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One fraction, many forms - class-VI

Description: one fraction, many forms
Number of Questions: 26
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Tags: decimal numbers decimal fractions fractions and decimal numbers fraction decimal forms decimal representation of rational numbers and operations maths
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Lakshmi is 150 cm tall .What is her height in metres?

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 metre

  2. 1.5 metres

  3. 15.0 metres

  4. 0.15 metres

Show answer
Correct Option: B
Explanation:
Since 1 m=100 cm
$\therefore$150 cm=$\displaystyle \frac{150}{100}=1.5m$

To convert $\displaystyle ^{\circ}C$ to $\displaystyle ^{\circ}F$ the formula used 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. $\displaystyle \left(C\times\frac{9}{5}\right)-32$

  2. $\displaystyle \left(C\times\frac{9}{5}\right)+32$

  3. $\displaystyle \left(C\times\frac{5}{9}\right)+32$

  4. none of these

Show answer
Correct Option: B
Explanation:

The conversion formula for celcius to farenheit is 

= $\left( C\times \dfrac { 9 }{ 5 }  \right) +32$
So, correct answer is option B.

Rs. $47$ and paise $50$ can be represented as

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. $47.50$

  2. Rs. $4.50$

  3. Rs. $4750$

  4. Rs. $475.0$

Show answer
Correct Option: A
Explanation:

1 paisa $= 0.01$ Rs


$\Rightarrow$ 50 paise $= 0.50$ Rs

Rs.$47$ and $50$ paise can hence be written as Rs. $47.50$

Express centimeters into meters.
$1458 \ cm$

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

  1. $14.58$m

  2. $1.458$m

  3. $1458$m

  4. $0.1458$m

Show answer
Correct Option: A
Explanation:

$1$m $= 100$cm


$\Rightarrow 1$cm $= 0.01$m
     $1458$cm $= 14.58$m

Express the following as rupees using decimals:
$235$ paise


Rs.$2.35$

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, $235$ paisa
So, $235 paisa = \dfrac{235}{100}$ Rs
                         $= 2.35 Rs$

Prerna has Rs. $5000$. She bought $2$ boxes of chocolates for Rs. $52.98$ each, $3$ packets of chips for Rs. $12.98$ each and $2$ books for Rs. $300.05$ each. How much money left with her?

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. $4255$

  2. Rs. $4750$

  3. Rs. $4000$

  4. Rs. $3875$

Show answer
Correct Option: A
Explanation:

Total expenditure $=Rs. ((2\times 52.98)+(3\times 12.98)+(2\times 300.05))$
$=Rs. (105.96+38.94+600.10)=Rs. 745$
Amount of money left with her$=Rs. (5000-745)=Rs. 4255$.

Rahul purchased $4$kg $500$g rice, $5$kg $650$g sugar and $12$kg $600$g atta. The total weight of his purchases was __________.

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

  1. $10.150$kg

  2. $22.750$kg

  3. $25.350$kg

  4. $18.250$kg

Show answer
Correct Option: B
Explanation:

Weight of rice $=4$kg $500$g $=4.500$kg
Weight of sugar $=5$kg $650$g $=5.650$ kg
Weight of atta $=12$kg $600$g $=12.600$ kg
$\therefore$ Total weight of all items $=(4.500+5.650+12.600)$kg
$=22.750$kg.

Fill in the banks: 
$88\, cm =...................... meter$

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

  1. $0.88$

  2. $0.66$

  3. $0.55$

  4. $0.99$

Show answer
Correct Option: A
Explanation:

$1$ meter $= 100$ cm


So, $88 \,  cm =$ $\dfrac{88}{100}  \, meter$

$= 0.88$ meter

A road is $4$ km $ 800$ m long. If trees are planted both its sides at intervals of $9.6$ m, how many trees were planted?

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

  1. $400$

  2. $500$

  3. $700$

  4. $1000$

Show answer
Correct Option: B
Explanation:

Total length $=4.8$kms $=4800$m


Interval $=9.6$ m

Number of trees planted $=\dfrac{4800}{9.6}=500$

Abhishek has Rs. $817.45$. He bought toys for Rs. $538.30$. The balance amount left with Abhishek 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. Rs. $279.30$

  2. Rs. $265.45$

  3. Rs. $279.15$

  4. Rs. $315.82$

Show answer
Correct Option: C
Explanation:

Amount of money Abhishek had $=Rs. 817.45$
Amount of money spent by him on toys $=Rs. 538.30$
$\therefore$ Amount of money left with him $=Rs. (817.45-538.30)=Rs. 279.15$.

