2 Mark Question - Maths STD 6 Questions - Vidyadip

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2 Mark Question

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77 questions · self-marked practice — reveal the answer and mark yourself.

Question 12 Marks

Express the following fractions as decimals:
$75\frac{1}{4}$

Answer

$75\frac{1}{4}=75+\frac{1}{4}$
$=75+\frac{1\times25}{4\times25}$
$=75+\frac{25}{100}=75.25$

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Question 22 Marks

Rahul bought 4kg, 90g apples, 2kg, 60g of grapes and 5kg, 300g mangoes. Find the weight of the fruits he bought in all.

Answer

Weight of the apples = 4kg, 90g = 4.090kg
Weight grapes = 2kg, 60g = 2.060kg
Weight of mangoes = 5kg, 300g = 5.300kg
Therefore, the total weight of fruits bought by rahul = (4.090 + 2.060 + 5.300)kg
= 11.450kg
The total weight of the fruits is 11.450kg.

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Question 32 Marks

Express as kilometer (km) using decimals:
5555m

Answer

We know that 1000m = 1km
Therefore $1\text{m}=\frac{1}{1000}\text{km}$
$5\text{m}=\frac{5}{1000}\text{km}$
$=5.555\text{km}$

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Question 42 Marks

Express as kilometer (km) using decimals:
555m

Answer

We know that 1000m = 1km
Therefore $1\text{m}=\frac{1}{1000}\text{km}$
$555\text{m}=\frac{555}{1000}\text{km}$
$=0.555\text{km}$

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Question 52 Marks

The sum of two number is 100. If one of them is 78.01, find the order.

Answer

One number is 78.01
Suppose the other number is x.
The sum of these numbers is 100
Therefore, 78.01 + x = 100
= x = 100 - 78.01
= x = 21.99
The other number is 21.99

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Question 62 Marks

Express the following without using decimals:
3.5cm

Answer

We know that 10mm = 1cm.
So, $1\text{mm}=\frac{1}{10}\text{cm}$
Therefore, 3.5 = 3 + 0.5
$=3+\frac{5}{10}$
= 3cm and 5mm

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Question 72 Marks

Express as kilogram (kg) using decimals:
36kg 50g

Answer

We know that 1000g = 1kg
Therefore $1\text{g}=\frac{1}{1000}\text{kg}=0.001\text{kg}$
36kg 50g = 36 + 501000
= 36.050kg

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Question 82 Marks

Express as centimetre (cm) using decimals:
175mm

Answer

We know that 10mm = 1cm
Therefore $1\text{mm}=\frac{1}{10}\text{cm}$
$175\text{mm}=\frac{175}{10}\text{cm}$
$=17.5\text{cm}$

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Question 92 Marks

Write the following decimal as fractions. Reduce the fractions to lowest form:
21.2

Answer

$=31+2\ \text{tenths}$
$=21+\frac{2}{10}$
$=\frac{21\times10}{10}+\frac{2}{10}$
$=\frac{210}{10}+\frac{2}{10}$
$=\frac{212}{10}$
$=\frac{106}{5}$

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Question 102 Marks

Express as metres (m) using decimals:
15cm

Answer

We know that 100cm = 1m.
Therefore, $1\text{cm}=\frac{1}{100}\text{m}$
$15\text{cm}=15\Big(\frac{1}{100}\text{m}\Big)=\frac{15}{100}\text{m}$
$=0.15\text{m}$

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Question 112 Marks

Express the following fractions as decimals:
$\frac{23}{10}$

Answer

$\frac{23}{10}=\frac{20+3}{10}$
$=\frac{20}{10}+\frac{3}{10}=2+\frac{3}{10}=2.3$

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Question 122 Marks

Express the following fractions as decimals:
$\frac{4375}{1000}$

Answer

$\frac{4375}{1000}=\frac{4000+300+70+5}{1000}$
$=\frac{4000}{1000}+\frac{30}{1000}+\frac{70}{1000}+\frac{5}{1000}$
$=4+\frac{3}{10}+\frac{70}{100}+\frac{5}{1000}=4.375$

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Question 132 Marks

Express the following fractions as decimals:
$\frac{139}{100}$

Answer

$\frac{139}{100}=\frac{100+30+9}{100}$
$=\frac{100}{100}+\frac{30}{100}+\frac{9}{100}$
$=1+\frac{3}{10}+\frac{9}{100}=1.39$

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Question 142 Marks

Choose the decimal (s) from the brackets which is (are) not equivalent to the given decimals:

25.1	(25.01, 25.10, 25.100, 25.001)

Answer

25.01 and 25.001 are not equivalent to the given decimal.
In 25.01, 0 is in the tenth place, whereas in 25.1, 1 is in the tenth place.
In 25.001, 0 is in the tenth place, whereas in 25.1, 1 is in the tenth place.

