AI tutor
Welcome to Bytelearn!
Let’s check out your problem:
Write the repeating decimal as a fraction.
Full solution
Q. Write the repeating decimal as a fraction.
- Rephrase the Problem: Let's first rephrase the ＂Convert the repeating decimal to a fraction.＂
- Identify Repeating Pattern: Identify the repeating pattern in the decimal. The digits ＂＂ repeat indefinitely, so we can write the decimal as
- Assign Variable: Let equal the repeating decimal, so
- Isolate Repeating Pattern: To isolate the repeating pattern, multiply by (since the pattern is two digits long), which gives us
- Subtract Decimals: Now, subtract the original from to get rid of the decimal part. This gives us
- Solve Equation: Perform the subtraction: and . This results in the equation .
- Divide by : To find the value of , divide both sides of the equation by . So, .
- Check for Simplification: Check the fraction to ensure it cannot be simplified further. Since and have no common factors other than , the fraction is in its simplest form.
