Tag: decimal fractions in the units of currency, length, weight, capacity

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Questions Related to decimal fractions in the units of currency, length, weight, capacity

Multiple choice maths fraction one fraction, many forms use of decimals in measure of length decimal fractions in the units of currency, length, weight, capacity

Convert $0.6$ km to centimeters.

  1. $60 cm$
  2. $600 cm$
  3. $6, 000 cm$
  4. $60, 000 cm$
  5. $600, 000$ cm
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The metric system uses powers of 10, so conversion between units can be done by moving the decimal point. First convert 0.6 km to meters. To do this, multiply 0.6 by 1000, or, equivalently, move the decimal point three places to the right. Add zeros as necessary.
$0.\underline{6}\underline{6}\underline{6}=600$
Therefore, there are 600 m in 0.6 km. Convert 600 m to centimeters by multiplying by 100 or, equivalently, by moving the decimal two places to the right.
$600.\underline{0}\,\underline{0}=60,000$
Thus, the correct answer is 60,000 cm.

Multiple choice maths fraction one fraction, many forms use of decimals in measure of length decimal fractions in the units of currency, length, weight, capacity

Prem went to a craft fair where he spent a total of Rs. $16.00$. He spent Rs. $6.00$ on admission and went to $8$ tables. He spent the same amount of money(m) at each table. The given expression can be used to find how much money he spend at each table.
$16=6+8m$
How much money did Prem spent at each table?

  1. Rs. $0.50$
  2. Rs. $0.80$
  3. Rs. $1.25$
  4. Rs. $2.00$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
We have, $16=6+8$m
$\Rightarrow 8m=16-6=10$
$\Rightarrow \displaystyle m=\frac{10}{8}=1.25$
So, Prem spent Rs. $1.25$ at each table.
Multiple choice maths fraction one fraction, many forms use of decimals in measure of length decimal fractions in the units of currency, length, weight, capacity

Let $D$ represent a repeating decimal. If $P$ denotes the $r$ figures of $D$ which do not repeat themselves, and $Q$ denotes the $s$ figures which do repeat themselves, then the incorrect expression is

  1. $D = P.QQQ....$
  2. $10^{r}D = P.QQQ...$
  3. $10^{r + s}D = PQ .QQQ .....$
  4. $10^{r}(10^{s} - 1)D = Q(P - 1)$
  5. $10^{r} . 10^{2s}D = PQ.QQQ...$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$D = .PQQQ .... = .a _{1} ...a _{r}b _{1} ...b _{x}b _{1} ...b _{s} ...$ So $(a), (b), (c)$ and $(e)$ are all correct choices. To check that $(d)$ is incorrect, we have
$10^{r + s}D - 10^{r}D = PQ - P. \therefore 10^{r}(10^{s} - 1)D = P(Q - 1)$.