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The sides of a rectangular tile are measured to the nearest centimeter, and they are found to be six centimeters and eight centimeters.
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Rounding to the same number of significant figures that the side lengths were measured to, what is the area of the tile?
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Okay, so in this question, we’ve been told that we’ve got a rectangular tile and the side lengths of this rectangular tile were measured to the nearest centimeter.
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We’ve been told that these measured values were six centimeters for one of the lengths and eight centimeters for the other length.
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And we’ve been asked to find the area of the tile rounded to the same number of significant figures that the lengths were measured to.
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In other words, even though we’ve been told the lengths were measured to the nearest centimeter, we do not want to round the area of a tile to the nearest centimeter.
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We want to round it to the same number of significant figures as the length measurements, six centimeters and eight centimeters, and that’s an important point to remember.
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But first, let’s recall that the area of a rectangle, we’ll call it 𝐴 subscript a rectangle, is equal to the length of the rectangle multiplied by the width of the rectangle.
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And we can see in our diagram that this is the length and then this must be the width.
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Therefore, to find the area of our rectangular tile, we can say that this is equal to six centimeters, which is the length, multiplied by eight centimeters, which is the width.
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And then, to evaluate this further, we firstly multiply the numbers, six times eight, and then we multiply the units together, centimeters times centimeters, which gives us square centimeters.
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Now, because six times eight is 48, we find that the area of our rectangular tile is 48 squared centimeters or 48 centimeters squared.
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But remember, this is not our final answer.
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We need to round our answer for the area to the same number of significant figures that the side lengths were measured to.
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And we can see that each side length, for example, eight centimeters, is measured to one significant figure because, in this particular case, eight is a significant figure and it’s the only one.
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And the same is true for six centimeters.
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It’s also measured to one significant figure.
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Which means that we need to give our answer for the area to one significant figure as well.
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Since this four here, this first number in our value, is a significant figure, this means we’re going to round at this position here.
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But in order to work out what happens to this four, we need to look at the next number.
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This value is an eight, and eight is larger than or equal to five, and so our four is going to round up.
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In other words then, to one significant figure, the area is 50 square centimeters.
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And hence, we found the answer to our question.
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If the side lengths of a rectangular tile are found to be six centimeters and eight centimeters, then the area of this tile, to one significant figure, is 50 square centimeters.