# PracticeConversion Factors 1

#### puremath

##### New member
Good morning, Mark. Before posting my linear speed and angular speed questions in the trig forum, I need to review conversion factors, which dates back to middle school for me. It has been decades since I last played with conversion factors.

We are all human beings and tend to forget things as we age. I'll post 4 conversion factor threads with 3 questions per thread in the pre-algebra forum. I will then return to the trig forum with my linear and angular speed questions, which I find to be interestingly hard.

Use conversion factors to convert as requested.

A. 80 km/hr to ft/sec

B. 2.5 rev/sec to radian/sec

C. 15 meters/sec to miles per hour

#### MarkFL

##### La Villa Strangiato
Math Helper
A. $$\displaystyle x\frac{\text{km}}{\text{hr}}=x\frac{\text{km}}{\text{hr}}\cdot\frac{50\text{ in}}{127\text{ cm}}\cdot\frac{1\text{ ft}}{12\text{ in}}\cdot\frac{100\text{ cm}}{1\text{ m}}\cdot\frac{1000\text{ m}}{1\text{ km}}\cdot\frac{1\text{ hr}}{3600\text{ s}}=\frac{3125}{3429}x\frac{\text{ft}}{\text{s}}$$

Give B abd C a try.

#### puremath

##### New member
A. $$\displaystyle x\frac{\text{km}}{\text{hr}}=x\frac{\text{km}}{\text{hr}}\cdot\frac{50\text{ in}}{127\text{ cm}}\cdot\frac{1\text{ ft}}{12\text{ in}}\cdot\frac{100\text{ cm}}{1\text{ m}}\cdot\frac{1000\text{ m}}{1\text{ km}}\cdot\frac{1\text{ hr}}{3600\text{ s}}=\frac{3125}{3429}x\frac{\text{ft}}{\text{s}}$$

Give B abd C a try.
1. What is x here?
2. Explain what you did in steps.

#### puremath

##### New member
Part B.

(2.5 rev)/sec • (2π rad)/(1 rev)

Yes?

#### puremath

##### New member
Part C.

(15 m)/sec • (0.001 miles)/1 meter • (60 sec)/hour

(15 • 0.001 miles • 60)/hour

0.90 miles/hour

Yes?

#### MarkFL

##### La Villa Strangiato
Math Helper
For part C, a mile isn't 1000 meters and an hour isn't 60 seconds.

#### puremath

##### New member
Part C.

(15 m)/sec • (0.001 miles)/1 meter • (3600 sec)/hr

Correct?

#### MarkFL

##### La Villa Strangiato
Math Helper
You are still equating 1 mile with a kilometer.

$$\displaystyle x\frac{\text{m}}{\text{s}}=x\frac{\text{m}}{\text{s}}\cdot\frac{50\text{ in}}{127\text{ cm}}\cdot\frac{100\text{ cm}}{1\text{ m}}\cdot\frac{1\text{ ft}}{12\text{ in}}\cdot\frac{1\text{ mi}}{5280\text{ ft}}\cdot\frac{3600\text{ s}}{1\text{ hr}}=\frac{3125}{1397}x\frac{\text{mi}}{\text{hr}}$$

Now we now that given a speed in m/s, to convert to mph, we multiply the given speed by 3125/1397. And we know this is exact.

#### puremath

##### New member
You are still equating 1 mile with a kilometer.

$$\displaystyle x\frac{\text{m}}{\text{s}}=x\frac{\text{m}}{\text{s}}\cdot\frac{50\text{ in}}{127\text{ cm}}\cdot\frac{100\text{ cm}}{1\text{ m}}\cdot\frac{1\text{ ft}}{12\text{ in}}\cdot\frac{1\text{ mi}}{5280\text{ ft}}\cdot\frac{3600\text{ s}}{1\text{ hr}}=\frac{3125}{1397}x\frac{\text{mi}}{\text{hr}}$$

Now we now that given a speed in m/s, to convert to mph, we multiply the given speed by 3125/1397. And we know this is exact.
This topic is making no sense to me.

#### MarkFL

##### La Villa Strangiato
Math Helper
Notice that each fraction is equal to 1 since the numerators are equal to the denominators,

#### puremath

##### New member
Notice that each fraction is equal to 1 since the numerators are equal to the denominators,
Cool. We will pick this up from my new spot.