1.75 repeating as a fraction in simplest form
1.45 repeating as a fraction in simplest form
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What is 1.75 repeating as a fraction in simples form
math
To convert the repeating decimal 1.75 repeating to a fraction in simplest form, you can follow these steps:
Step 1: Let x be the decimal equivalent of the repeating decimal. In this case, x = 1.75.
Step 2: Multiply both sides of the equation x = 1.75 by a power of 10 to eliminate the repeating part. Since there is only one digit repeating, multiply both sides by 100.
100x = 175.75
Step 3: Subtract the equation from Step 1 from the equation in Step 2 to eliminate the non-repeating part.
100x - x = 175.75 - 1.75
99x = 174
Step 4: Simplify the equation by dividing both sides by the coefficient of x, which is 99.
99x/99 = 174/99
x = 174/99
Step 5: Reduce the fraction to its simplest form by dividing both the numerator and denominator by their greatest common divisor.
The greatest common divisor of 174 and 99 is 3.
174/3 ÷ 99/3 = 58/33
Therefore, the repeating decimal 1.75 repeating can be expressed as the fraction 58/33 in simplest form.