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Question 152 Marks

Write the following as decimals:
$40\frac{2}{5}$

Answer

$40\frac{2}{5}+40+\frac{2}{5}$
To write in decimal, we need to make the denominator 10 by multiplying it by a number. But to maintain the value of the fractoin, we should also multiply the numerator by the same number. Thus we get,
$=40+\frac{2\times2}{5\times2}$
$=40+\frac{4}{10}$
$=40.4$

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Question 162 Marks

Write the following decimal as fractions. Reduce the fractions to lowest form:
3.8

Answer

$=3+8\ \text{tenths}$ $=3+\frac{8}{10}$ $=\frac{3\times10}{10}+\frac{8}{10}$$=\frac{30}{10}+\frac{8}{10}$
$=\frac{38}{10}=\frac{19}{5}$

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Question 172 Marks

Choose the decimal (s) from the brackets which is (are) not equivalent to the given decimals:

45.05

(45.050, 45.005, 45.500, 45.0500)

Answer

45.005 and 45.500 are not equivalent to the given decimal.
In 45.005, 0 is in the hundredth place, whereas in 45.05, 5 is in the hundredth place.
In 45.500, 5 is in the tenth place, whereas in 45.05, 0 is in the tenth place.

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Question 182 Marks

Express the following without using decimals:
3.50km

Answer

We know that 100cm = 1m
Therefore 7.54 = 7 + 0.54
$=7+\frac{54}{100}$
$=7\text{m}\ 54\text{m}$

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Question 192 Marks

Write the following as decimals:
$4\frac{3}{5}$

Answer

$4\frac{3}{5}=4+\frac{3}{5}$
To write in decimal, we need to make the denominator 10 by multiplying it by a number. But, to maintain the value of the fraction, we should also multiply the numerator by the same number. Thus, we get,
$=4+\frac{3\times2}{5\times2}$
$=4+\frac{6}{10}$
$=4.6$

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Question 202 Marks

Express as kilometer (km) using decimals:
5m

Answer

We know that 1000m = 1km
Therefore $1\text{m}=\frac{1}{1000}\text{km}$
$5\text{m}=\frac{5}{1000}\text{km}$
$=0.005\text{km}$

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Question 212 Marks

Which is greater? Give reason for your answer?
5.64 or 5.603

Answer

5.64 > 5.603
The whole parts and the tenth parts are both equal. Comparing the hundredth parts, we have 4 > 0.
Therefore, $5+\frac{6}{10}+\frac{4}{100}>5+\frac{6}{10}+\frac{0}{100}+\frac{3}{1000}$

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Question 222 Marks

Express the following fractions as decimals:
$15\frac{1}{25}$

Answer

$15\frac{1}{25}=15+\frac{1}{25}$
$=15+\frac{1\times4}{25\times4}$
$=15+\frac{4}{100}$
$=15.04$

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Question 232 Marks

Write the following decimal as fractions. Reduce the fractions to lowest form:
6.4

Answer

$=6+4\ \text{tenths}$
$=6+\frac{4}{10}$
$=\frac{6\times10}{10}+\frac{4}{10}$
$=\frac{60}{10}+\frac{4}{10}$
$=\frac{64}{10}=\frac{32}{5}$

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Question 242 Marks

Express as Rupee (Rs) using decimals:
5 paisa

Answer

We know that 100 paisa = Rs. 1.
Therefore, 1 paisa $=\text{Rs}.\frac{1}{100}$
5 paisa $=\frac{5}{100}=\text{Rs}.0.05$

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Question 252 Marks

Victor drove 89.050km on Saturday and 73.9km on Sunday. How many kilometres more did he drive on Saturday?

