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The population of Columbus, Ohio, in 2014 was about 823,000. The population of the United States was

about 319 million in 2014.
(a) Write each population in scientific notation.
(b) About how many times larger was the population of the United States than the population of
Columbus, Ohio? Show your work.

3 answers

(a) To express the populations in scientific notation:

  • The population of Columbus, Ohio, in 2014 was about 823,000. In scientific notation, this can be written as: \[ 823,000 = 8.23 \times 10^5 \]

  • The population of the United States in 2014 was about 319 million. In scientific notation, this can be written as: \[ 319,000,000 = 3.19 \times 10^8 \]

(b) To find out how many times larger the population of the United States was than that of Columbus, Ohio, we need to divide the population of the United States by the population of Columbus.

Using their values in scientific notation: \[ \text{Population of the United States} = 3.19 \times 10^8 \] \[ \text{Population of Columbus, Ohio} = 8.23 \times 10^5 \]

Now we divide: \[ \text{Ratio} = \frac{3.19 \times 10^8}{8.23 \times 10^5} \]

We can divide the coefficients and subtract the exponents: \[ \text{Ratio} = \frac{3.19}{8.23} \times 10^{8-5} = \frac{3.19}{8.23} \times 10^3 \]

Calculating the coefficient: \[ \frac{3.19}{8.23} \approx 0.387 \]

Now we can multiply: \[ \text{Ratio} \approx 0.387 \times 10^3 = 387 \]

Thus, the population of the United States was about 387 times larger than the population of Columbus, Ohio.

Answer question B with simple words, and show your work

Sure! Let's break it down step by step using simple words.

Step 1: Write Down the Populations

  • Population of Columbus, Ohio: 823,000
  • Population of the United States: 319,000,000

Step 2: Find Out How Many Times Larger

To find out how many times larger the U.S. population is than the Columbus population, we can do a division:

\[ \text{Number of times larger} = \frac{\text{Population of the U.S.}}{\text{Population of Columbus}} \]

Step 3: Plug in the Numbers

Now we put the numbers into the equation:

\[ \text{Number of times larger} = \frac{319,000,000}{823,000} \]

Step 4: Do the Division

When we divide, we can simplify the numbers.

To make it easier, we can ignore the thousands: \[ \frac{319,000,000}{823,000} = \frac{319,000,000 \div 1,000}{823,000 \div 1,000} = \frac{319,000}{823} \]

Now we can actually do the division:

  1. Calculate \( 319 \div 823 \).

    • This gives us about 0.387.

  2. Now since we simplified both numbers by 1,000 earlier, the total number comes out with three more zeros: \[ 0.387 \times 1000 = 387 \]

Conclusion

The population of the United States is approximately 387 times larger than the population of Columbus, Ohio.