Video Transcript
The width of a human hair is
measured to be 17.0701 micrometers. What is this length expressed in
meters? 1.71 times 10 to the negative five
meters. 1.70701 times 10 to the negative
five meters. 1.70701 times 10 to the negative
six meters. 1.0701 times 10 to the negative
five meters. 1.0701 times 10 to the negative six
meters.
This question is asking us to
relate the unit micrometers to the unit meters. The first thing that we notice is
that the word “micrometers” consists of two parts: the prefix micro- and the unit
meters. We can recall that when we add a
prefix to a unit, the prefix stands for a power of 10. In particular, the prefix micro-
stands for 10 to the negative six. So we can write that micro- is
equal to 10 to the negative six, where what we mean by this equality is that
whenever we have a prefix micro- affixed to a unit, we can always replace that with
10 to the negative six times that unit without changing the overall value of the
quantity. This also means that we can write
that micrometers are equal to 10 to the negative six meters.
Now, our value is 17.0701
micrometers, which using our relationship we can rewrite as 17.0701 times 10 to the
negative six meters. This is almost our answer. However, all of our choices have
exactly one digit to the left of the decimal point. But 17.0701 has two digits to the
left of the decimal point. So we need to move the decimal
point one place to the left. When we move the decimal point one
place to the left, this is the same thing as dividing by 10. So, in order to counteract this
division by 10 and keep the same value, we also need to multiply the number by 10
elsewhere. 10 to the negative six times 10 is
10 to the negative five. So 1.7071 times 10 to the negative
five is equal to 17.0701 times 10 to the negative six.
So, looking at our answer options,
we see that the correct answer is (B). 17.0701 micrometers is equal to
1.70701 times 10 to the negative five meters.
