NCERT Exercise 2.5 Solution
Fractions and Decimals 7th Math
NCERT Exercise 2.5 Solution
Question (1) Which is greater?
(i) 0.5 or 0.05
Solution :
Given, 0.5 or 0.05
Thus, greater = ?
To find greater among decimal numbers, if there is no number before decimal, then numbers given after the decimal are compared.
To compare the numbers are decimals, first number of digits after decimal are made equal after putting required number of zeros.
Thus, 0.5 can be written as 0.50
Now, the number of digits after decimal in both of the number is equal, i.e. equal to 2 digits
i.e. 0.50 or 0.05
Now, clearly, 50 is greater than 05
Thus, 0.5 > 0.05
Thus, 0.5 is greater. Answer
Alternate Method to compare decimal numbers
We have, 0.5 or 0.05
`=5/10 or 05/100`
`=(5xx10)/(10xx10) or 5/100`
`=50/100 or 5/100`
Thus, it is clear that, `50/100 > 5/100`
Thus, 0.5 > 0.05
Thus, 0.5 is greater Answer
(ii) 0.7 or 0.5
Solution :
Given, 0.7 or 0.5
Thus, greater = ?
To find greater among decimal numbers, if there is no number before decimal, then numbers given after the decimal are compared.
Here number after decimal are 7 and 5
Thus, clearly, 7 > 5
This means 7 is greater.
Hence, 0.7 is greater. Answer
Alternate Method
Given, 0.7 or 0.5
Thus, greater = ?
After converting given decimal numbers into fraction, we get
0.7 = 7/10 and 0.5 = 5/10
Thus, clearly, `7/10 > 5/10`
That means `7/10` is greater.
Thus, 0.7 is greater Answer
(iii) 7 or 0.7
Solution
Given, 7 or 0.7
Thus, greater = ?
Here, 7 = 7.0
To find greater among decimal numbers, if there is number before decimal, then numbers given before decimal are compared.
Thus, clearly, 7 > 0
This means 7 is greater.
Thus, 7 > 0.7
Thus, 7 is greater Answer
(iv) 1.37 or 1.49
Solution :
Given, 1.37 or 1.49
Thus, greater = ?
To find greater among decimal numbers, if there is same number before decimal, then numbers given after the decimal are compared.
Here, numbers before decimal are same.
And numbers after decimal are 37 and 49
Thus, clearly, 49 is greater than 37
Thus, 1.37 < 1.49
This, means 1.49 is greater.
Thus, 1.49 is greater Answer
(v) 2.03 or 2.30
Solution :
Given, 2.03 or 2.30
Thus, greater = ?
To find greater among decimal numbers, if there is same number before decimal, then numbers given after the decimal are compared.
Here, numbers before decimal are same.
And numbers at first place after decimal are 0 and 3
Thus, clearly, 0 < 3
This, means 3 is greater.
Thus, clearly, 2.03 < 2.30
This means 2.30 is greater Answer
Alternate Method
Given, 2.03 or 2.30
Thus, greater = ?
Here, `2.03 = 203/100`
And, `2.30 = 230/100`
Thus, clearly, `203/100 < 230/100`
This means `230/100` is greater.
Thus, 2.03 < 2.30
This means 2.30 is greater Answer
(vi) 0.8 or 0.88
Solution :
Given, 0.8 or 0.88
Thus, greater = ?
Here, 0.8 = 0.80
Thus, numbers are 0.80 and 0.88
If there is no number before decimal, then numbers after decimal are compared.
Now, clearly, 80 < 88 (numbers after decimal)
Thus, 0.80 < 0.88
Or, 0.8 < 0.88
Thus, clearly, 0.88 is greater. Answer
Alternate Method to compare decimal numbers
Given, 0.8 or 0.88
Thus, greater = ?
Here, 0.8 = 0.80
Thus, numbers are 0.80 and 0.88
After converting given decimal numbers into fraction, we get
`0.80 = 80/100` and `0.88 = 88/100`
Now, denominators in both of the numbers are same, i.e. equal to 100.
