Question

Show that 0.7777....or 0.7 can be expressed in the form of p/q . Where p and q are integers and q is not equal to 0

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Answer 1

${Solution}$

Given to express the number in Rational form

0.77777..

SOLUTION:-

Let the number be

x = 0.7777 .. ___ eq 1

Hence here only 1 number that is 7 is frequently repeating So, the periodicity of a number is 1

Since multiply by 10 on both sides

10x = 10× 0.7777

10x = 7.7777.. ___ eq 2

Subtracting eq1 from eq2

10x = 7.7777 ..

x = 0.7777

___________

9x = 7.0000

9x = 7

x = 7/9

So, the rational form (p/q) form of 0.7777 is 7/9

___________________

Know more :-

The given number which we can express in p/q form is called rational number

• p is called Denominator
• q is called Numerator

Rational number can be positive , negative even zero also

Answer 2

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Given :-

Given to express the number in Rational form

0.77777..

SOLUTION :-

Let the number be

x = 0.7777 .. ___ eq 1

Hence here only 1 number that is 7 is frequently repeating So, the periodicity of a number is 1

Since multiply by 10 on both sides

10x = 10× 0.7777

10x = 7.7777.. ___ eq 2

Subtracting eq1 from eq2

10x = 7.7777 ..

x = 0.7777

___________

9x = 7.0000

___________

9x = 7

x = 7/9

So, the rational form (p/q) form of 0.7777 is 7/9.

@SweetestBitter