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Question Video: Recalling the Number of Femtometers in a Meter Physics • 9th Grade

Which of the following is the number of femtometers (fm) in a meter? [A] 10⁹ [B] 10¹² [C] 10¹³ [D] 10¹⁴ [E] 10¹⁵

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Video Transcript

Which of the following is the number of femtometers, abbreviated fm, in a meter? (A) 10 to the power of nine, (B) 10 to the power of 12, (C) 10 to the power of 13, (D) 10 to the power of 14, (E) 10 to the power of 15.

Okay, so we’re being asked in this question to work out which of these five numbers, each of which is a power of 10, is equal to the number of femtometers in one meter. Let’s begin by recalling that femto- or lowercase f is a unit prefix, and it means a factor of 10 to the negative 15.

When we’re talking about units of femtometers then, the unit prefix of femto- modifies the base unit of meters. Since femto- means a factor of 10 to the negative 15, then one femtometer is equal to 10 to the negative 15 meters. This relation shown here tells us that the number of meters in one femtometer is equal to 10 to the negative 15.

In this question though, we’re asked what the number of femtometers in one meter is. That is, rather than a statement that says one femtometer is equal to some number of meters, we want a statement that says some number of femtometers is equal to one meter. Then the value that fits in this blank here will be our answer to this question.

To work out what this value is, we’ll begin from this equation here. We know that one femtometer is equal to 10 to the negative 15 meters. Let’s now multiply both sides of this by 10 to the power of 15. This gives us that 10 to the 15 femtometers is equal to 10 to the negative 15 multiplied by 10 to the 15 meters. Let’s recall that when we multiply a number raised to a power by that same number raised to a different power, we add together those powers. That is, 10 to the power of 𝑎 multiplied by 10 to the power of 𝑏 is equal to 10 to the power of 𝑎 plus 𝑏.

That means that on the right-hand side of this equation, 10 to the power of negative 15 multiplied by 10 to the power of 15 is equal to 10 to the power of negative 15 plus 15. When we add together negative 15 and 15, we get a result of zero. And so this 10 to the power of negative 15 plus 15 is just 10 to the power of zero.

Let’s now recall that any number raised to the power of zero is simply equal to one. Notice that in this case, we’ve used 𝑥 here to represent any general number. Applying this general equation to the right-hand side of our equation relating femtometers and meters, we know that 10 to the power of zero is simply equal to one. We have then that 10 to the power of 15 femtometers is equal to one meter. This equation tells us that the number of femtometers in one meter is equal to 10 to the power of 15.

We can notice that this matches the value given in answer option (E). We therefore choose option (E) as our answer. The number of femtometers in a meter is equal to 10 to the power of 15.

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