Question

directions: find each quotient. round to the nearest hundredth.

1. \\((8.4 \times 10^8) \div (2.2 \times 10^6)\\)

Explanation:

Step1: Separate coefficients and powers of 10

We can rewrite the division as the quotient of the coefficients times the quotient of the powers of 10: \(\frac{8.4\times10^{8}}{2.2\times10^{6}}=\frac{8.4}{2.2}\times\frac{10^{8}}{10^{6}}\)

Step2: Divide the coefficients

Calculate \(\frac{8.4}{2.2}\approx3.81818\)

Step3: Divide the powers of 10

Using the rule of exponents \(a^{m}\div a^{n}=a^{m - n}\), we have \(\frac{10^{8}}{10^{6}} = 10^{8-6}=10^{2}=100\)

Step4: Multiply the results

Multiply the result from Step2 and Step3: \(3.81818\times100 = 381.818\)

Step5: Round to the nearest hundredth

The number \(381.818\) rounded to the nearest hundredth is \(381.82\) (since the thousandth digit is 8, which is greater than or equal to 5, we round up the hundredth digit)

Answer:

\(381.82\)