Let's tackle each part of your question step-by-step.
(a) Write each population in scientific notation.
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Population of Columbus, Ohio (2014): 823,000 can be expressed in scientific notation as: \[ 823,000 = 8.23 \times 10^5 \]
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Population of the United States (2014): 319 million can be expressed in scientific notation as: \[ 319,000,000 = 3.19 \times 10^8 \]
(b) About how many times larger was the population of the United States than the population of Columbus, Ohio? Show your work.
To find out how many times larger the population of the United States is compared to Columbus, you can divide the population of the United States by the population of Columbus:
\[ \text{Times larger} = \frac{\text{Population of the United States}}{\text{Population of Columbus}} \]
Substituting the scientific notation of the populations:
\[ \text{Times larger} = \frac{3.19 \times 10^8}{8.23 \times 10^5} \]
To perform this division, divide the coefficients and subtract the exponents:
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Divide the coefficients: \[ \frac{3.19}{8.23} \approx 0.387 \]
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Subtract the exponents: \[ 10^{8 - 5} = 10^3 \]
Putting it all together:
\[ \frac{3.19 \times 10^8}{8.23 \times 10^5} \approx 0.387 \times 10^3 = 387 \]
Therefore, the population of the United States was approximately 387 times larger than the population of Columbus, Ohio in 2014.