Repeating decimals are ________ rational numbers.
A. sometimes
B. never
C. always
SOMETIMES
So what is the answer? A, B, or C?
its a always
The correct answer is A. sometimes.
To understand why repeating decimals are sometimes rational numbers, let's first define what a repeating decimal is. A repeating decimal is a decimal number in which one or more digits repeat indefinitely after a certain point. For example, the decimal representation of the fraction 1/3 is 0.333..., where the digit 3 repeats infinitely.
Now, let's talk about rational numbers. A rational number is any number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. Rational numbers can be written as terminating decimals (where the decimal representation ends after a certain number of digits) or repeating decimals.
So, some repeating decimals can be rational numbers. Fractions that have repeating decimal representations are rational numbers. For example, the fraction 4/11 can be expressed as the repeating decimal 0.363636..., where the digit 36 repeats infinitely. Since 4/11 is a fraction and can be expressed as a ratio of two integers, it is a rational number.
However, not all repeating decimals are rational numbers. For example, the decimal representation of π (pi) is a non-terminating and non-repeating decimal, so it is irrational.