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scZoUnD [109]
4 years ago
5

What exponent would complete this equation 0.005 = 5 x 10? To the ? Power

Mathematics
1 answer:
schepotkina [342]4 years ago
8 0

Answer:

-3

Step-by-step explanation:

0.005 = 5 * 10^?

0.005 = 5 * 0.001

Thus, to find what 10 should be raised to, we should find which exponent of 10 gives us 0.001

We can do this by just testing a few numbers from 10^1 and down:

10^1 = 10\\10^0 = 1\\10^{-1} = 0.1\\10^{-2} = 0.01\\10^{-3} = 0.001

As we can see, 10^{-3}  = 0.001, thus the exponent in our equation is -3

A shorthand of this is counting the number of zeroes, 10^-1 has one zero, 10^-2 has two zeroes, and 10^-3 has three zeroes.

Since we were looking for 0.001, which has 3 zeroes, we can see that the correct exponent should be -3.

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