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

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

Convert $0.6$ km to centimeters.

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

  1. $60 cm$

  2. $600 cm$

  3. $6, 000 cm$

  4. $60, 000 cm$

  5. $600, 000$ cm

Show answer
Correct Option: D
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.

Fill in the banks: 
$7\, kg\, 250\, grams =...................... kg$

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

  1. $7.250$

  2. $7.75$

  3. $7$

  4. $7.35$

Show answer
Correct Option: A
Explanation:

$1$ kg $= 1000$ gm


So, $7$ kg $250$ gm = $7$ kg $+ 250$ gm


$= 7$ kg + $\dfrac{250}{1000}$

$= 7$ kg $+ 0.250$ kg

$= 7.250$ kg

State true or false.

$77$ rupees $7$ paise is equal to Rs.$77.07$.

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

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

As we know,

1 Rs = 100 paisa

Given, 77 Rs 7 paisa
So, 77 Rs 7 paisa = 77 + $\frac{7}{100}$ Rs
= 77 + 0.07 Rs
= 77.07 Rs

Fill in the banks: 
$\text{3 litre 500 millilitres =.................... litres}$

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

  1. $3.500$

  2. $3.45$

  3. $3.35$

  4. $3.25$

Show answer
Correct Option: A
Explanation:

$1$ litre $= 1000$ milliliters


So, $3$ liters $500$ millilitres $= 3$ litre $+\dfrac{500}{1000}$ litre


$= 3 + 0.500$ litres

$= 3.500$ litres

Fill in the blanks with proper method:
1 sq m = ____ sq cm

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

  1. 10,00

  2. 10,000

  3. 10

  4. 100

Show answer
Correct Option: B
Explanation:

1 m = 100 cm 

As, 1 sq m = 100 x 100 sq cm
1 sq m = 10000 sq m

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?

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

  1. Rs. $0.50$

  2. Rs. $0.80$

  3. Rs. $1.25$

  4. Rs. $2.00$

Show answer
Correct Option: C
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.

State true or false.
$10cm$ in kilometre is $0.0001km$

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

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

As we know,


$1$ m $= 100$ m


$1$ km $= 1000$ m

Given, $10$ cm

So, $10$ cm $= \dfrac{10}{100}$ m$= 0.1$ m

$0.1$ m = $\dfrac{0.1}{1000}$ km $= 0.0001$ km

So, $10$ cm $= 0.0001$ km

State true or false.

$9$ paise is equal to Rs.$0.09$.

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

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

As we know,

1 Rs = 100 paisa

Given, 9 paisa
So, 9 paisa = $\frac{9}{100}$ Rs
= 0.09 Rs

Fill in the banks: 
$1765$ grams $=................... kg$

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

  1. $1.765$

  2. $1.65$

  3. $1.55$

  4. $1.25$

Show answer
Correct Option: A
Explanation:

$1$ kg $= 1000$ gm


So, $1765$ grams $= \dfrac{1765}{1000}$ kg


$= 1.765$ kg 

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

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

  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. $10^{r} . 10^{2s}D = PQ.QQQ...$

Show answer
Correct Option: D
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
$10^{r + s}D - 10^{r}D = PQ - P. \therefore 10^{r}(10^{s} - 1)D = P(Q - 1)$.