Question

question 8
about $5.67811 \times 10^5$ liters of water flow over niagara falls per second. there are $3.15576 \times 10^7$ seconds in 1 year. the number of liters of water that flow over niagara falls each year should be about $(5.67811 \times 10^5) \times (3.15576 \times 10^7)$.
which of the following is a reasonable estimate for the number of liters that flow over niagara falls each year?
1.791875241e13 1e12
1.92559524e-44 179187524.1

Explanation:

Step1: Multiply coefficients

Multiply \(5.67811\) and \(3.15576\). Estimate: \(5.67811\approx5.7\), \(3.15576\approx3.2\), so \(5.7\times3.2 = 18.24\).

Step2: Add exponents of 10

For \(10^{5}\times10^{7}\), use \(a^{m}\times a^{n}=a^{m + n}\), so \(10^{5 + 7}=10^{12}\).

Step3: Combine results

Multiply the coefficient estimate and the power of 10: \(18.24\times10^{12}=1.824\times10^{13}\). The option \(1.791875241e13\) (which is \(1.791875241\times10^{13}\)) is close to this estimate.

Answer:

\(1.791875241e13\)