Question

divide. also, estimate to see if the answer is reasonable.
$5.2\overline{)42.64}$

$5.2\overline{)42.64}$ = 8.2 (type an integer or a decimal.)
find an estimate for the quotient.
\boxed{} (round to the nearest integer as needed.)

Explanation:

Step1: Approximate the numbers

To estimate the quotient of \(42.64\div5.2\), we can round the dividend and the divisor to numbers that are easier to divide. Round \(42.64\) to \(40\) (or a closer multiple of the rounded divisor) and round \(5.2\) to \(5\).

Step2: Perform the division

Now, divide the approximated numbers: \(40\div5 = 8\). Alternatively, we can also round \(42.64\) to \(42\) and \(5.2\) to \(5\), then \(42\div5 = 8.4\), and rounding \(8.4\) to the nearest integer gives \(8\) as well. Another way is to note that \(5\times8 = 40\) and \(5\times9=45\), and \(42.64\) is closer to \(40\) than to \(45\), so the estimate is \(8\).

Answer:

\(8\)