Find the mixed number or rational fraction in lowest terms represented by the repeating decimal.
1.363636
1 + 36/99
= 1 + 4/11
= 1 4/11 or 15/11
1+36/99=1+(9*4)/(9*11)=1+4/11
To find the mixed number or rational fraction represented by the repeating decimal 1.363636..., we can use basic algebraic techniques.
Let's represent the repeating decimal as "x = 1.363636...".
Step 1: Multiply both sides of the equation by a power of 10 to eliminate the repeating decimal. Since there are two repeating digits after the decimal point (36), we'll multiply both sides by 100:
100x = 136.363636...
Step 2: Subtract the original equation (x = 1.363636...) from the equation obtained in step 1 (100x = 136.363636...):
100x - x = 136.363636... - 1.363636...
Simplifying,
99x = 135
Step 3: Divide both sides of the equation by 99 to solve for x:
99x/99 = 135/99
x = 1.363636... = 135/99
To express the fraction 135/99 in lowest terms, we can simplify it by dividing both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 135 and 99 is 9.
Dividing both the numerator and denominator by 9, we get:
135 ÷ 9 / 99 ÷ 9
= 15/11
Therefore, the mixed number or rational fraction in lowest terms represented by the repeating decimal 1.363636... is 15/11.