: 2’ 10 3/4 “
Check: 2 + 10.75/12 = 2.8958’ which is higher because we rounded up.

Example 5
Write 0.3’ to the nearest 8th of an inch.
0.3 of a foot
0.3 ft * 12 in/ft
3.6 of an inch
3 inches and .6 of an inch
Here we will use 8ths to find the boundaries:
4/8 = .50
.60
5/8 = .625
The decimal 0.6 is closer to 5/8 so Sketchup will round up.
Answer: 3 5/8 inches
Check: 3+(⅝)/12 = 3.302083' which his higher because we rounded up.

Example 6
Convert 6,289 feet to yards and feet.
First convert to yards
6,289 feet * ⅓ yards/foot = 2096.3333 yards
2096 yards + .333... of a yard
[You can keep the repeating decimal in your calculator by subtracting 2096.]
0.333 ... * 3 feet/yard = 1 foot
Answer: 2096 yards and 1 foot
Check: 2096 * 3 + 1 = 6,289

Example 7
What is 0.75 yards written in feet and inches?
0.75 yards * 3 feet/yard = 2.25 feet
2 feet + .25 of a foot
2feet + .25 * 12in/ft
2 feet 3 inches
This one comes out even.
Answer: 2 feet 3 inches or 2 ¼ feet
Check: 2.25/3 = 0.75 yards

MATH 360 Problem Set is posted here and on Blackboard.

>>>>Application Problem >>>>
A1. The window on my microwave measures 10” by 5 7/16”. What is the length of the diagonal of the window to the nearest 16 of an inch?

Calculation: use the Pythagorean theorem to find the measure of the diagonal
11.3827 inches = I1 inches + 0.3827 of an inch
The decimal 0.3821 is closest to which sixteenths of an inch?
I tried 5/16 = .3125, and then went to 6/16 = .375 and then to 7/16 = .4375
The decimal is closest to 6/16.
The window on the door of my microwave is approximately 11 6/16 inches or 11 3/8 inches long.

Create and then check your own problems. Consider submitting to this Wiki.
*This lesson was first taught in a geometry class in Fall 2012. I like how the students can use SketchUp to check their work.