Using your knowledge of metric units, English units, and the information on the back inside cove

Using your knowledge of metric units, English units, and the...

Key Concepts

Dimensional Analysis

Dimensional analysis is the process of converting one set of units to another using conversion factors. It involves multiplying by fractions that equal one, ensuring that units cancel appropriately until the desired unit is achieved. This method is fundamental for verifying that equations and calculations are dimensionally consistent.

Conversion Factor

A conversion factor is a ratio that expresses how many of one unit are equivalent to another unit. It is essentially a fraction equal to one that can be used to multiply a measurement, allowing it to be expressed in different units while maintaining its value. Knowing exact conversion factors is crucial in achieving accurate unit conversions.

Metric System

The metric system is an internationally recognized decimal-based system of measurement. It includes units such as meters, grams, and liters, which are often interconnected by powers of ten. This system simplifies conversions and calculations by allowing the easy scaling up or down of units through multiplication or division by ten or its powers.

English Units

The English system, also known as the Imperial system, consists of units such as inches, feet, pounds, etc. These units are not based on a decimal system, which often requires specific conversion factors to translate measurements into the metric system. Understanding these factors is key to accurately converting values between systems.

Area Conversion

When converting units for area measurements, the conversion factors must be squared because area is a two-dimensional measure. This means that if a single linear unit conversion is known, converting area units involves squaring the value of that conversion factor. This concept ensures precision when switching between units such as square feet and square centimeters.

Transcript

00:01 For examples in which we want to determine the conversion factors in order to convert from one unit to another.

00:07 So we're going to be using prior knowledge and just kind of be practicing going from one unit to another.

00:13 So here we have inches to centimeters, pounds to grams, micrograms to grams, and squared feet to squared centimeters.

00:25 So we can go ahead and start with inches to centimeters.

00:28 And this is one of the easier conversion factors.

00:31 There's not a lot to know.

00:32 But if we wanted to go ahead and write it down, that we know that for every inch, so if you take a look at a ruler, and you want to, in a sense, kind of line up the number of centimeters that are present within one single inch, you'll see that for every inch, we can put one inch here, we can put one ion, is equal to 2 .0 .2.

00:59 5, 4 centimeters.

01:03 So that's a conversion factor that is good to know.

01:06 It's one also one of the more known ones as well.

01:10 And it's rather easy also to remember.

01:14 So it's definitely something that i'd recommend to kind of keep in your mind.

01:19 So this would be the conversion factor from going from inches to centimeters.

01:23 You would just multiply whatever inches you are dealing with at times 2 .54 and then you'll get them in.

01:30 Centimeters.

01:32 For the next one, we want to convert pounds to grams.

01:35 And in order for us to do this with what we know, what we would want to do is go from convert pounds to kilograms because we do have a conversion factor between kilograms and pounds and then convert kilograms to grams.

01:50 So we can start with dimensional analysis here.

01:53 We can put one pound, one lb.

01:58 And then what we can do here we know what the conversion factor that's really crucial here is that for every kilogram one kilogram is equivalent to 2 .2 pounds so we're going to put 2 .2 pounds in the bottom because we want to make sure that our pounds cancel so lbs right and then one kilogram at the top for one kilogram we can we have 2 .2 pounds all righty and now from kilograms we want to convert to so we know that for every kilogram, there are 1 ,000 grams present.

02:38 That is another conversion factor.

02:40 Kilo, the prefix kilo means 1 ,000.

02:42 So that's where we get the 1 ,000 grams from.

02:45 So 1 kilogram is equal to 1 ,000 grams.

02:55 And then this would be the math that you would do.

02:57 You can go ahead and divide 1 ,000 by 2 .2 pounds, and then you'd be able to get the amount in grams.

03:06 So let's go ahead and just to see that everything cancels out.

03:10 You see that now we end up in just grams.

03:14 I mean just going to start labeling these one and two here.

03:17 The third one is micrograms to grams...