HOTS Question: Fractions and Decimals

Q1: Express as rupees as decimals:
(i) 7 paise
Ans:
We know that,
= ₹ 1 = 100 paise
= 1 paise = ₹ (1/100)
∴ 7 paise = ₹ (7/100)
= ₹ 0.07

(ii) 7 rupees 7 paise
Ans:
We know that,
= ₹ 1 = 100 paise
= 1 paise = ₹ (1/100)
∴ 7 rupees 7 paise = ₹ 7 + ₹ (7/100)
= ₹ 7 + ₹ 0.07
= ₹ 7.07

(iii) 77 rupees 77 paise
Ans:
We know that,
= ₹ 1 = 100 paise
= 1 paise = ₹ (1/100)
∴ 77 rupees 77 paise = ₹ 77 + ₹ (77/100)
= ₹ 77 + ₹ 0.77
= ₹ 77.77

(iv) 50 paise
Ans:
We know that,
= ₹ 1 = 100 paise
= 1 paise = ₹ (1/100)
∴ 50 paise = ₹ (50/100)
= ₹ 0.50

(v) 235 paise
Ans:
We know that,
= ₹ 1 = 100 paise
= 1 paise = ₹ (1/100)
∴ 235 paise = ₹ (235/100)
= ₹ 2.35

Q2: Express in kilogram:
(i) 200 gram
Ans:
We know that,
= 1 kg = 1000 gram
Then,
= 1 g = (1/1000) kg
= 200 g = (200/1000) kilogram
= (2/10)
= 0.2 kg

(ii) 3470 gram
Ans:
We know that,
= 1 kg = 1000 gram
Then,
= 1 g = (1/1000) kilogram
= 3470 g = (3470/1000) kilogram
= (3470/100)
= 3.470 kg

(iii) 4 kg 8 g
Ans:
We know that,
= 1 kg = 1000 gram
Then,
= 1 g = (1/1000) kilogram
= 4 kg 8 g is equal to 4 kg + (8/1000) kilogram
= 4 kg + 0.008
= 4.008 kilogram

Q3: Shyama bought around 5 kg 300 g apples and 3 kg 250 g mangoes. Sarala then bought 4 kg 800 g oranges and 4 kg 150 g bananas. Who bought more fruits?
Ans:
From the above question, it is given that,
Fruits bought by Shyama is = 5 kg 300 g
= 5 kg + (300/1000) kg
= 5 kg + 0.3 kg
= 5.3 kg
Fruits bought by Sarala is = 4 kg 800 g + 4 kg 150 g
= (4 + (800/1000)) + (4 + (150/1000))
= (4 + 0.8) kg + (4 + .150) kg
= 4.8 kg + 4.150kg
= 8.950 kg
So, Sarala bought more fruits.

Q4: Find:
(i) 1.3 × 10
Ans:
On multiplying the decimal by 10, the decimal point is shifted to the right by one place.
We have,
= 1.3 × 10 = 13

(ii) 36.8 × 10
Ans:
On multiplying the decimal by 10, the decimal point is shifted to the right by one place.
We have,
= 36.8 × 10 = 368

(iii) 153.7 × 10
Ans:
On multiplying the decimal by 10, the decimal point is shifted to the right by one place.
We have,
= 153.7 × 10 = 1537

(iv) 168.07 × 10
Ans:
On multiplying the decimal by 10, the decimal point is shifted to the right by one place.
We have,
= 168.07 × 10 = 1680.7

(v) 31.1 × 100
Ans:
On multiplying the decimal by 100, the decimal point is shifted to the right by two places.
We have,
= 31.1 × 100 = 3110

(vi) 156.1 × 100
Ans:
On multiplying the decimal by 100, the decimal point is shifted to the right by two places.
We have,
= 156.1 × 100 = 15610

(vii) 3.62 × 100
Ans:
On multiplying a decimal by the number 100, the decimal point is shifted to the right by two places.
We have,
= 3.62 × 100 = 362

(viii) 43.07 × 100
Ans:
On multiplying a decimal by the number 100, the decimal point is shifted to the right by two places.
We have,
= 43.07 × 100 = 4307

Q5: Find the following:
(a) 2.5 × 0.3
Ans:
We have,
= (25/10) × (3/10)
= (75/100)
On dividing the decimal by 100, the decimal point is shifted to the left by two places.
Then,
= 0.75

