MCQ test, Set 4

Answer: (D) $0.0615$

$10000$ has $4$ zeros: move the point $4$ places to the left.

$\displaystyle \frac{615}{10000} = 0.0615$

Answer: (B) $2.705$

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

$\displaystyle \frac{27.05}{10} = 2.705$

Answer: (D) $0.61$

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

$0.0061 \times 100 = 0.61$

Answer: (D) $10000$

The point moved $4$ places to the right, so we multiplied by $10000$.

Answer: (B) $400.001$

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: $000400.0010 = 400.001$

Answer: (A) $6008.06$

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

Thousands $6$, hundreds $0$, tens $0$, ones $8$, tenths $0$, hundredths $6$

$= 6008.06$

Answer: (D) $40$

$4$ is in the tens place of $643.18$.

$\text{Place value} = 40$

Answer: (B) $2.25$

$\displaystyle \frac{9}{4} = \frac{9 \times 5 \times 5}{2 \times 2 \times 5 \times 5}$

$\displaystyle = \frac{225}{10 \times 10} = \frac{225}{100} = 2.25$

Answer: (C) $1.65$

$33 - 20 = 13$, $130 - 120 = 10$, $100 - 100 = 0$

$\displaystyle \therefore \frac{33}{20} = 1.65$

The first remainder $13$ is not the decimal part: keep dividing.

Answer: (A) $\displaystyle \frac{9}{24}$

$\displaystyle \frac{9}{24} = \frac{3}{8}$, and $8 = 2 \times 2 \times 2$: 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: (A) $0.1\overline{6}$

$10 - 6 = 4$, $40 - 36 = 4$: the remainder repeats.

$\displaystyle \frac{1}{6} = 0.1666666\ldots = 0.1\overline{6}$

Answer: (C) $\displaystyle \frac{8}{5}$

$\displaystyle 1.6 = \frac{16}{10} = \frac{8}{5}$

Answer: (A) $9$

$100x = 9.090909\ldots$, $x = 0.090909\ldots$

Subtracting, the repeating parts cancel: $100x - x = 9$

Answer: (B) $\displaystyle \frac{7}{90}$

$100x = 7.777777\ldots$, $10x = 0.777777\ldots$

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

(Short method: $\displaystyle \frac{7 - 0}{90}$)

Answer: (B) $6.827$

Keep the decimal points in one line:

$\begin{array}{r} 0.580 \\ +\;6.247 \\ \hline 6.827 \end{array}$

Answer: (D) $5.683$

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

$\begin{array}{r} 8.050 \\ -\;2.367 \\ \hline 5.683 \end{array}$

Subtract $2.367$ from $8.05$ means $8.05 - 2.367$.

Answer: (C) $0.01$

Multiply without the points: $25 \times 4 = 100$

Decimal places: $2 + 2 = 4$

$0.25 \times 0.04 = 0.0100 = 0.01$

Answer: (C) $6$

Multiply without the points: $48 \times 125 = 6000$

Decimal places: $1 + 2 = 3$

$4.8 \times 1.25 = 6.000 = 6$

Answer: (A) $1.69$

$(1.3)^2 = 1.3 \times 1.3$

$13 \times 13 = 169$; decimal places $1 + 1 = 2$

$(1.3)^2 = 1.69$ (not $1.3 \times 2$)

Answer: (A) $0.0103$

$\displaystyle \frac{0.0927}{9} = \frac{927}{10000 \times 9}$

$927 \div 9 = 103$

$\displaystyle = \frac{103}{10000} = 0.0103$

Answer: (C) $120$

$\displaystyle \frac{4.8}{0.04} = \frac{4.8 \times 100}{0.04 \times 100} = \frac{480}{4}$

$480 \div 4 = 120$

Answer: (D) $0.14$

$0.3 \times 0.2 = 0.06$, $0.4 \times 0.2 = 0.08$

$0.06 + 0.08 = 0.14$

Answer: (D) $0.975$

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

$\displaystyle \frac{1}{8} + \frac{3}{5} + \frac{1}{4} = \frac{5 + 24 + 10}{40} = \frac{39}{40}$

$= 0.975$

Answer: (C) $9.6$

$0.64 = 6.4 \div 10$ and $15 = 1.5 \times 10$

The changes cancel: $0.64 \times 15 = 9.6$

Answer: (B) $0.396$

$\displaystyle x = \frac{1.4652}{3.7} = \frac{14.652}{37}$

$= 0.396$

Check: $0.396 \times 3.7 = 1.4652$