the volume of a raisin is $4.5 \\times 10^{-1}\\ \\text{cm}^3$. the volume of a swimming pool is $9 \\times…

the volume of a raisin is $4.5 \\times 10^{-1}\\ \\text{cm}^3$. the volume of a swimming pool is $9 \\times 10^8\\ \\text{cm}^3$.\nhow many raisins would it take to fill the swimming pool?

the volume of a raisin is $4.5 \\times 10^{-1}\\ \\text{cm}^3$. the volume of a swimming pool is $9 \\times 10^8\\ \\text{cm}^3$.\nhow many raisins would it take to fill the swimming pool?

Answer

Explanation:

Step1: Set up division formula

To find the number of raisins, divide the pool's volume by one raisin's volume: $$\text{Number of raisins} = \frac{9 \times 10^8}{4.5 \times 10^{-1}}$$

Step2: Split into coefficient and exponent parts

Separate the numerical coefficients and the powers of 10: $$= \frac{9}{4.5} \times \frac{10^8}{10^{-1}}$$

Step3: Calculate coefficient quotient

Solve the coefficient division: $$\frac{9}{4.5} = 2$$

Step4: Simplify exponent division

Use exponent rule $\frac{10^a}{10^b}=10^{a-b}$: $$\frac{10^8}{10^{-1}} = 10^{8 - (-1)} = 10^9$$

Step5: Multiply results

Combine the two parts: $$2 \times 10^9$$

Answer:

$2 \times 10^9$