(a) To write each population in scientific notation:
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Population of Columbus, Ohio (2014):
- 823,000 can be written as \( 8.23 \times 10^5 \).
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Population of the United States (2014):
- 319,000,000 can be written as \( 3.19 \times 10^8 \).
(b) To find how many times larger the population of the United States was compared to the population of Columbus, Ohio, we can divide the population of the United States by the population of Columbus, Ohio:
\[ \text{Ratio} = \frac{\text{Population of the US}}{\text{Population of Columbus}} = \frac{319,000,000}{823,000} \]
Now, plugging in the scientific notation values we calculated earlier:
\[ \text{Ratio} = \frac{3.19 \times 10^8}{8.23 \times 10^5} \]
To divide these:
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Divide the coefficients: \[ \frac{3.19}{8.23} \approx 0.387 \]
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Subtract the exponents (since the bases are the same): \[ 10^{8 - 5} = 10^3 \]
So, combining both results:
\[ \text{Ratio} \approx 0.387 \times 10^3 = 387 \]
Thus, the population of the United States was approximately 387 times larger than the population of Columbus, Ohio in 2014.
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