# Question Video: Expressing a Small Quantity Using Base Units Physics • 9th Grade

The width of a human hair is measured to be 17.0701 micrometers. What is this length expressed in meters?

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### 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.