Question

A reporter determines a baseball player's batting average, which is a ratio of the number of hits to the number of times at-bats. The result is shown on a calculator as 0.2121.... Write this repeating decimal as a fraction.

A) 7/33
B) 21/99
C) 2121/10000
D) 4242/20000

Answer 1

To write the repeating decimal 0.2121... as a fraction, use long division. The fraction equivalent of the decimal is 7/33.

Step-by-step explanation:

To write the repeating decimal 0.2121... as a fraction, we can use a method called long division. Let x = 0.2121... First, we write x as a fraction over 1, so it becomes x = 0.2121.../1. Next, we multiply both sides of the equation by 100 to eliminate the decimal point, giving us 100x = 21.2121... We then subtract the original equation from the multiplied equation to eliminate the repeating decimals: 100x - x = 21.2121... - 0.2121..., which simplifies to 99x = 21. Multiply both sides by 1/99 to solve for x: (99x)/(99) = (21)/(99). Finally, we simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 3 in this case. The simplified fraction is x = 7/33, so the answer is option A) 7/33.