The repeating decimal is expressed as a geometric series Write the decimal as the ratio of two integers.
A)
B)
C)
D)
E)

Question

The repeating decimal  is expressed as a geometric series  Write the decimal  as the ratio of two integers. ​​
A) ​ 
B) ​ 
C) ​ 
D) ​ 
E) ​

Quizplus · Accepted Answer

The given repeating decimal can be expressed as a geometric series with first term 1.1 and common ratio 16. This is because each place value after the first four digits repeats every 16 digits.

Using the formula for the sum of an infinite geometric series, we have:

S = a/(1-r) = 1.1/(1-16) = -1/15

To convert this to a fraction, we multiply numerator and denominator by -1:

-1/-15 = 1/15

Therefore, the decimal 11ea8970_6ab4_3a03_861b_eb5f21c2e8c7_TB1301_11 can be expressed as the ratio of 1 to 15, and the best choice is C.

The Repeating Decimal Is Expressed as a Geometric Series