(b) 0.1 × 51.7
Ans:
We have,
= (1/10) × (517/10)
= (517/100)
On dividing the decimal by 100, the decimal point is shifted to the left by two places.
Then,
= 5.17

(c) 0.2 × 316.8
Ans:
We have,
= (2/10) × (3168/10)
= (6336/100)
On dividing the decimal by 100, the decimal point is shifted to the left by two places.
Then,
= 63.36

(d) 1.3 × 3.1
Ans:
We have,
= (13/10) × (31/10)
= (403/100)
On dividing the decimal by 100, the decimal point is shifted to the left by two places.
Then,
= 4.03.

Q6:  (i) Express 5 centimeters in meter and kilometre
Ans:
We all know that,
= 1 meter = 100 centimeter
Then,
= 1 cm = (1/100) meter
= 5 cm = (5/100)
= 0.05 m
Now,
= 1 km = 1000 meter
Then,
= 1 m = (1/1000) kilometer
= 0.05 m = (0.05/1000)
= 0. 00005 kilometer
(ii) Express 35 mm in cm, m and km
Ans:
We know that,
= 1 cm = 10 mm
Then,
= 1 mm = (1/10) cm
= 35 mm = (35/10) cm
= 3.5 cm
And,
= 1 meter = 100 cm
Then,
= 1 cm = (1/100) m
= 3.5 cm = (3.5/100) m
= (35/1000) m
= 0.035 m
Now,
= 1 km = 1000 m
Then,
= 1 m = (1/1000) km
= 0.035 m = (0.035/1000)
= 0. 000035 km

Q7: Write the following in decimal numbers in their expanded form:
(i) 20.03
Ans:
We have that,
20.03 = (2 × 10) + (0 × 1) + (0 × (1/10)) + (3 × (1/100))

(ii) 2.03
Ans:
We have that,
2.03 is equal to (2 × 1) + (0 × (1/10)) + (3 × (1/100))

(iii) 200.03
Ans:
We have,
200.03 is (2 × 100) + (0 × 10) + (0 × 1) + (0 × (1/10)) + (3 × (1/100))

(iv) 2.034
Ans:
We have,
2.034 gets equal to (2 × 1) + (0 × (1/10)) + (3 × (1/100)) + (4 × (1/1000)).

Q8: Write the place value of 2 in the following decimal numbers:
(i) 2.56
Ans:
From the above question, we can observe that,
The place value of 2 in the decimal 2.56 is ones.

(ii) 21.37
Ans:
From the above question, we can observe that,
The place value of 2 in the decimal 21.37 is tens.

(iii) 10.25
Ans:
From the above question, we can observe that,
The place value of 2 in the decimal 10.25 is tenths.

(iv) 9.42
Ans:
From the above question, we can observe that,
The place value of 2 in the decimal 9.42 is the hundredth.

(v) 63.352
Ans:
From the above question, we can observe that,
The place value of 2 in the decimal 63.352 is the thousandth.

Q9: How much less is 28 km as compared to 42.6 km?
Answer :-
Now, we have to find the difference between 42.6 km and 28 km.
42.6
-28.0
14.6
Hence, 14.6 km less is 28 km than 42.6 km.

Q10: A two-wheeler covers a total distance of 55.3 km in one litre of petrol. How much total distance will it cover in 10 litres of petrol?
Ans:
From the above question, it is given that,
Distance covered by the two-wheeler in 1L of petrol = 55.3 km
Now,
Distance covered by the two-wheeler in 10L of petrol is = (10 × 55.3)
= 553 km
Hence the Two-wheeler covers a distance of 10L of petrol 553 km.

Q11: Find:
(i) 7 ÷ 3.5
Ans:
We have,
= 7 ÷ (35/10)
= 7 × (10/35)
= 1 × (10/5)
= 2

(ii) 36 ÷ 0.2
Ans:
We have,
= 36 ÷ (2/10)
= 36 × (10/2)
= 18 × 10
= 180

(iii) 3.25 ÷ 0.5
Ans:
We have,
= (325/100) ÷ (5/10)
= (325/100) × (10/5)
= (325 × 10)/ (100 × 5)
= (65 × 1)/ (10 × 1)
= 65/10
= 6.5