Question

Write the decimal expansion of the following rational numbers without actual division.(i) 35/50 (ii) 21/25 (iii) 7/8

Answer 1

We know that

25/100=0.25

1/100=0.01

i)35/50

Multiply the numerator and denominator by 2

=70/100

=0.7

ii)21/25

Multiply the numerator and denominator by 4

=84/100

=0.84

iii)100 is not divisible by 8 but 1000 is divisible by 8

So,

Multiply numerator and denominator by 125

=875/1000

=0.875

Answer 2

Answer:

i ) 0.7

ii ) 0.84

iii ) 0.875

Step-by-step explanation:

i ) 35/50

= 35/( 2¹ × 5² )

= ( 35 × 2 )/( 2² × 5² )

= 70/( 10 )²

= 70/100

= 0.7 ( decimal form )

ii ) 21/25

= 21/5²

= ( 21 × 2² )/( 5² × 2² )

= ( 84 )/( 10 )²

= 84/100

= 0.84 ( decimal form )

iii ) 7/8

= 7/2³

= ( 7 × 5³ )/( 2³ × 5³ )

= 875/10³

= 875/1000

= 0.875 ( decimal form )

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