The length of this rug is 38.4 in. and the width is 24.2 in.
d. Calculate the area of the rug, in square centimeters, to the correct number of significant figures. (Area = Length x Width)

Question

The length of this rug is 38.4 in. and the width is 24.2 in.

d. Calculate the area of the rug, in square centimeters, to the correct number of significant figures. (Area = Length x Width)

Accepted Answer

Welcome back everyone. A rectangular floor mat has a width of 105 inches and a length of 215 inches. What is its area in squared centimeters express the answer to the correct number of sig figs. And we're told that the area of a rectangle is the product of its width and length. So taking the area of our rectangular floor mat, we're told that it's given by the product between the width of the format expressed by the variable W multiplied by the length of our format expressed by the variable L. So plugging in our variables, we're given a width of 105 inches and this is multiplied by the given length of 215 inches and taking the product between these two terms, we get a area equal to 22,575 squared inches. Now note that we're told to give the area in centimeters squared. So we're gonna take our area in squared inches, 22,575 squared inches. And we're going to set this equal or sorry, we're going to multiply by our conversion factor to go from inches in the denominator to centimeters in the numerator. And let's recall that for one inch in the denominator, we have an equivalent of 2.54 centimeters. Now to get this to be squared, we're going to take this entire conversion factor in parentheses and raise it to a power of two which will allow us to then cancel out squared inches and leaves us with squared centimeters. So this results in our area now equal to 145,000 644.87 squared centimeters. Now, to determine our correct number of sig figs note that our width and length both consist of three sig figs total. And so our final answer should have three significant figures as the least precise measurement. And so to round this to about three sig figs, we're gonna use scientific notation to multiply by a power of 10. And so we're gonna take our decimal point and move it so that we have just three significant figures expressed, which would give us 1.45 times 10 to the positive fifth power since we moved our decimal 0.5 times or five places. And so this is going to be in squared centimeters and this would be our final answer to complete this example as the area of our rectangular floor mat 1.46 times 10 to the fifth power squared centimeters. And this will correspond to choice a as the correct answer. So I hope this made sense and let us know if you have any questions.

The length of this rug is 38.4 in. and the width is 24.2 in.
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d. Calculate the area of the rug, in square centimeters, to the correct number of significant figures. (Area = Length x Width)

Verified video answer for a similar problem:

Key Concepts

Area Calculation

Unit Conversion

Significant Figures