Given that 1 meter is 3.28 feet, convert the following: __m²= 543 ft²

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In order to convert between different units of measurement, we use what is called a conversion factor. A conversion factor is a ratio (written as a fraction) where one of the units is the numerator and one is the denominator. In order to convert one type of unit to another, you will cross-multiply the starting value by the conversion factor. *We decide which unit goes on the top based on what we are trying to convert. Basically, the units have to match - the units of one numerator should be the same as the numerator of the second fraction. In this case, we know the conversion factor to be the number of feet in one meter. This can be written as either of the following: ^{1 m} / _{3.28 ft} OR ^{3.28 ft} / _{1 m} These can both be used as conversion factors because the ratio of feet to meters is the SAME in both. In order to decide which version to use, we come to our problem. We are asked to convert 543 ft² to meters. Since the number of meters is unknown, we're going to represent it as x. In order to solve using ratios, we need to write the first ratio as a fraction. We know that we have 543 ft², so that will be the numerator in our fraction (ratio) to start. We have decided to use x to represent the unknown number of meters (which will also be squared), so our fraction (ratio) will look like this: ^{543 ft2}/_x Now, we know which version of the conversion factor to use. Feet is the unit used in the numerator, so we will use the conversion factor that also has feet in the numerator: ^{3.28 ft} / _{1 m} Now we can set the ratios equal to one another in preparation to solve. ^{543 ft2}/_x= ^{3.28 ft} / _{1 m} However, before we can move forward, we have to make sure the units match. Even though we're using meters and feet in each, the left hand side of the equation has squared units, while the right hand side does not. We cannot combine terms if they don't have the same units. Remember that when something is "squared," it means that it has been multiplied by itself. For example: 2²= 4 3²= 9 2 meters • 2 meters = 4m² Therefore, in order to "square" the right side of the equation, we are going to multiply the entire ratio (fraction) by itself (and round any decimals to the nearest tenth to make the math easier!) _{^{3.28 ft} / 1 m}• ^{3.28 ft} / _{1 m}₌^10.76ft2/_1m Now, we can move forward and solve. ^{543 ft2}/_x = ^10.76ft2/_1m2 Cross multiply across the equal sign to eliminate the ratios. This means you multiply the first numerator by the second denominator, and the first denominator by the second numerator. 543 ft² • 1m² = x • 10.76 ft² 543 ft²m² = x • 10.76 ft² Now, we can see that we have the 10.76 ft² multiplying the x, so we have to divide both sides by 10.76 ft² . Note that when you divide, you also divide by the units. This cancels out the ft² on the left hand side as well. Round the answer to the nearest tenth. 543 ft²m² ÷ 10.76 ft² = x • 10.76 ft²÷ 10.76 ft² 50.47 m²= x Answer: 50.47 m²= 543 ft²

Given That 1 Meter Is 3