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# Approximating with powers of 10

Video transcript

- [Voiceover] In 2014,
the population of the United States was about
318,900,000 people. Choose the best approximation of the United States population in 2014. So they say three times
10 to the eighth people or three times 10 to the ninth people. This is a big difference. This is a factor of 10. This is 10 times this right over here. So which one's closer? So if I were to round this to the nearest hundred million, this
would go to 300,000,000. 300,000,000, this is
three times 100,000,000. This is the same thing as three times, three times 100,000,000. And 100,000,000 we see has eight zeros. So this is the same thing as
three times 10 to the eighth. Three times 10 to the eighth power, which they have right over here. Three times 10 to the ninth, that would be 3,000,000,000. That would be almost 10 times as large as this. So we would definitely
wanna go with this one. Three times 10 to the eight people is a pretty good approximation. This is 300,000,000 people. So we're kind of rounding
to the nearest 100,000,000. In 2014, the population of the world was about 7,125,000,000 people. Choose the best approximation of the world population in 2014. Well here we're dealing with, this is billions here, so let me just round
to the nearest billion. So we could say this is
roughly 7,000,000,000. So approximately 7,000,000,000 if we're rounding to the nearest billion. A billion is 10 to the ninth. We see we have nine zeros here. So this is going to be equal to seven times 10 to the ninth power. Which is this right over here. This would be 700,000,000. This is less than a 10th of the actual world population. This is 7,000,000,000, which is, if you're rounding
to the nearest billion, how many people there were in 2014. Approximately how many times larger was the world population, how many times larger
was the world population than the United States population in 2014? Well what was the world population? Once again, they're taking approximately. They're saying two, 20, 200. So if we're saying approximately, see the world population, if we're using the approximation, was seven times 10 to the ninth power, and the United States population, we said it was roughly, in 2014, three times 10 to the eighth. So we could divide the world population, or our approximation of
the world population, by our approximation of the
United States population. So our approximation
of the world population divided by the approximation of the United States population, three times 10 to the eight power, well what's that going to be? This is going to be approximately, well, this is actually
going to be exactly 7/3. So we could say seven divided by three, that's 7/3, times, what's 10 to the ninth divided by 10 to the eighth power? Well that's just going to be 10. 10 to the ninth is 10
to the eighth times 10, and if we divide that by 10 to the eighth, we're just gonna be left with 10. Or, if we think about exponent properties, we have the same base, 10 to the ninth, divided by 10 to the eighth, you can subtract this, the exponent in the denominator, from the exponent in the numerator. So it's going to be 10 to
the nine minus eight power, 10 to the first. This is going to be times 10. Well that's not exactly what they have over here, but we see 7/3, this is 2 1/3 times 10. So we could say this is
equal to 2 1/3 times 10, which is approximately equal to, which is approximately
equal to two times 10 if we're just rounding, once again, this is all
for the sake of roughness, which is 20, which is 20, which is that right over there.