The following examples begin with a measurement in decimal form. The measurements are converted to fractions of an inch as seen in the architecture template. Uploaded - June 2014

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.

## The following examples begin with a measurement in decimal form. The measurements are converted to fractions of an inch as seen in the architecture template. Uploaded - June 2014

HOMEExample 1Convert 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 2Convert 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 3Convert 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 4Write 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 5Write 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 6Convert 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 7What 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.