Video Transcript
Sophia uses a centimeter ruler to
measure the length of a straight line as shown in the diagram. She determines that the length of
the line is 9.4 centimeters. Which of the following statements
explains why the answer is incorrect? A) The zero marker of the ruler was
not positioned at the start of the line. Thus, the line is actually shorter
than 9.4 centimeters. B) The zero marker of the ruler was
not positioned at the start of the line. Thus, the line is actually longer
than 9.4 centimeters. C) The ruler is not parallel to the
line. D) The maximum resolution of the
ruler is one centimeter. Thus, the length of the line should
be recorded as nine centimeters. E) Measurements using a ruler
should always be rounded up. Thus, the length of the line should
be recorded as 10 centimeters.
Okay, so first things first, here’s
the line that we’re trying to measure. We can see that the line is
pointing in this direction, and so is the edge of the ruler that we use to make
measurements. They’re both aligned. And therefore, the line and the
ruler are in fact parallel. This means that option C is
immediately ruled out because they say that the ruler is not parallel to the
line.
So Sophia has done this
correctly. She has aligned the ruler with the
straight line. Now let’s consider options D and E
before we do anything else. Looking at option D, this says that
the maximum resolution of the ruler is one centimeter. Well, this is clearly not true. Of course, there are markings every
centimeter, but there are also smaller markings every millimeter. And so the maximum resolution of
the ruler is not one centimeter. It’s actually one millimeter. So option D is not our answer
either.
Moving on to option E, this one
says that measurements using a ruler should always be rounded up. Well, that is definitely bad
practice. We should not be doing this,
because if we’re rounding everything up, then unless some length that we’re
measuring is perfectly on a centimeter mark, we would always end up rounding it
up. And so we would always measure it
to be longer than it actually is.
The idea with rounding though is
that, on average, half of the time we would round up and half of the time we would
round down. This way, any errors in the
rounding up would be canceled out by the errors in the rounding down. That’s if we’re measuring different
lengths of course. But if we’re always rounding up,
then we’re introducing a systematic error. And so option E is out of the
question as well.
So let’s now look at options A and
B. They start off very similarly. Both of them say that the zero
marker of the ruler was not positioned at the start of the line. Option B says exactly the same
thing. And that, in fact, is true. Here’s the zero marker of the line,
and here is the start of the line. So this is going to result in an
error in the measurement. But what is the consequence of
this?
Well, option A says that the line
is actually shorter than 9.4 centimeters. That’s shorter than what Sophia
measured it to be, which happens to be a reading here at 9.4 centimeters on the
ruler, whereas option B says that the line is actually longer than 9.4
centimeters. So which is it?
Well, to answer this question, we
need to imagine that we correctly placed a ruler next to the line. We need to ensure that the zero
mark — that’s this mark over here — meets up with the start of the line. To do this, we would either have to
move the ruler left or move the straight line to the right. Either way, we would have to do
this until this end of the line moved to the zero mark. And we can imagine this as just
moving the straight line to the right.
But then in that situation, this
end of the line moves to the right as well. And so once we’ve aligned the line
correctly, the actual reading is going to be larger than 9.4 centimeters. It’s gonna be somewhere closer to
10 centimeters. And hence, the line is actually
longer than 9.4 centimeters. That is what option B says, and so
option A is incorrect.
Hence, we found our answer to the
question. The length of the line as measured
by Sophia is incorrect because the zero marker of the ruler was not positioned at
the start of the line and thus the line is actually longer than 9.4 centimeters.
