Question Video: Calculating the Area of an Object to an Appropriate Number of Significant Figures | Nagwa Question Video: Calculating the Area of an Object to an Appropriate Number of Significant Figures | Nagwa

Question Video: Calculating the Area of an Object to an Appropriate Number of Significant Figures Physics • First Year of Secondary School

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The lengths of the sides of a sheet of paper are measured to be 7.8 cm and 14 cm. What is the area of the sheet? Give your answer to the nearest square centimeter.

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Video Transcript

The lengths of the sides of a sheet of paper are measured to be 7.8 centimeters and 14 centimeters. What is the area of the sheet? Give your answer to the nearest square centimeter. Is it (A) 22 square centimeters, (B) 110 square centimeters, (C) 55 square centimeters, (D) 44 square centimeters, or (E) six square centimeters?

So in this question, we’ve got the lengths of the sides of a sheet of paper. And we know that these two lengths are measured to be 7.8 centimeters and 14 centimeters. So here is our sheet of paper and here are its dimensions. We’re asked to find the area of the sheet. To find out the sheet’s area, we know that we have to multiply the length of the sheet by the width of the sheet, which, in other words, happens to be 7.8 centimeters times 14 centimeters. Plugging this into our calculator gives us an answer of 109.2 centimeters squared. But this isn’t our final answer, because we haven’t yet rounded to an appropriate number of significant figures.

Also, as a quick aside, we know that the units are centimeters squared because the two lengths that we had were both in centimeters. So we multiplied the two numbers together to give us 109.2 and the centimeters by the centimeters to give us centimeters squared.

Anyway, let’s get back to rounding. Now in the question, we’ve been given two quantities, 7.8 centimeters and 14 centimeters. If we look carefully, we see that both of these values have been given to two significant figures. Look, here’s the first significant figure and here’s the second. Similarly, for 14 centimeters, here’s the first significant figure and here’s the second. Now, the rule for physics calculations is that we have to give our final answer to the same number of significant figures as the contributing quantity with the least number of significant figures in the question. Now if that sounds a bit confusing, let’s break it down.

Basically, the question will give us lots of different values usually. We need to find the one value that has the lowest number of significant figures. And we need to give our final answer to that number of significant figures as well. In this case, they both have two significant figures, so we don’t need to worry so much. All we need to do is to give our answer to two significant figures.

So in our answer for the area, here’s the first significant figure and here’s the second. Now, it’s the one afterwards — it’s the third significant figure — that will tell us what happens to the second one. If this third significant figure is greater than or equal to five, then our second significant figure rounds up. If, however, it’s less than five, then our second significant figure stays the same. So we look carefully at our third significant figure; it’s a nine. Nine is larger than five. So the second significant figure rounds up. The zero is going to become a one. And so, our answer becomes 110 centimeters squared.

Finally, the question tells us to round to the nearest square centimeter. And our value happens to already be written to that precision, so this is our final answer. Therefore, option (B) is correct. The area of the sheet of paper is 110 square centimeters.

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