How do conversions

Notice that putting "kg" on the bottom makes the units cancel and gives an answer with the units of "lb". How do unit conversions work? Chemistry Measurement Unit Conversions. Jun 17, Explanation: Watch How to Convert between units here. Ernest Z. Explanation: For example, you buy a 1. How much is this in pounds? Dimensional analysis is a technique used to convert measurements. Some measurements have one dimension, for example length.

A square shape area has two dimensions e. Converting between measurement units is a very important skill when working within and between measurement systems. This problem-solving method is based on the principle that quantities are defined as equalities.

A conversion factor is an expression for the relationship between units that is used to change the units of a measured quantity without changing the value. A conversion ratio or unit factor always equals one 1 , where the numerator and the denominator have the same value expressed in different units.

A numerator represents the parts out of the whole or how much you have. A denominator represents the total number of parts of the whole. Performing the math calculation 3 divided by 4 transforms the number into a decimal fraction, 0. This method uses the fact that any number or expression can be multiplied by "one" without changing its value. This allows the conversion of units by multiplying the initial measurement by one or more forms of the number 1.

Numbers with units, like Once you grasp this, you see at once why the laws of units work as they do. Obvious, right?

Because multiplying by 1—a carefully chosen form of 1—is the key to converting units. Let me illustrate with an example. Summary: to convert units, construct a fraction that is equal to 1, multiply the original measurement by that fraction, and simplify. How is that multiplying by 1? A number with units is different from a number without units or with different units, just as 8 x is different from both 8 and 8 y.

Think of it this way: 3. If the top and bottom of the fraction are equal, the fraction equals 1 and the value after multiplying is the same as the value before multiplying—but expressed in different units, which of course is the whole point. Anybody knows that to convert hours to minutes you have to multiply by But I deliberately chose a simple example to show the method. If you follow the procedures on this page, it will be impossible for you to multiply by a conversion factor where you should divide, or vice versa.

If you ended up with 0. But second best is to work the problem carefully and apply some test for reasonableness, like this one. You might be wondering how I knew to pick that particular fraction that was equal to 1.

There are just two simple steps :. Find a conversion factor between the given units and the desired units, and write it as an equation. Either equation will work equally well.

Convert that equation to a fraction with the desired units on top and the given units on the bottom. More formally, divide both sides by the value of the side that contains the given units. Example: To convert from miles to kilometers, you need a fraction with the desired units kilometers on top and the given units miles on the bottom. Based on the above conversion factors, that fraction must be either. Either one will work just fine for the conversion.

Example: If the original measure was Many books have tables of conversions, including the venerable Handbook of Chemistry and Physics. There are also several good sources on line. Looking at such references, you may note that this article uses common abbreviations like sec seconds and hr hours , rather than the official abbreviations s and h, respectively. That is deliberate, since most students are more familiar with the longer forms. If you can remember some conversions, you may be able to combine them to avoid looking up a specific conversion.

The problem asks us to convert weeks to minutes, so the units we want are minutes. Step 3: Find conversion factors that will help get the units we want. We need to convert weeks to days to hours to minutes so we will need the following conversions:. Since the runner only runs for 1 hour per day, that is the unit conversion we use instead. Step 4: Arrange conversion factors so unwanted units cancel out. We know that Sara has been training for 18 weeks, so we need to change weeks to days.

Now we have:. Solution Video 1 - 4 Transcript. First, convert minutes into seconds. In this problem, we have a pound turkey, so the units we have are pounds. The problem asks us to find out how many hours we need to cook the turkey for, so the unit we want is hours. We know that our turkey is 15 lbs, which need to be converted to minutes, then to hours.

We can set it up like this:.