Question Detail

Evaluate
\begin{aligned}
3.\overline{14}
\end{aligned}

\begin{aligned} 3\frac{14}{99} \end{aligned}
\begin{aligned} \frac{14}{99} \end{aligned}
\begin{aligned} 3\frac{14}{90} \end{aligned}
\begin{aligned} 3\frac{1400}{99} \end{aligned}

Answer: Option A

Explanation:

when there is bar above a number, we can simplify it by dividing with 9's (equal to the number below bar, in this question 2 digits are below bar)

1. \begin{aligned}
(0.34\overline{67} + 0.13\overline{33}) = ?
\end{aligned}

\begin{aligned} 0.048\overline{01} \end{aligned}
\begin{aligned} 4.8\overline{01} \end{aligned}
\begin{aligned} 48.\overline{01} \end{aligned}
\begin{aligned} 0.48\overline{01} \end{aligned}

Answer: Option D

Explanation:

\begin{aligned}
(0.34\overline{67} + 0.13\overline{33})\end{aligned}
\begin{aligned} =
\frac{3467-34}{9900} + \frac{1333-13}{9900}
\end{aligned}
\begin{aligned}
= \frac{3433 + 1320}{9900}
= \frac{4753}{9900}
\end{aligned}
\begin{aligned}
= \frac{4801 - 48}{9900}
= 0.48\overline{01}
\end{aligned}

2. 34.95 + 240.016 + 23.98 = ?

288.946
298.946
198.946
188.946

Answer: Option B

3. What decimal of an hour is a second

.0028
.0027
.0026
.0025

Answer: Option B

Explanation:

1/(60*60) = 1/3600 = .0027

4. Evaluate
\begin{aligned} \frac{10.3 \times 10.3 \times 10.3 + 1}{10.3 \times 10.3 - 10.3 + 1}
\end{aligned}

113
1.13
11.3
113

Answer: Option C

Explanation:

\begin{aligned}
a^3 + b^3 = (a+b)(a^2 + b^2 - ab)
\end{aligned}

\begin{aligned}
= \frac{10.3^3 + 1^3}
{10.3^2 + 1^2 - 10.3 \times 1}
\end{aligned}

\begin{aligned}
= (a+b) = (10.3+1) = 11.3
\end{aligned}