NCERT Exercise 2.6 Solution
Fractions and Decimals 7th Math
NCERT Exercise 2.6 Solution
Multiplication of decimal numbers
Question (1) Find:
(i) 0.2 × 6
Solution :
Given, 0.2 × 6
`=2/10xx6`
`=12/10`
= 1.2 Answer
Alternate Method to multiply a decimal number with a whole number
Given, 0.2 × 6
The decimal number is multiplied as simple method ignoring the decimal. After that a decimal is given after digits in product counting from left equal to number of digits after decimal in number to be multiplied.
Thus, 0.2 × 6
= 1.2 Answer
(ii) 8 × 4.6
Solution :
Given, 8 × 4.6
`=8xx46/10`
`=368/10`
= 36.8 Answer
Alternate Method to multiply a decimal number with a whole number
Given, 8 × 4.6
The decimal number is multiplied as simple method ignoring the decimal. After that a decimal is given after digits in product counting from left equal to number of digits after decimal in number to be multiplied.
Thus, 8 × 4.6
= 36.8 Answer
(iii) 2.71 × 5
Solution :
Given, 2.71 × 5
`=271/100xx5`
`= 1355/100`
= 13.55 Answer
Alternate Method to multiply a decimal number with a whole number
Given, 2.71 × 5
The decimal number is multiplied as simple method ignoring the decimal. After that a decimal is given after digits in product counting from left equal to number of digits after decimal in number to be multiplied.
Thus, 2.71 × 5
= 13.55 Answer
(iv) 20.1 × 4
Solution :
Given, 20.1 × 4
`=201/10xx4`
`=804/10`
= 80.4 Answer
Alternate Method to multiply a decimal number with a whole number
Given, 20.1 × 4
The decimal number is multiplied as simple method ignoring the decimal. After that a decimal is given after digits in product counting from left equal to number of digits after decimal in number to be multiplied.
Thus, 20.1 × 4
= 80.4 Answer
(v) 0.05 × 7
Solution :
Given, 0.05 × 7
`=5/100xx7`
`=35/100`
= 0.35 Answer
Alternate Method to multiply a decimal number with a whole number
Given, 0.05 × 7
The decimal number is multiplied as simple method ignoring the decimal. After that a decimal is given after digits in product counting from left equal to number of digits after decimal in number to be multiplied.
Thus, 0.05 × 7
= 0.35
(vi) 211.02 × 4
Solution :
Given, 211.02 × 4
`=21102/100xx4`
`=84408/100`
= 844.08 Answer
Alternate Method to multiply a decimal number with a whole number
Given, 211.02 × 4
The decimal number is multiplied as simple method ignoring the decimal. After that a decimal is given after digits in product counting from left equal to number of digits after decimal in number to be multiplied.
Thus, 211.02 × 4
= 844.08 Answer
(vii) 2 × 0.86
Solution :
Given, 2 × 0.86
`=2xx86/100`
`= 172/100`
= 1.72 Answer
Alternate Method to multiply a decimal number with a whole number
Given, 2 × 0.86
The decimal number is multiplied as simple method ignoring the decimal. After that a decimal is given after digits in product counting from left equal to number of digits after decimal in number to be multiplied.
Thus, 2 × 0.86
= 1.72 Answer
Question (2) Find the area of rectangle whose length is 5.7 cm and breadth is 3 cm.
Solution :
Given, length of rectangle = 5.7 cm
And, breadth of rectangle = 3 cm
Thus, area = ?
We know that, area of a rectangle = length × breadth
Thus, area of given rectangle = 5.7 cm × 3 cm
`=57/100xx3` cm2
`=171/100` cm2
= 1.71 cm2
Thus, area of given rectangle = 1.71 cm2 Answer
Alternate Method to multiply a decimal number with a whole number
Given, length of rectangle = 5.7 cm
And, breadth of rectangle = 3 cm
Thus, area = ?
We know that, area of a rectangle = length × breadth
Thus, area of given rectangle = 5.7 cm × 3 cm
The decimal number is multiplied as simple method ignoring the decimal. After that a decimal is given after digits in product counting from left equal to number of digits after decimal in number to be multiplied.
Thus, area of given rectangle = 1.71 cm2 Answer
Question (3) Find:
(i) 1.3 × 10
Solution :
Given, 1.3 × 10
`=13/10xx10`
= 13 Answer
Alternate method
Given, 1.3 × 10
We know that, when a decimal number is multiplied by 10, 100 or 1000, the digits in the product are same as in the decimal number, but the decimal point in the product is shifted to the right by as, many of places as there are zeros over one.
Thus, 1.3 × 10
= 13 Answer
(ii) 36.8 × 10
Solution :
Given, 36.8 × 10
`=368/cancel10xxcancel10`
= 368 Answer
Alternate method to multiply a decimal number by 10
Given, 36.8 × 10
We know that, when a decimal number is multiplied by 10, 100 or 1000, the digits in the product are same as in the decimal number, but the decimal point in the product is shifted to the right by as, many of places as there are zeros over one.
