Final answer:
To convert the repeating decimal 0.25 to a fraction in simplest form, we can multiply it by 100 and subtract the original decimal to eliminate the repeating part. Then, we solve for the original decimal and simplify the resulting fraction. In this case, the decimal 0.25 is equivalent to the fraction 1/4.
Step-by-step explanation:
To convert a repeating decimal to a fraction, we can use the concept of place value. Let's call the repeating decimal 0.25. The repeating part consists of two digits, so we can multiply the decimal by 100, which will shift the decimal point to the right two places. Doing so, we get 25. Now, let's subtract the original decimal from the multiplied decimal: 25 - 0.25 = 24.75. Now, we can set up an equation where x represents the original decimal: x = 0.25. We can multiply both sides of the equation by 100 to get rid of the decimal: 100x = 25. Subtracting the original equation from this new one, we get: 100x - x = 25 - 0.25 -> 99x = 24.75. Dividing both sides by 99, we get: x = 24.75/99. This fraction can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 24.75. After simplifying, we have: 24.75/99 = 3/12 = 1/4. Therefore, the decimal 0.25 can be expressed as the fraction 1/4 in simplest form.
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