MCQ test, Set 9

Answer: (D) $13.02$

$100$ has $2$ zeros: move the point $2$ places to the left.

$\displaystyle \frac{1302}{100} = 13.02$

Answer: (A) $0.018$

Dividing by $10$: move the point $1$ place to the left.

$\displaystyle 0.18 \times \frac{1}{10} = 0.018$

Answer: (A) $9006$

Multiplying by $1000$: move the point $3$ places to the right.

$9.006 \times 1000 = 9006.0 = 9006$

Answer: (D) $100$

The point moved $2$ places to the right, so we multiplied by $100$.

Answer: (B) $1.001$

Only the zeros in front of the whole part and at the end of the decimal part can be removed.

Zeros in the middle stay: $001.00100 = 1.001$

Answer: (D) $30.408$

Write each digit in its place and put $0$ where a place is missing.

Tens $3$, ones $0$, tenths $4$, hundredths $0$, thousandths $8$

$= 30.408$

Answer: (C) $\displaystyle \frac{1}{1000}$

$1$ is in the thousandths place of $0.4813$.

$\displaystyle \text{Place value} = \frac{1}{1000}$

Answer: (D) $3.2$

$\displaystyle 3\frac{1}{5} = 3 + \frac{1}{5}$

$\displaystyle \frac{1}{5} = \frac{2}{10} = 0.2$

$3 + 0.2 = 3.2$

Answer: (A) $1.775$

$71 - 40 = 31$, $310 - 280 = 30$, $300 - 280 = 20$, $200 - 200 = 0$

$\displaystyle \therefore \frac{71}{40} = 1.775$

The first remainder $31$ is not the decimal part: keep dividing.

Answer: (B) $\displaystyle \frac{7}{15}$

$15 = 3 \times 5$ has a factor other than $2$ and $5$, so it is non-terminating recurring.

The other denominators have only $2$s and $5$s, so they terminate.

Answer: (C) $0.\overline{2}$

$20 - 18 = 2$: the remainder repeats.

$\displaystyle \frac{2}{9} = 0.222222\ldots = 0.\overline{2}$

Answer: (B) $\displaystyle \frac{6}{25}$

$\displaystyle 0.24 = \frac{24}{100} = \frac{6}{25}$

Answer: (A) $28$

$10x = 31.111111\ldots$, $x = 3.111111\ldots$

Subtracting, the repeating parts cancel: $10x - x = 28$

Answer: (C) $\displaystyle \frac{5}{6}$

$100x = 83.333333\ldots$, $10x = 8.333333\ldots$

$(-)$ $90x = 75$, $\displaystyle x = \frac{75}{90} = \frac{5}{6}$

(Short method: $\displaystyle \frac{83 - 8}{90}$)

Answer: (B) $1.406$

Keep the decimal points in one line:

$\begin{array}{r} 0.066 \\ +\;1.340 \\ \hline 1.406 \end{array}$

Answer: (D) $150.35$

Keep the decimal points in one line (fill zeros):

$\begin{array}{r} 250.25 \\ -\;99.90 \\ \hline 150.35 \end{array}$

Answer: (A) $0.00045$

Multiply without the points: $15 \times 3 = 45$

Decimal places: $2 + 3 = 5$

$0.15 \times 0.003 = 0.00045$

Answer: (B) $4.59$

Multiply without the points: $102 \times 45 = 4590$

Decimal places: $2 + 1 = 3$

$1.02 \times 4.5 = 4.590 = 4.59$

Answer: (C) $0.000216$

$(0.06)^3 = 0.06 \times 0.06 \times 0.06$

$6 \times 6 \times 6 = 216$; decimal places $2 + 2 + 2 = 6$

$(0.06)^3 = 0.000216$ (not $0.06 \times 3$)

Answer: (C) $0.004$

$\displaystyle \frac{0.072}{18} = \frac{72}{1000 \times 18}$

$72 \div 18 = 4$

$\displaystyle = \frac{4}{1000} = 0.004$

Answer: (D) $0.012$

$\displaystyle \frac{0.0144}{1.2} = \frac{0.0144 \times 10}{1.2 \times 10} = \frac{0.144}{12}$

$\displaystyle \frac{0.144}{12} = \frac{144}{1000 \times 12}$

$144 \div 12 = 12$

$\displaystyle = \frac{12}{1000} = 0.012$

Answer: (C) $1.2$

$\displaystyle = \frac{1.2}{4} + \frac{3.6}{4} = \frac{1.2 + 3.6}{4}$

$\displaystyle = \frac{4.8}{4} = 1.2$

Answer: (C) $0.775$

LCM of $4$, $8$, $5$ is $40$.

$\displaystyle \frac{1}{4} + \frac{1}{8} + \frac{2}{5} = \frac{10 + 5 + 16}{40} = \frac{31}{40}$

$= 0.775$

Answer: (A) $279$

$45 = 4.5 \times 10$ and $6.2 = 0.62 \times 10$

So $45 \times 6.2 = 2.79 \times 100 = 279$

Answer: (B) $1.72$

$\displaystyle x = \frac{7.396}{4.3} = \frac{73.96}{43}$

$= 1.72$

Check: $1.72 \times 4.3 = 7.396$