Thus, 36.8 × 10
= 368 Answer
(iii) 153.7 × 10
Solution :
Given, 153.7 × 10
`=1537/cancel10xxcancel10`
= 1537 Answer
Alternate method to multiply a decimal number by 10
Given, 153.7 × 10
We know that, when a decimal number is multiplied by 10, 100 or 1000, the digits in the product are same as in the decimal number, but the decimal point in the product is shifted to the right by as, many of places as there are zeros over one.
Thus, 153.7 × 10
= 1537 Answer
(iv) 168.07 × 10
Solution :
Given, 168.07 × 10
`=16807/(cancel100 10)xxcancel10`
= 1680.7 Answer
Alternate method to multiply a decimal number by 10
Given, 168.07 × 10
We know that, when a decimal number is multiplied by 10, 100 or 1000, the digits in the product are same as in the decimal number, but the decimal point in the product is shifted to the right by as, many of places as there are zeros over one.
Thus, 168.07 × 10
= 1680.7 Answer
(v) 31.1 × 100
Solution :
Given, 31.1 × 100
`=311/cancel10xxcancel100 10`
= 311 × 10
= 3110 Answer
Alternate method to multiply a decimal number by 100
Given, 31.1 × 100
We know that, when a decimal number is multiplied by 10, 100 or 1000, the digits in the product are same as in the decimal number, but the decimal point in the product is shifted to the right by as, many of places as there are zeros over one.
Thus, 31.1 × 100
= 3110 Answer
(vi) 156.1 × 100
Solution :
Given, 156.1 × 100
`=1561/cancel10xxcancel100 10`
= 1561 × 10
= 15610 Answer
Alternate method to multiply a decimal number by 100
Given, 156.1 × 100
We know that, when a decimal number is multiplied by 10, 100 or 1000, the digits in the product are same as in the decimal number, but the decimal point in the product is shifted to the right by as, many of places as there are zeros over one.
Thus, 156.1 × 100
= 15610 Answer
(vii) 3.62 × 100
Solution :
Given, 3.62 × 100
`=362/cancel100xxcancel100`
= 362 Answer
Alternate method to multiply a decimal number by 100
Given, 3.62 × 100
We know that, when a decimal number is multiplied by 10, 100 or 1000, the digits in the product are same as in the decimal number, but the decimal point in the product is shifted to the right by as, many of places as there are zeros over one.
Thus, 3.62 × 100
= 362 Answer
(viii) 43.07 × 100
Solution :
Given, 43.07 × 100
`=4307/cancel100xxcancel100`
= 4307 Answer
Alternate method to multiply a decimal number by 100
Given, 43.07 × 100
We know that, when a decimal number is multiplied by 10, 100 or 1000, the digits in the product are same as in the decimal number, but the decimal point in the product is shifted to the right by as, many of places as there are zeros over one.
Thus, 43.07 × 100
= 4307 Answer
(ix) 0.5 × 10
Solution :
Given, 0.5 × 10
`=5/cancel10xxcancel10`
= 5 Answer
Alternate method to multiply a decimal number by 100
Given, 0.5 × 10
We know that, when a decimal number is multiplied by 10, 100 or 1000, the digits in the product are same as in the decimal number, but the decimal point in the product is shifted to the right by as, many of places as there are zeros over one.
Thus, 0.5 × 10
= 5 Answer
(x) 0.08 × 10
Solution :
Given, 0.08 × 10
`=08/(cancel100 10)xx10`
`=8/10`
= 0.8 Answer
Alternate method to multiply a decimal number by 100
Given, 0.08 × 10
We know that, when a decimal number is multiplied by 10, 100 or 1000, the digits in the product are same as in the decimal number, but the decimal point in the product is shifted to the right by as, many of places as there are zeros over one.
Thus, 0.08 × 10
= 0.8 Answer
(xi) 0.9 × 100
Solution :
Given, 0.9 × 100
`=9/cancel10xxcancel100 10`
= 9 × 10
= 90 Answer
Alternate method to multiply a decimal number by 100
Given, 0.9 × 100
We know that, when a decimal number is multiplied by 10, 100 or 1000, the digits in the product are same as in the decimal number, but the decimal point in the product is shifted to the right by as, many of places as there are zeros over one.
Thus, 0.9 × 100
= 90 Answer
(xii) 0.03 × 1000
Solution :
Given, 0.03 × 1000
`=03/cancel100xxcancel1000 10`
= 3 × 10
= 30 Answer
Alternate method to multiply a decimal number by 100
Given, 0.03 × 1000
We know that, when a decimal number is multiplied by 10, 100 or 1000, the digits in the product are same as in the decimal number, but the decimal point in the product is shifted to the right by as, many of places as there are zeros over one.
Thus, 0.03 × 1000
= 030.00
= 30 Answer
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