Final answer:
The decimals 1/10 and 1/100 get progressively closer to the value of 1/9, which is approximately 0.111... The powers of 10 in the denominators denote the number of decimal places to the left, implying a smaller fraction.
Step-by-step explanation:
The subject of your question is Mathematics, specifically, fractions and decimals. To find fractions that get closer and closer to 1/9, we can consider fractions with denominators that are powers of 10. For example, 1/10 and 1/100. As the denominator increases, the value of these fractions gets closer and closer to zero, progressing towards 1/9.
Now, to convert the fraction 1/9 to a decimal form, you would divide 1 by 9, which gives you approximately 0.111.... As you can see, the value of 1/9 in decimal form is larger than both 1/10 and 1/100, indicating that these fractions are getting closer to 1/9. So the correct answer to your question would be option A) 1/10, 1/100, 0.111...
Remember, the power (exponent) of 10 in the denominator of the fractions means the number of places the decimal is shifted to the left in their decimal forms. So in this case fractions with larger powers of ten in the denominator get smaller and closer to zero, approaching the value of 1/9.
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