Answer

Distance travelled on Saturday = 89.050km
Distance travelled on Sunday = 73.9km
Subtracting the distance travelled on Sunday from the distance travelled on Saturday = 89.050 - 73.9km.
= 15.15km
Therefore, victor drove 15.15km more on Saturday.

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Question 262 Marks

Write the following decimals as fractions. Reduce the fractions to lowest form:
0.04

Answer

$= 0 + 0.04$
$=0+0.4\ \text{hundredths}$
$=0+\frac{4}{100}$
$=\frac{4}{100}$
$=\frac{1}{25}$

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Question 272 Marks

Express as Rupee (Rs) using decimals:
2 rupees 60 paisa.

Answer

We know that 100 paisa = Rs. 1.
Therefore, 1 paisa $=\text{Rs}.\frac{1}{100}$
2 rupees and 60 paisa $=2+\frac{60}{100}$
= Rs. 2.60

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Question 282 Marks

Convert the following sets of unlike decimals to like decimal:
5.296, 5.2, 5.29

Answer

Of the three given decimals, 5.296 has the highest number of decimal places, i.e., three, so we change the other two decimals so that they also have three decimal places.
Therefore, the like decimals are 5.296, 5.200 and 5.290.

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Question 292 Marks

Express the following without using decimals:
0.2cm

Answer

We know that 1cm = 10mm.
Therefore, $0.2=\frac{2}{10}$
= 2mm

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Question 302 Marks

Raju bought a book For Rs. 35.65. He gave Rs. 50 to the shopkeeper. How much money did he get back from the shopkeeper?

Answer

Price of the book = Rs. 365
Amount given to the shopkeeper = Rs. 50
Therefore, balance returned by the shopkeeper = Rs. (50 - 35.65)
= Rs. 14.35

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Question 312 Marks

Express as kilometer (km) using decimals:
55m

Answer

We know that 1000m = 1km
Therefore $1\text{m}=\frac{1}{1000}\text{km}$
$55\text{m}=\frac{55}{1000}\text{km}$
$=0.055\text{km}$

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Question 322 Marks

Express as metres (m) using decimals:
8cm

Answer

We know that 100cm = 1m
Therefore $1\text{cm}=\frac{1}{100}\text{m}$
$8\text{cm}=8\Big(\frac{1}{100}\text{m}\Big)=\frac{8}{100}\text{m}$
$=0.08\text{cm}$

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Question 332 Marks

Convert the following decimals as fractions:
75.35

Answer

$=75+0.35$
$=75+\frac{35}{100}$
$=75+\frac{\frac{35}{5}}{\frac{100}{5}}$
$=75+\frac{7}{20}$
$=75\frac{7}{20}$
$=\frac{1507}{20}$

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Question 342 Marks

Express as kilogram (kg) using decimals:
2750g

Answer

We know that 1000g = 1kg
Therefore $1\text{g}=\frac{1}{1000}\text{kg}=0.001\text{kg}$
$2750\text{g}=\frac{2750}{1000}\text{kg}$
$=2.750\text{kg}$

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Question 352 Marks

Convert the following sets of unlike decimals to like decimal:
0.6, 5.8, 12.765

Answer

Of the three given decimals, 12.765 has the highest number of decimal places, i.e., three, so we change the other two decimals so that they also have three decimal places.
Therefore, the like decimals are 0.600, 5.800 and 12.765.

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Question 362 Marks

Express as Rupee (Rs) using decimals:
350 paisa

Answer

We know that 100 paisa = Rs. 1.
Therefore, 1 paisa $=\text{Rs}.\frac{1}{100}$
350 paisa $=\frac{350}{100}=\text{Rs}.3.50$

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Question 372 Marks

Express the following without using decimals:
Rs. 5.25

Answer

We know that 100 paisa = 1 rupee.
So, 1 paisa $=\frac{1}{100}\ \text{rupee}$
Therefore, Rs. 5.25 = 5 + 0.25
$=5+\frac{25}{100}$
= Rs. 5 and 25 paisa

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Question 382 Marks

Express the following fractions as decimals:
$25\frac{1}{8}$

Answer

$25\frac{1}{8}=25+\frac{1}{8}$
$=25+\frac{1\times125}{8\times125}$
$=25+\frac{125}{1000}$
$=25.125$

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Question 392 Marks

Express as kilometer (km) using decimals:
15km 35m

Answer

We know that 1000m = 1km
Therefore $1\text{m}=\frac{1}{1000}\text{km}$
15km 35m = 15 + 351000
= 15.035km

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Question 402 Marks

Nasreen bought 3m 20cm cloth for her shirt and 2m 5cm cloth for skirt. Find the total cloth bought by her.

