2009 Grade 8 CEMC Gauss Problems/Problem 5

Problem

Rounded to $2$ decimal places, $\frac79$ is

$\text{ (A) }\ 0.70 \qquad\text{ (B) }\ 0.77 \qquad\text{ (C) }\ 0.78 \qquad\text{ (D) }\ 0.79 \qquad\text{ (E) }\ 0.80$

Solution

We can use the fact that $\frac79 = 0.\overline{777}$ .

Rounding this number to the nearest hundredth (to $2$ decimal places), we get $\boxed {\textbf {(C) } 0.78}$ because the thousandths place is greater than or equal to $5$ , so it is closer to $0.78$ than $0.77$ .

~anabel.disher

Solution 2 (answer choices)

We can go backwards by multiplying answer choices by $9$ and seeing how they compare to $7$

Multiplying $0.78$ by $9$ , we get:

$0.78 \times 9 = 7.02$

This makes $0.79$ and $0.80$ too large and $0.70$ too small, eliminating them as answers

$0.77 \times 9 = 6.93$

We can now look at which answer $7$ is closest to, using the distance to $7$ :

$7 - 6.93 = 0.07$

$7.02 - 7 = 0.02$

$7.02$ is closer to $7$ , so the answer is $\boxed {\textbf {(C) } 0.78}$

~anabel.disher

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2009 Grade 8 CEMC Gauss Problems/Problem 5

Problem

Solution

Solution 2 (answer choices)