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4. Write [tex]$0 . \overline{12}$[/tex] as a fraction.

Let [tex]$x=$[/tex] [tex]$\square$[/tex]

[tex]$100x=$[/tex] [tex]$\square$[/tex]

[tex]$100x - x=$[/tex] [tex]$\square$[/tex]

[tex]$\square$[/tex]

[tex]$99x=$[/tex] [tex]$\square$[/tex]

[tex]$x=$[/tex] [tex]$\square$[/tex]

[tex]$\square$[/tex]

So [tex]$0 . \overline{12}$[/tex] is equal to [tex]$\square$[/tex]



Answer :

GinnyAnswer
Let's solve the problem of writing [tex]\(0.\overline{12}\)[/tex] as a fraction step-by-step.

1. Let [tex]\( x = 0.\overline{12} \)[/tex]. This means [tex]\( x \)[/tex] is the repeating decimal [tex]\( 0.121212\ldots \)[/tex].

[tex]\[ x = 0.\overline{12} \][/tex]

2. Multiply both sides of the equation by 100 to shift the decimal point two places to the right.

[tex]\[ 100x = 12.\overline{12} \][/tex]

3. Now we have two equations:

[tex]\[ x = 0.\overline{12} \][/tex]
[tex]\[ 100x = 12.\overline{12} \][/tex]

4. Subtract the first equation from the second equation to eliminate the repeating part.

[tex]\[ 100x - x = 12.\overline{12} - 0.\overline{12} \][/tex]

5. Simplify the left-hand side and the right-hand side of the equation.

[tex]\[ 99x = 12 \][/tex]

6. Solve for [tex]\( x \)[/tex] by dividing both sides by 99.

[tex]\[ x = \frac{12}{99} \][/tex]

7. Simplify the fraction [tex]\(\frac{12}{99}\)[/tex] by finding the greatest common divisor (GCD) of 12 and 99. The GCD of 12 and 99 is 3.

[tex]\[ \frac{12 \div 3}{99 \div 3} = \frac{4}{33} \][/tex]

So [tex]\( 0.\overline{12} \)[/tex] is equal to [tex]\( \frac{4}{33} \)[/tex].