Answer

Cloth for shirt = 3m 20cm = 3.20m
Cloth for skirt = 2m 50m = 2.05m
Total cloth bought by nasreen = (3.20 + 2.05)m
= 5.25m
Total cloth bought by nasreen is 5.25m

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Question 412 Marks

Express as kilogram (kg) using decimals:
5kg 750g

Answer

We know that 1000g = 1kg
Therefore $1\text{g}=\frac{1}{1000}\text{kg}=0.001\text{kg}$
5kg 750g = 5 + 7501000
= 5.750kg

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Question 422 Marks

Write the decimals shown in the following place value table:

	Thousands	Hundreds	Tens	Ones	Tenths	Hundredths	Thousandths
i		3	0	7	1	2
ii	9	5	4	3	0	2	5
iii			1	2	5	0	3

Answer

The decimals shown in the above place-value table can be written as follows.

307.12
9543.025
12.503

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Question 432 Marks

Write the following as decimals:
$39\frac{2}{10}$

Answer

$39\frac{2}{10}=39+\frac{2}{10}$
Here, the denominator is 10.
Therefore, the decimal is 39.2

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Question 442 Marks

Convert the following sets of unlike decimals to like decimal:
4.3294, 43.29, 432.94

Answer

Among the three given decimals, 4.3294 has the highest number of decimal places, i.e., four, so we change all the decimals so that they also have four decimal places.
Therefore, the like decimals are 4.3294, 43.2900 and 432.9400.

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Question 452 Marks

Convert the following sets of unlike decimals to like decimal:
2.02, 3.2

Answer

Of the two given decimals, 2.02 has more decimal places, i.e., two, so we change 3.2 so that it has two decimal places.
Therefore, the like decimals are 2.02 and 3.20.

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Question 462 Marks

Express as metres (m) using decimals:
3m 65cm

Answer

We know that 100cm = 1m
Therefore $1\text{cm}=\frac{1}{100}\text{m}$
$3\text{m}\ \text{65}\ \text{cm}=3+\frac{65}{100}\text{m}$
$=3.65\text{m}$

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Question 472 Marks

Express the following fractions as decimals:
$18\frac{3}{24}$

Answer

$18\frac{3}{24}=18+\frac{3}{24}$
$18+\frac{1}{8}=18+\frac{125\times1}{125\times8}$
$=18+\frac{125}{1000}=18.125$

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Question 482 Marks

Write the following decimals as fractions. Reduce the fractions to lowest form:
1.20

Answer

$=1+0.20$
$=1+20\ \text{hundredths}$
$=1+\frac{20}{100}$
$=\frac{100}{100}+\frac{20}{100}$
$=\frac{120}{100}$
$=\frac{6}{5}$

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Question 492 Marks

Convert the following decimals as fractions:
54.26

Answer

$=54+0.26$
$=54+\frac{26}{100}$
$=54+\frac{\frac{26}{2}}{\frac{100}{2}}$
$=54+\frac{13}{50}$
$=54\frac{13}{50}$
$=\frac{2713}{50}$

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Question 502 Marks

Express as Rupee (Rs) using decimals:
15 paisa

Answer

We know that 100 paisa = Rs. 1.
Therefore, 1 paisa $=\text{Rs}.\frac{1}{100}$
15 paisa $=\frac{15}{100}=\text{Rs}.0.15$

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Question 512 Marks

Express as centimetre (cm) using decimals:
5mm

Answer

We know that 10mm = 1cm
Therefore $1\text{mm}=\frac{1}{10}\text{cm}$
$5\text{mm}=\frac{5}{10}\text{cm}$
$=0.5\text{cm}$

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Question 522 Marks

Raju bought a book for Rs. 35.65. He gave Rs. 50 to the shopkeeper. How much money did he get back from the shopkeeper?

