MCQ test, Set 1

Answer: (D) $0.023$

$1000$ has $3$ zeros: move the point $3$ places to the left.

$\displaystyle \frac{23}{1000} = 0.023$

Answer: (D) $0.00572$

Dividing by $1000$: move the point $3$ places to the left.

$\displaystyle \frac{5.72}{1000} = 0.00572$

Answer: (A) $820.7$

Multiplying by $100$: move the point $2$ places to the right.

$8.207 \times 100 = 820.7$

Answer: (A) $1000$

The point moved $3$ places to the right, so we multiplied by $1000$.

Answer: (D) $30.04$

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: $0030.0400 = 30.04$

Answer: (C) $305.209$

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

Hundreds $3$, tens $0$, ones $5$, tenths $2$, hundredths $0$, thousandths $9$

$= 305.209$

Answer: (A) $\displaystyle \frac{6}{100}$

$6$ is in the hundredths place of $25.463$.

$\displaystyle \text{Place value} = \frac{6}{100}$

Answer: (A) $0.875$

$\displaystyle \frac{7}{8} = \frac{7 \times 5 \times 5 \times 5}{2 \times 2 \times 2 \times 5 \times 5 \times 5}$

$\displaystyle = \frac{875}{10 \times 10 \times 10} = \frac{875}{1000} = 0.875$

Answer: (B) $1.875$

$15 - 8 = 7$, $70 - 64 = 6$, $60 - 56 = 4$, $40 - 40 = 0$

$\displaystyle \therefore \frac{15}{8} = 1.875$

The first remainder $7$ is not the decimal part: keep dividing.

Answer: (B) $\displaystyle \frac{9}{25}$

$25 = 5 \times 5$: only $2$s and $5$s, so it terminates.

Each of the others has a factor other than $2$ and $5$ in its denominator (simplest form).

Answer: (D) $0.\overline{36}$

$40 - 33 = 7$, $70 - 66 = 4$: the remainder repeats.

$\displaystyle \frac{4}{11} = 0.363636\ldots = 0.\overline{36}$

Answer: (A) $\displaystyle \frac{9}{20}$

$\displaystyle 0.45 = \frac{45}{100} = \frac{9}{20}$

Answer: (D) $\displaystyle \frac{4}{9}$

$10x = 4.444444\ldots$, $x = 0.444444\ldots$

$(-)$ $9x = 4$, $\displaystyle x = \frac{4}{9}$

Answer: (D) $\displaystyle \frac{7}{30}$

$100x = 23.333333\ldots$, $10x = 2.333333\ldots$

$(-)$ $90x = 21$, $\displaystyle x = \frac{21}{90} = \frac{7}{30}$

(Short method: $\displaystyle \frac{23 - 2}{90}$)

Answer: (B) $30.18$

Keep the decimal points in one line:

$\begin{array}{r} 26.48 \\ +\;3.70 \\ \hline 30.18 \end{array}$

Answer: (C) $36.72$

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

$\begin{array}{r} 64.30 \\ -\;27.58 \\ \hline 36.72 \end{array}$

Subtract $27.58$ from $64.3$ means $64.3 - 27.58$.

Answer: (A) $0.28$

Multiply without the points: $4 \times 7 = 28$

Decimal places: $1 + 1 = 2$

$0.4 \times 0.7 = 0.28$

Answer: (C) $3.92$

Multiply without the points: $16 \times 245 = 3920$

Decimal places: $1 + 2 = 3$

$1.6 \times 2.45 = 3.920 = 3.92$

Answer: (C) $0.027$

$(0.3)^3 = 0.3 \times 0.3 \times 0.3$

$3 \times 3 \times 3 = 27$; decimal places $1 + 1 + 1 = 3$

$(0.3)^3 = 0.027$ (not $0.3 \times 3$)

Answer: (B) $1.03$

$\displaystyle \frac{6.18}{6} = \frac{618}{100 \times 6}$

$618 \div 6 = 103$

$\displaystyle = \frac{103}{100} = 1.03$

Answer: (D) $20$

$\displaystyle \frac{0.06}{0.003} = \frac{0.06 \times 1000}{0.003 \times 1000} = \frac{60}{3}$

$60 \div 3 = 20$

Answer: (B) $3$

$0.4 \times 0.6 = 0.24$

$\displaystyle \frac{0.24}{0.08} = \frac{24}{8} = 3$

Answer: (C) $0.97$

LCM of $4$, $5$, $25$ is $100$.

$\displaystyle \frac{1}{4} + \frac{3}{5} + \frac{3}{25} = \frac{25 + 60 + 12}{100} = \frac{97}{100}$

$= 0.97$

Answer: (C) $260$

$325 = 3.25 \times 100$

So $325 \times 0.8 = 2.6 \times 100 = 260$

Answer: (B) $3.18$

$\displaystyle x = \frac{6.042}{1.9} = \frac{60.42}{19}$

$= 3.18$

Check: $3.18 \times 1.9 = 6.042$