Now, since numerator in second number, i.e. `88/100` is greater
Thus, `80/100 < 88/100`
This means `88/100` is greater.
Thus, 0.8 < 0.88
Thus, 0.88 is greater Answer
Question (2) Express as rupees using decimals:
(i) 7 paise
Solution :
Given, 7 paise
Thus, value in rupees using decimals = ?
We know that, paises are converted into rupees by dividing by 100
Thus, 7 paise `=7/100` Rupees
= 0.07 rupees Answer
Alternate Method to convert paise into rupees
Given, 7 paise
∵ 100 paise = 1 rupee
∴ 1 paise `=1/100` rupee
∴ 7 paise `=1/100xx7` rupee
= 0.07 rupee Answer
(ii) 7 rupees 7 paise
Solution
Given, 7 rupees 7 paise
Thus, value in rupees using decimals = ?
We know that, paises are converted into rupees by dividing by 100
Thus, 7 rupees 7 paise `=7+7/100` rupees
= 7 + 0.07 rupees
= 7.07 rupees Answer
Alternate Method to convert paise into rupees
Given, 7 rupees 7 paise
∵ 100 paise = 1 rupee
∴ 1 paise `=1/100` rupee
∴ 7 paise `=1/100xx7` rupee
Thus, 7 paise = 0.07 rupee
Thus, 7 rupees 7 paise = 7 rupees + 0.07 rupees
= 7.07 rupees Answer
(iii) 77 rupees 77 paise
Solution
Given, 77 rupees 77 paise
Thus, value in rupees using decimals = ?
We know that, paises are converted into rupees by dividing by 100
Thus, 77 rupees 77 paise `=77+77/100` rupees
= 77 + 0.77 rupees
= 77.77 rupees Answer
Alternate Method to convert paise into rupees
Given, 77 rupees 77 paise
∵ 100 paise = 1 rupee
∴ 1 paise `=1/100` rupee
∴ 77 paise `=1/100xx77` rupee
Thus, 77 paise = 0.77 rupee
Thus, 77 rupees 77 paise = 77 rupees + 0.77 rupees
= 77.77 rupees Answer
(iv) 50 paise
Solution :
Given, 50 paise
Thus, value in rupees using decimals = ?
We know that, paises are converted into rupees by dividing by 100
Thus, 50 paise `=50/100` Rupees
= 0.50 rupees or 0.5 Answer
Alternate Method to convert paise into rupees
Given, 50 paise
∵ 100 paise = 1 rupee
∴ 1 paise `=1/100` rupee
∴ 50 paise `=1/100xx50` rupee
= 0.5 rupee Answer
(v) 235 paise
Given, 235 paise
Thus, value in rupees using decimals = ?
We know that, paises are converted into rupees by dividing by 100
Thus, 235 paise `=235/100` Rupees
= 2.35 rupees Answer
Alternate Method to convert paise into rupees
Given, 235 paise
∵ 100 paise = 1 rupee
∴ 1 paise `=1/100` rupee
∴ 235 paise `=1/100xx235` rupee
= 2.35 rupee Answer
Question (3) (i) Express 5 cm in meter and kilometer
Solution :
Given, to express 5 cm in meter and kilometer
We know that, 1 cm `=1/100` meter
Thus, 5 cm `=5/100` meter
Thus, 5 cm = 0.05 meter
And we know that, 1 cm `=1/100000` km
Thus, 5 cm `= 5/100000` km
= 0.00005 km
Thus, 5 cm = 0.05 meter and 0.00005 km Answer
(ii) Express 35 mm in cm, m and km
Solution :
Given, 35 mm
Thus, values in cm, m and km using decimals = ?
We know that, 1 mm `=1/10` cm
Thus, 35 mm `=35/10` cm = 3.5 cm
We know that, 1 mm `=1/1000` m
Thus, 35 mm `=35/1000` m
= 0.035 m
We know that, 1 mm `=1/1000000` km
Thus, 35 mm `=35/1000000` km
= 0.000035 km
Thus, 35 mm = 3.5 cm, 0.35 m and 0.000035 km Answer
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