Answer

Price of the book = Rs. 35.65
Amount given to the shopkeeper = Rs. 50
Therefore, balance returned by the shopkeeper = Rs. (50 - 35.65)
= Rs. 14.35

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Question 532 Marks

Express the following fractions as decimals:
$39\frac{7}{35}$

Answer

$39\frac{7}{35}=39+\frac{7}{35}$
$=39+\frac{1}{5}$
$=39+\frac{1\times2}{5\times2}$
$=39+\frac{2}{10}$
$=39.2$

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Question 542 Marks

Waheeda's school is at a distance of 5km 350m from her house. She travels 1km 70m on foot and the rest she travels by bus. How much distance does she travel by bus?

Answer

Distance travelled on foot = 1km 70m
Suppose the distance travelled by bus = x km
Total distance of school from residence = 5km 350m = 5.350km
So, 1.070 + x = 5.350
= x = 5.350 - 1.070
= x = 4.280km
Therefore, distance travelled by bus is 4.280km

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Question 552 Marks

Write the following decimals as fractions. Reduce the fractions to lowest form:
2.34

Answer

$=2+0.34$
$=2+34\ \text{hundredths}$
$=2+\frac{34}{100}$
$=\frac{2\times100}{100}+\frac{34}{100}$
$=\frac{200}{100}+\frac{34}{100}$
$=\frac{234}{100}$
$=\frac{117}{50}$

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Question 562 Marks

Convert the following sets of unlike decimals to like decimal:
7.8, 7.85

Answer

Of the two given decimals, 7.85 has more decimal places, i.e., two, so we change 7.8 so that it has two decimal places.
Therefore, the like decimals are 7.80 and 7.85.

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Question 572 Marks

Express the following fractions as decimals:
$12\frac{1}{2}$

Answer

$12\frac{1}{2}=12+\frac{1}{2}$
$=12+\frac{1\times5}{2\times5}$
$=12+\frac{5}{10}=12.5$

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Question 582 Marks

Express the following fractions as decimals:
$\frac{111}{250}$

Answer

$\frac{111}{250}=\frac{111\times4}{250\times4}$
$=\frac{444}{1000}$
$=0.444$

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Question 592 Marks

Write of the following as decimals:
$\frac{888}{1000}$

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Question 602 Marks

Express the following without using decimals:
8.354kg

Answer

We know that 1000 g = 1kg.
So, $1\text{g}=\frac{1}{1000}\text{kg}$
Therefore, 8.354 = 8 + 0.354
$=8+\frac{354}{1000}$
$=8\text{kg}\ \text{354}\text{g}$

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Question 612 Marks

Write the following decimals as fractions. Reduce the fractions to lowest form:
0.342

Answer

$=0+342\ \text{thousandths}$
$=\frac{342}{1000}$
$=\frac{171}{500}$

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Question 622 Marks

Express the following without using decimals:
7.54m

Answer

We know that 1kg = 1000g
Therefore, 15.005 = 15 + 0.005
$=15+\frac{5}{1000}$
$=15\text{kg},5\text{g}$

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Question 632 Marks

Write the following as decimals:
$25\frac{1}{2}$

Answer

$25\frac{1}{2}=25+\frac{1}{2}$
To write in decimal, we need to make the denominator 10 by multiplying it by a number. But, to maintain the value of the fraction, we should also multiply the numerator by the same number. Thus we get,
$=25+\frac{1\times5}{2\times5}$
$=25+\frac{5}{10}$
$=25.5$

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Question 642 Marks

Express as kilogram (kg) using decimals:
8g

Answer

We know that 1000g = 1kg
Therefore $1\text{g}=\frac{1}{1000}\text{kg}=0.001\text{kg}$
$8\text{g}=\frac{8}{1000}\text{kg}$
$=0.008\text{kg}$

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Question 652 Marks

Express the following without using decimals:
12.05m

Answer

We know that 1m = 100cm.
Therefore, 12.05 = 12 + 05
$=12+\frac{5}{100}$
= 12m and 5cm

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Question 662 Marks

Express as centimetre (cm) using decimals:
60mm

Answer

We know that 10mm = 1cm
Therefore $1\text{mm}=\frac{1}{10}\text{cm}$
$60\text{mm}=\frac{60}{10}\text{cm}$
$=6\text{cm}$

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Question 672 Marks

Write the decimal number represented by the points on the given number line: A, B, C, D.

