Final answer:
The repeating decimal 0.47 can be converted to a fraction using a method that sets up an equation, multiplies that equation to shift the repeating part, subtracts the original equation, and solves. The final fraction in simplest form is 47/99.
Step-by-step explanation:
To convert a repeating decimal to a fraction, we use a method that involves setting the decimal as a variable, multiplying that variable, subtracting equations, and then solving for the variable. In this case, the repeating decimal is 0.47. Here is how you would do it:
- First, set up an equation: Let x = 0.47 (repeating)
- Next, multiply that equation by a power of 10 that shifts the repeating part to the left of the decimal point. Because the repeating part is two digits (47), we will use 100: 100x = 47.47 (repeating)
- Now, subtract the first equation from the second: 100x - x = 47.47 - 0.47, which simplifies to 99x = 47
- Finally, solve for x by dividing both sides of the equation by 99: x = 47/99
- Therefore, the fraction in simplest form is 47/99.
Learn more about Converting Repeating Decimals