Study Guide

# Algebraic Expressions - Unit Conversion

## Unit Conversion

Here's a video to showcase unit conversion in action.

Okay, now how do you use all this newfound knowledge to do something practical? There are a bazillion ways (estimated) to use formulas, but one common one is unit conversion, the converting of a number to an equivalent value that's expressed in different terms. This can mean translating a temperature in Celsius to Fahrenheit, translating U.S. dollars to yen, or translating any one of our silly American systems of measurement over to the far superior metric system. Boy oh boy, if only we could get our hands on the wise guy who invented the foot...

If you'd like to see a huge list of conversion formulas, including conversions between units you've probably never even heard of, check this out.

For our purposes, however, we'll go through a much smaller selection of conversion formulas having to do with temperature, weight, distance, speed, and money.

• ### Temperatures

Let F be degrees Fahrenheit, a unit commonly used in the United States, and let C be degrees Celsius, used almost everywhere else. Oh, but ours is the right one. Sure...

We can convert from one temperature system to the other using the following formulas:  ### Sample Problem

If the temperature is 86 degrees Fahrenheit, what is the temperature in Celsius?

First of all, it shouldn't matter. We're at home, indoors, mostly naked, and standing in the kitchen with the refrigerator door wide open.

Okay, we'll play along.

Let F = 86. Then C = 5/9(86 – 32) = 5/9(54) = 30, so the temperature is 30 degrees Celsius.

That sounds deceptively cool. No wonder everywhere else is crazy.

• ### Weights

While some conversion formulas force you to round up or down, they're close enough for reliable estimates. If you're cooking, for example, you probably won't ruin your cookies by being a single degree off. Unless you're a total perfectionist like Mrs. Fields, in which case you need to get yourself an oven with a more elaborate temperature dial.

Let's try another one. To convert from kilograms to pounds (approximately), multiply the number of kilograms by 2.2. To go the other way, divide the number of pounds by 2.2. Letting represent pounds and K represent kilograms, we get the following formulas: P = 2.2K

If The Merchant of Venice's Shylock wanted a pound of flesh, you could give him about 0.45 kilograms of flesh, and that would be the same thing. Hopefully it doesn't tick him off that you're using a different system of measurement. He doesn't seem like someone whose bad side you would want to be on.

### Sample Problem

A bread recipe from Germany says to add 0.5 kg of flour. How many pounds of flour is this?

When K = 0.5, P = 2.2(0.5) = 1.10. Therefore, 0.5 kg of flour is 1.1 pounds of flour. That's a lot of bread. We may need to pick up some more cold cuts.

• ### Distances and Speeds

Let's talk kilometers and miles for a sec. If you're an American and you ever visit Canada, you might be thrown off by the speed limit signs. We know we were. That's because everything is in kilometers per hour instead of miles per hour when you get up north. Likewise, a Canadian might be super confused by America's mph signs—they'll look really slow compared to what Canadians are used to. So how do we convert between the two?

Let M be miles, and let be kilometers:

K = 1.609M
M = 0.6214K

Since (this is one of those important formulas you should probably commit to memory), in order to convert a speed from miles per hour (mph) to kilometers per hour (kph), we multiply by 1.609: To convert a speed from kph to mph, we multiply by 0.6214.

### Sample Problem

A sign in Canada says "Speed Limit 110 kph (eh)." How fast is this speed in mph?

To convert a speed from kph to mph, we multiply the speed by 0.6214. Therefore, 110 kph is 0.6214(110) = 68.354, or approximately 68 mph. That should be just fast enough to power your way through a moose.

• ### Money

At this website, you can figure out how much your dollar is worth in about any currency unit in the world. This site may be particularly useful to you if you do, in fact, have only one dollar. In that case, you might want to consider moving to Bali to get the most bang for your buck.

On October 29, 2015—nothing special about this date; we just needed to pick one, and this one seemed as good as any—\$1 was worth 0.65258 British pounds, and 1 British pound was worth \$1.53237. If we let be U.S. dollars and P be British pounds, we can convert between dollars and pounds using the following formulas:

P = 0.65258D
D
= 1.53237P

Awesome. Now we can buy a bap (that's a type of bread, for those of you not in the know) with American money or a deep-fried Twinkie (a type of "bread"?) with British currency. How worldly we are.

Bear in mind, though, that currency conversions change literally every day, depending on the world market. Pop over here if you're curious about how much an American buck is worth in British pounds right this second.

### Sample Problem

On October 29, 2015, how many British pounds could you get for \$1,000,000?

When D = 1,000,000 then P = 0.65258(1,000,000) = 652,580. One million dollars gets you 652,580 pounds. Should be easier to squeeze into a briefcase at least.

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