volume_mute

Use front-end rounding to estimate the sum

publish date2025/06/09 21:09:00 UTC

\[ \begin{array}{r} \phantom{0}6,\phantom{0}\!7\phantom{0}8\phantom{0}0 \\ \phantom{0}3,\phantom{0}\!2\phantom{0}7\phantom{0}8 \\ \phantom{00}5\phantom{0}6\phantom{0}6 \\ \phantom{0}4,\!\phantom{0}2\phantom{0}3\phantom{0}0 \\ +\phantom{0}1,\phantom{0}\!9\phantom{0}2\phantom{0}3 \\ \hline \end{array} \]

Rounded Answer =

Correct Answer

(1) 16600

Explanation

The actual sum will be 

\[
\begin{array}{r}
\phantom{0}6,\phantom{0}\!7\phantom{0}8\phantom{0}0 \\
\phantom{0}3,\phantom{0}\!2\phantom{0}7\phantom{0}8 \\
\phantom{00}5\phantom{0}6\phantom{0}6 \\
\phantom{0}4,\!\phantom{0}2\phantom{0}3\phantom{0}0 \\
+\phantom{0}1,\phantom{0}\!9\phantom{0}2\phantom{0}3 \\ \hline
\phantom{0}1\phantom{0}6,\phantom{0}\!7\phantom{0}7\phantom{0}7 \\
\end{array}
\]

After using the front-end rounding, it can be written like that

\[
\begin{array}{r}
\phantom{0}7,\phantom{0}\!0\phantom{0}0\phantom{0}0 \\
\phantom{0}3,\phantom{0}\!0\phantom{0}0\phantom{0}0 \\
\phantom{00}6\phantom{0}0\phantom{0}0 \\
\phantom{0}4,\!\phantom{0}0\phantom{0}0\phantom{0}0 \\
+\phantom{0}2,\phantom{0}\!0\phantom{0}0\phantom{0}0 \\ \hline
\phantom{0}1\phantom{0}6,\phantom{0}\!6\phantom{0}0\phantom{0}0 \\
\end{array}
\]

The difference between the original sum and the rounded sum = 16777 - 16600 = 177 which is very close

Reference

Mathematics for college students, go-math-science.com


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