Mohan bought $500$ g of cabbage, $250$ g of onions, $750$ g of potatoes, $600$ g of apples.
Calculate total weight in kilograms.

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

  1. $2100$kg

  2. $21.00$kg

  3. $2.100$kg

  4. $0.2100$kg

Show answer
Correct Option: C
Explanation:
Weight of cabbage is $500$ gm

Weight of onions is $250$ gm

Weight of potatoes is $750$ gm

Weight of apples is $600$ gm

Total weight of fruits and vegetables in grams is:

$500+250+750+600=2100$ gm

We know that $1$ kg $=1000$ gm

Therefore, $2100$ gm can be converted in kgs as follows:

$\dfrac {2100}{1000}=2.100$ kg

Hence, the total weight is $2.1$ kg.

$1\ km\ 250\  m =....................km$
Fill in the blank by chosing correct option from the following options

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

  1. $10.360$

  2. $10250$

  3. $1.250$

  4. $10.625$

Show answer
Correct Option: C
Explanation:

We know that $1\ m$=$1000\ km$.


Now, let us convert $250\ m$ in kms by dividing it by $1000$ as follows:

$\dfrac {250}{1000}=0.25$

Therefore, $250\ m$=$0.25\ km$

Thus we have:

$1\ km$ $250\ m$=$(1+0.25)\ km$=$1.25\ km$

Hence, $1\ km$ $250\ m$=$1.25\ km$

What is the ratio of 1 mm to 1 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. 1: 100

  2. 10: 1

  3. 1: 10

  4. 100:1

Show answer
Correct Option: C
Explanation:

As we know that

$1\ cm =10\ mm$
Ratio of $1\ mm $ to $1\ cm$  is $1\ mm:1\ cm=1\ mm :10\ mm=1:10$

The cost of 1kg of sugar is Rs.18.What is cost of 250gms of sugar?

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

  1. $Rs.9$

  2. $Rs.4.5$

  3. $Rs.8$

  4. $Rs.5.5$

Show answer
Correct Option: B
Explanation:

We know that $1$kg=$1000$gm.


It is given that the cost of $1$kg sugar is Rs.$18$ which means that the cost of $1000$g sugar is Rs.$18$ then cost of one gram sugar will be:


$\dfrac {18}{1000}=0.018$

Therefore, $1$gm sugar costs Rs.$0.018$.

Now, the cost of $250$gms of sugar will be as follows:

Cost$\times$number of grams$=0.018\times 250=4.5$

Hence, the cost of $250$gms of sugar is Rs.$4.5$.

How much pure alcohol should be added to $400 ml$ of strength $15\%$ to make its strength $32\%$?

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

  1. $50 ml$

  2. $75 ml$

  3. $100 ml$

  4. $150 ml$

Show answer
Correct Option: C
Explanation:

The amount of alcohol in $400ml$ solution of $15\%$ strength

$=400\times \cfrac { 15 }{ 100 } ml=60ml$

Let the required amount of alcohol to be added $=x$ ml.
It will increase the amount of the solution by $x$ ml.

$\therefore $ The amount of alcohol now $=(60+x)ml$
and the amount of the solution$=(400+x)ml$.
Then, the strength $=32\%=\cfrac { 60+x }{ 400+x } =\cfrac { 32 }{ 100 }$

$\Rightarrow 25x+1500=3200+8x\ \Rightarrow 17x=1700\ \Rightarrow x=100$.
So, the required amount of pure alcohol to be added $=100 ml$.

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

$2+\dfrac {1}{2}$ In the decimal form

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

  1. $2.5$

  2. $1.5$

  3. $3.5$

  4. $2$

Show answer
Correct Option: A
Explanation:

$2+\dfrac{1}{2}$

As $\dfrac{1}{2}=0.5$
So $2+0.5=2.5$

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