Answer

0.8, since A is at the eighth place between 0 and 1.
1.3, since B is at the third place between 1 and 2.
1.9, since C is at the ninth place between 1 and 2.
2.6, since D is at the sixth place between 2 and 3.

Disclaimer: The image given in the book is not consistent; as the number of periods between 0 and 1 is ten but the number of periods between 1 and 2 are seven. So, ignoring the position of the given numbers 1, 2 and 3. it has been assumed that there are ten periods between every two consecutive numbers starting from the first point taken as zero.

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Question 682 Marks

Convert the following decimals as fractions:
0.7575

Answer

$=\frac{7575}{10000}$$=\frac{\frac{7575}{25}}{\frac{10000}{25}}$
$=\frac{303}{400}$

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Question 692 Marks

Express as metres (m) using decimals:
135cm

Answer

We know that 100cm = 1m
Therefore $1\text{m}=\frac{1}{100}\text{m}$
$135\text{cm}=135\Big(\frac{1}{100}\text{m}\Big)=\frac{135}{100}\text{m}$
$=1.35\text{m}$

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Question 702 Marks

Write the following decimals as fractions. Reduce the fractions to lowest form:
17.38

Answer

$=17+0.38$
$=17+38\ \text{hundredths}$
$=17+\frac{38}{100}$
$=\frac{17\times100}{100}+\frac{38}{100}$
$=\frac{1700}{100}+\frac{38}{100}$
$=\frac{1738}{100}$
$=\frac{869}{50}$

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Question 712 Marks

Express as kilogram (kg) using decimals:
150g

Answer

We know that 1000g = 1kg
Therefore $1\text{g}=\frac{1}{1000}\text{kg}=0.0001\text{kg}$
$150\text{g}=\frac{150}{1000}\text{kg}$
$=0.150\text{kg}$

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Question 722 Marks

Choose the decimal (s) from the brackets which is (are) not equivalent to the given decimals:

0.8	(0.80, 0.85, 0.800, 0.08)

Answer

0.85 and 0.08 are not equivalent to the given decimal.
In 0.85, we have 5 in the hundredth place, where as in 0.8 we have nothing in the hundredth place.
In 0.08, 0 is in the tenth place, whereas in 0.8, 8 is in the tenth place.

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Question 732 Marks

Express the following without using decimals:
15.005kg

Answer

We know that 1m = 100cm
Therefore 12.05 = 12 + 0.05
$=12+\frac{5}{100}$
$=12\text{m},5\text{cm}$

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Question 742 Marks

Express as centimetre (cm) using decimals:
4cm 5mm

Answer

We know that 10mm = 1cm
Therefore $1\text{mm}=\frac{1}{10}\text{cm}$
$4\text{cm}\ 5\text{mm}=4+\frac{5}{10}$
$=4.5\text{cm}$

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Question 752 Marks

Write the following decimals in the place value table:

52.5
12.57
15.05
74.059
0.503

Answer

	Thousands	Hundreds	Tens	Ones	Tenths	Hundredths	Thousand
i			5	2	5
ii			1	2	5	7
iii			1	5	0	5
iv			7	4	0	5	9
v					5	0	3

The given decimals can be written as above in the place-value table.

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Question 762 Marks

Radhika's mother gave her Rs. 10.50 and her father gave her Rs. 15.80, find the total amount given to Radhika by her parents.

Answer

Radhika's mother gave her Rs. 10.50
Radhika's father gave her Rs. 15.80
Total amount given to Radhika,
= 10.50 + 15.80
= Rs. 26.30

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Question 772 Marks

Convert the following decimals as fractions:
2.3675

Answer

$=2+0.3675$
$=2+\frac{3675}{10000}$
$=2+\frac{\frac{3675}{25}}{\frac{10000}{25}}$
$=2+\frac{147}{400}$
$=2\frac{147}{400}$
$=\frac{947}{400}$

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