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.
