Question

solve. write the answer using scientific notation.
1 the age of the earth is approximately 4.5 x 10⁹ years. if a person is 12 years old, approximately how many times older is the earth than that person?
2 you walk approximately 1.2 x 10³ steps to school each day. if you also walk home, how many steps would you walk in one month? (assume 5 days per week for 4 weeks = one month.)
find the value of the missing exponent.
1 (2.7 x 10⁷) • (4.3 x 10ᵧ) = 1,161,000
2 \\(\frac{2.17 \times 10^9}{3.5 \times 10^y} = 6.2 \times 10^1\\)
3 \\(\frac{71,400,000,000}{1.4 \times 10^7} = 5.1 \times 10^x\\)
4 (6.2 x 10⁶)(2.9 x 10⁷) = 1.798 x 10^z

Explanation:

Problem 1 (Top - Left, Solve using scientific notation: Age comparison)

Step 1: Identify the formula

To find how many times older the Earth is than the person, we divide the Earth's age by the person's age. The Earth's age is $4.5\times10^{9}$ years and the person's age is 12 years (or $1.2\times10^{1}$ years). So the formula is $\frac{4.5\times 10^{9}}{1.2\times 10^{1}}$.

Step 2: Divide the coefficients and subtract exponents

First, divide the coefficients: $\frac{4.5}{1.2} = 3.75$. Then, subtract the exponents of 10: $10^{9 - 1}=10^{8}$. Multiply these results together: $3.75\times10^{8}$.

Step 1: Determine daily round - trip steps

You walk $1.2\times10^{3}$ steps to school and the same back home, so daily steps are $2\times(1.2\times10^{3})=2.4\times10^{3}$ steps.

Step 2: Calculate weekly steps

You walk 5 days a week, so weekly steps are $5\times(2.4\times10^{3}) = 12\times10^{3}=1.2\times10^{4}$ steps.

Step 3: Calculate monthly steps

There are 4 weeks in a month, so monthly steps are $4\times(1.2\times10^{4})=4.8\times10^{4}$ steps.

Step 1: Rewrite the equation

We have $(2.7\times10^{?})\cdot(4.3\times10^{3}) = 1,161,000$. First, rewrite $1,161,000$ in scientific notation. $1,161,000 = 1.161\times10^{6}$.

Step 2: Divide both sides by $(4.3\times10^{3})$

$\frac{(2.7\times10^{?})\cdot(4.3\times10^{3})}{4.3\times10^{3}}=\frac{1.161\times10^{6}}{4.3\times10^{3}}$. Simplify the left - hand side to $2.7\times10^{?}$. For the right - hand side, divide the coefficients: $\frac{1.161}{4.3}=0.27$, and subtract the exponents: $10^{6 - 3}=10^{3}$. So $0.27\times10^{3}=2.7\times10^{2}$. Thus, the missing exponent is 2.

Answer:

$3.75\times 10^{8}$

Problem 2 (Top - Right, Steps in a month)