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Q10.
Prove algebraically that the recurring decimal 0.178 can be written as the fraction 59/330

Q10 Prove Algebraically That The Recurring Decimal 0178 Can Be Written As The Fraction 59330 class=

Sagot :

Answer:

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Step-by-step explanation:

Recurring decimal is decimal representation of a number whose digits are periodic and infinite. Proved algebraically that the recurring decimal 0.178 can be written as the fraction 59/330 below.

Given information;

Given number in the decimal form is [tex]0. 1 \overline 7 \overline 8[/tex]

Suppose the number is equal to the x,

[tex]x=0. 1 \overline 7 \overline 8[/tex]

Recurring decimal

Recurring decimal is decimal representation of a number whose digits are periodic and infinite.

As the number 78 is the recurring number. Thus the recurring number can be written as,

[tex]x=0.1787878.....[/tex]                      .......equation 1.

Suppose this is equation number 1.

Multiply the above equation with 100 both the sides,

[tex]100\times x=100\times0. 1 787878....[/tex]

[tex]100x=100\times0.1787878...[/tex]

[tex]100x=17.87878...[/tex]

Subtract the above equation from equation number 1. Thus,

[tex]\begin{aligned}\ 100x-x&=17.87878-0.1787878\\ 99x&=17.7\\ \end[/tex]

Solve for x ,

[tex]x=\dfrac{17.7}{99} [/tex]

Multiply with 10 in both numerator and denominator,

[tex]x=\dfrac{177}{990} \\ x=\dfrac{59}{330} \\[/tex]

Hence proved algebraically that the recurring decimal 0.178 can be written as the fraction 59/330

Learn more about the recurring decimal here;

https://brainly.com/question/820308

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