NCERT Exercise 2.6 solution-2
Fractions and Decimals 7th Math
NCERT Exercise 2.6 solution-2
Multiplication of Decimal Numbers
Question (4) A two wheeler covers a distance of 55.3 km in one litre of petrol. How much distance will it cover in 10 litre of petrol?
Solution :
Given, distance covered by a two wheeler in 1 litre of petrol = 55.3 km
Thus, distance covered in 10 litre of petrol = ?
∵ In 1 litre of petrol distance covered = 55.3 km
∴ In 10 litre of petrol distance covered = 55.3 km × 10
`=553/cancel10xxcancel10` km
= 553 km Answer
Question (5) Find:
(i) 2.5 × 0.3
Solution :
Given, 2.5 × 0.3
Step (1)
Given numbers are multiplied without taking decimals into consideration.
Given numbers after omitting decimal are 25 × 3
= 25 × 3
= 75
Step (2)
Now, since sum of the numbers of digits to the right after decimal in both of the numbers i.e. one digit in each of the two given number = 2
Thus, put a decimal point left after the digits in the product counting from right to left.
Thus, 2.5 × 0.3
= 0.75 Answer
Alternate method to multiply given decimal numbers
Given, 2.5 × 0.3
`=25/10xx3/10`
`= (25xx3)/(10xx10)`
`=75/100`
= 0.75 Answer
(ii) 0.1 × 51.7
Solution :
[The decimal numbers are multiplied as whole numbers ignoring decimal point. Then decimal point is given in product after the number of digits to be counted is obtained by adding number of digits to the right of the decimal point in the decimal numbers that are being multiplied.]
Given, 0.1 × 51.7
= 5.17 Answer
Alternate method to multiply given decimal numbers
Given, 0.1 × 51.7
`=1/10xx517/10`
`=517/100`
= 5.17 Answer
(iii) 0.2 × 316.8
Solution :
[The decimal numbers are multiplied as whole numbers ignoring decimal point. Then decimal point is given in product after the number of digits to be counted is obtained by adding number of digits to the right of the decimal point in the decimal numbers that are being multiplied.]
Given, 0.2 × 316.8
= 63.36 Answer
Alternate method to multiply given decimal numbers
Given, 0.2 × 316.8
`=2/10xx3168/10`
`=(2xx3168)/(10xx10)`
`=6336/100`
= 63.36 Answer
(iv) 1.3 × 1.3
Solution :
Given, 1.3 × 1.3
= 1.69 Answer
Alternate method to multiply given decimal numbers
Given, 1.3 × 1.3
`=13/10xx13/10`
`=169/100`
= 1.69 Answer
(v) 0.5 × 0.05
Solution :
Given, 0.5 × 0.05
= 0.025 Answer
Alternate method to multiply given decimal numbers
Given, 0.5 × 0.05
`=5/10xx5/100`
`=25/1000`
= 0.025 Answer
(vi) 11.2 × 0.15
Solution :
Given, 11.2 × 0.15
= 1.68 Answer
Alternate method to multiply given decimal numbers
Given, 11.2 × 0.15
`= 112/10xx15/100`
`= 1680/1000`
= 1.680 or 1.68 Answer
(vii) 1.07 × 0.02
Solution :
Given, 1.07 × 0.02
= 0.0214 Answer
Alternate method to multiply given decimal numbers
Given, 1.07 × 0.02
`=107/100xx2/100`
`=214/10000`
=0.0214 Answer
(viii) 10.05 × 1.05
Solution :
Given, 10.05 × 1.05
= 10.5525 Answer
Alternate method to multiply given decimal numbers
Given, 10.05 × 1.05
`=1005/100xx105/100`
`= 105525/10000`
= 10.5525 Answer
(ix) 101.01 × 0.01
Solution :
Given, 101.01 × 0.01
= 1.0101 Answer
Alternate method to multiply given decimal numbers
Given, 101.01 × 0.01
`=10101/100xx1/100`
`=10101/10000`
= 1.0101 Answer
(x) 100.01 × 1.1
Solution :
Given, 100.01 × 1.1
= 110.011 Answer
Alternate method to multiply given decimal numbers
Given, 100.01 × 1.1
`=10001/100xx11/10`
`=110011/1000`
= 110.011 Answer
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