MCQ test, Set 3

Answer: (D) $0.00085$

$100000$ has $5$ zeros: move the point $5$ places to the left.

$\displaystyle \frac{85}{100000} = 0.00085$

Answer: (B) $1.489$

Dividing by $100$: move the point $2$ places to the left.

$\displaystyle 148.9 \times \frac{1}{100} = 1.489$

Answer: (C) $452000$

Multiplying by $10000$: move the point $4$ places to the right.

$45.2 \times 10000 = 452000.0 = 452000$

Answer: (C) $1000$

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

Answer: (B) $0.05$

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: $00.05000 = 0.05$

Answer: (D) $40.705$

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

Tens $4$, ones $0$, tenths $7$, hundredths $0$, thousandths $5$

$= 40.705$

Answer: (A) $2$

After the point: tenths, hundredths, thousandths, ten-thousandths.

The thousandths digit of $47.0825$ is $2$.

Answer: (A) $2.625$

$\displaystyle 2\frac{5}{8} = 2 + \frac{5}{8}$

$\displaystyle \frac{5}{8} = \frac{625}{10 \times 10 \times 10} = \frac{625}{1000} = 0.625$

$2 + 0.625 = 2.625$

Answer: (D) $2.8125$

$45 - 32 = 13$, $130 - 128 = 2$, $20 - 16 = 4$, $40 - 32 = 8$, $80 - 80 = 0$

$\displaystyle \therefore \frac{45}{16} = 2.8125$

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

Answer: (C) $\displaystyle \frac{13}{80}$

$80 = 2 \times 2 \times 2 \times 2 \times 5$: 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) $0.\overline{6}$

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

$\displaystyle \frac{2}{3} = 0.666666\ldots = 0.\overline{6}$

Answer: (D) $\displaystyle \frac{2}{125}$

$\displaystyle 0.016 = \frac{16}{1000} = \frac{2}{125}$

Answer: (A) $\displaystyle \frac{4}{3}$

$10x = 13.333333\ldots$, $x = 1.333333\ldots$

$(-)$ $9x = 12$, $\displaystyle x = \frac{12}{9} = \frac{4}{3}$

Answer: (C) $\displaystyle \frac{25}{18}$

$100x = 138.888888\ldots$, $10x = 13.888888\ldots$

$(-)$ $90x = 125$, $\displaystyle x = \frac{125}{90} = \frac{25}{18}$

(Short method: $\displaystyle \frac{138 - 13}{90}$)

Answer: (A) $175.95$

Keep the decimal points in one line:

$\begin{array}{r} 148.30 \\ +\;27.65 \\ \hline 175.95 \end{array}$

Answer: (B) $62.54$

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

$\begin{array}{r} 100.00 \\ -\;37.46 \\ \hline 62.54 \end{array}$

Answer: (B) $0.065$

Multiply without the points: $13 \times 5 = 65$

Decimal places: $1 + 2 = 3$

$1.3 \times 0.05 = 0.065$

Answer: (C) $0.2226$

Multiply without the points: $53 \times 42 = 2226$

Decimal places: $2 + 2 = 4$

$0.53 \times 0.42 = 0.2226$

Answer: (B) $0.0016$

$(0.04)^2 = 0.04 \times 0.04$

$4 \times 4 = 16$; decimal places $2 + 2 = 4$

$(0.04)^2 = 0.0016$ (not $0.04 \times 2$)

Answer: (A) $0.49$

$\displaystyle \frac{2.45}{5} = \frac{245}{100 \times 5}$

$245 \div 5 = 49$

$\displaystyle = \frac{49}{100} = 0.49$

Answer: (A) $3$

$\displaystyle \frac{0.15}{0.05} = \frac{0.15 \times 100}{0.05 \times 100} = \frac{15}{5}$

$15 \div 5 = 3$

Answer: (C) $0.6$

$0.064 - 0.016 = 0.048$

$\displaystyle \frac{0.048 \times 100}{0.08 \times 100} = \frac{4.8}{8} = 0.6$

Answer: (D) $0.93$

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

$\displaystyle \frac{2}{5} + \frac{1}{4} + \frac{7}{25} = \frac{40 + 25 + 28}{100} = \frac{93}{100}$

$= 0.93$

Answer: (B) $1.081$

Decimal places: $1 + 2 = 3$

So $2.3 \times 0.47 = 1.081$

Answer: (C) $4.5$

$\displaystyle x = \frac{28.35}{6.3} = \frac{283.5}{63}$

$= 4.5$

Check: $4.5 \times 6.3 = 28.35$