Convert the decimal 3.88888 to a fraction.
A) $39 / 8$
B) $38 / 9$
C) $38 / 99$
D) $8 / 9$
Answer (1)
Let x = 3.88888...
Multiply by 10: 10 x = 38.88888...
Subtract the equations: 9 x = 35
Solve for x : x = 9 35 . The correct answer is 9 35
Explanation
Understanding the Problem We are asked to convert the decimal 3.88888... to a fraction. This is a repeating decimal, which can be converted to a fraction using algebra.
Setting up the Equation Let x = 3.88888... . We want to find a fraction that is equal to x .
Multiplying by 10 Multiply both sides of the equation by 10: 10 x = 38.88888...
Subtracting the Equations Subtract the original equation from the new equation: 10 x − x = 38.88888... − 3.88888...
Simplifying Simplify the equation: 9 x = 35
Solving for x Solve for x : x = 9 35
Checking the Options and Re-evaluating Now we check the given options to see which one matches 9 35 .
Option A: 8 39 = 4.875 Option B: 9 38 = 4.222... Option C: 99 38 = 0.3838... Option D: 9 8 = 0.888... None of these options match 9 35 = 3.888... . However, we made an error in the options provided. Let's re-evaluate the problem. We have x = 3.88888... = 3 + 0.88888... . Let y = 0.88888... . Then 10 y = 8.88888... . Subtracting the equations gives 9 y = 8 , so y = 9 8 . Therefore, x = 3 + 9 8 = 9 27 + 9 8 = 9 35 .
Finding the Correct Option Since x = 9 35 , we need to find an equivalent fraction among the options. However, none of the options are equal to 9 35 . The closest option is B) 9 38 which is not correct. There seems to be a typo in the options. The correct fraction is 9 35 .
Final Answer The correct conversion of the decimal 3.88888... to a fraction is 9 35 . However, this is not among the options. The closest option is B) 9 38 , but that is not correct.
Examples
Converting repeating decimals to fractions is useful in various real-life scenarios, such as calculating precise measurements in construction or engineering, where accuracy is crucial. For instance, if a design requires a component to be exactly 3.888... inches long, converting this to a fraction, 35/9 inches, allows for more accurate cutting and fitting, reducing errors and ensuring the final product meets the required specifications. This conversion also helps in financial calculations where recurring decimals might appear in interest rates or currency conversions, ensuring accurate accounting and preventing discrepancies.
