Question

Express 0.7.....
${ \frac{p}{q} } = form. \\let \: x \: = 0.777..... = 0.7 \\ eq {}n(1) - eqn(2) \\ 10x - x = | \: |$
${ \frac{p}{q} } = form. \\let \: x \: = 0.777..... = 0.7 \\ eq {}n(1) - eqn(2) \\ 10x - x = ( \: \: \: ) \\ \\ 9x = ( \: \: \: \: \: \: \: \ ) \\ \\ \\ x = ( \: \: \: \: \: )$


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Answer 1

Correct Question :

• Express $\rm{0.7.......}$ in $\rm{\dfrac{p}{q}}$ form

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Let x = $\rm{0.7777...}$          ---- [1]

• Multiply 10 to Both Sides of the Equation

$\longrightarrow$ 10x = $\rm{7.777...}$          ---- [2]

• Subtract Equation [1] from Equation [2]

$\longrightarrow$ 10x - x = $\rm{7.777-0.777}$

$\longrightarrow$ 9x = $\rm{7}$

• Dividing Both Sides by 9

$\longrightarrow$ x = $\rm{\dfrac{7}{9}}$

Answer 2

Answer:

Express \rm{0.7.......}0.7....... in \rm{\dfrac{p}{q}}qp form

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Let x = \rm{0.7777...}0.7777...          ---- [1]

Multiply 10 to Both Sides of the Equation

\longrightarrow⟶ 10x = \rm{7.777...}7.777...          ---- [2]

Subtract Equation [1] from Equation [2]

\longrightarrow⟶ 10x - x = \rm{7.777-0.777}7.777−0.777

\longrightarrow⟶ 9x = \rm{7}7

Dividing Both Sides by 9

\longrightarrow⟶ x = \rm{\dfrac{7}{9}}97