# Question Video: Identifying the Power of Ten Represented by a Unit Prefix Physics • 9th Grade

Which of the following is equal to one femtosecond when multiplied by one second? [A] 1 × 10¹⁵ [B] 1 × 10⁻¹⁵ [C] 10 × 10⁹ [D] 0.1 × 10⁻⁹ [E] 1 × 10⁻¹²

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### Video Transcript

Which of the following is equal to one femtosecond when multiplied by one second? One times 10 to the 15, one times 10 to the negative 15, 10 times 10 to the nine, 0.1 times 10 to the negative nine, one times 10 to the negative 12.

This question is asking us about one femtosecond and specifically how to relate one femtosecond to one second. All of our answer choices are numbers, and we are asked which of these numbers when multiplied by one second is equal to one femtosecond. In other words, how many seconds are in one femtosecond?

Now, the answer to this question is just a fact that we will need to memorize in one of two ways. But before we get to that, let’s understand qualitatively what we mean when we write something like one femtosecond. Inside the word femtosecond, we see the word second, which is one of the base units we use in physics. We see then that femto- is a prefix for the base unit. That is, it’s a part of the word that comes before the main part.

Adding a prefix to a base unit is a shorthand way of expressing some number of that unit. In particular, almost all prefixes used in physics correspond to a power of 10 where the exponent is a multiple of three. For example, the prefix milli- corresponds to 10 to the negative three, or one one thousandth. So when we say, for example, one millisecond, what we mean is one one thousandth of a second. It’s important to understand exactly what we mean when we write this equality. What we mean is that we can replace 10 to the negative three times a base unit with the prefix milli- attached to that base unit without changing the quantity and vice versa. So five times 10 to the negative three seconds and five milliseconds represent exactly the same value of a physical quantity.

As an aside, just like we represent units with single letters, we also represent prefixes with single letters. So s is seconds and ms is milliseconds because the m stands for milli-, so mg would be milligrams, mm is millimeters, and so on.

We now return to answering our question. And as we said before, to answer this question, we simply need to memorize which power of 10 corresponds to the prefix femto-. Unit prefixes are used all over physics, so it is worth memorizing them. And unfortunately, there is no way to derive which exponent corresponds to which prefix name, so memorization really is our only option. Here is a list of the first five prefixes and associated powers of 10 for describing quantities that are smaller than those described by the base unit. As we can see, the last prefix on this list is femto-, which corresponds to 10 to the negative 15. And the question was asking us about femtoseconds, so we can see from our list that one femtosecond is 10 to the negative 15 seconds. And the correct answer is (B) one times 10 to the negative 15 multiplied by one second is equal to one femtosecond.

Now, we mentioned that there are two ways to memorize this answer. The first is to simply memorize this list of correspondences. The second is to memorize both the name and order of each prefix. So milli- is first, then micro-, then nano-, then pico-, then femto-. Then, anytime we need to figure out which exponent corresponds to which prefix, we simply recall that when counting the exponents, we count by multiples of three. So we recall that this list is the correct ordering of the first five prefixes for quantities smaller than the base unit. And then, all we need to do is count by multiples of three, starting with negative three for milli- and then negative six for micro-, negative nine for nano-, negative 12 for pico-, and negative 15 for femto-.

So even though we need to memorize the answer to this question, we have two ways to do it. Once we know the name of each prefix, we can either memorize the corresponding powers of 10 or the corresponding order and from that order work out the corresponding powers of 10. It’s important to stress that it doesn’t matter what method we use to memorize these correspondences as long as we memorize them correctly.