Jayne uses long division to convert a rational number ab to a decimal. Which of the following statements cannot be true?
The decimal form of ab terminates in zeros.
The decimal form of ab eventually repeats.
The decimal form of ab is a whole number.
The decimal form of ab never repeats or terminates.
D
review rational numbers
and that's a/b, not just ab
To determine which statement cannot be true, we need to understand how long division works to convert a rational number to a decimal.
In long division, we divide the numerator (a) by the denominator (b) to obtain the decimal representation of the rational number ab. The process involves dividing, multiplying, and subtracting until we obtain a remainder of zero or reach a repeating pattern.
Now let's analyze each statement:
1. The decimal form of ab terminates in zeros.
This statement can be true. If the remainder becomes zero at some point, then the decimal representation of ab will terminate. For example, when dividing 2 by 5, the decimal form of 2/5 is 0.4, which terminates.
2. The decimal form of ab eventually repeats.
This statement can be true. If there is a repeating pattern in the remainder obtained during the long division process, then the decimal representation of ab will eventually repeat. For example, when dividing 1 by 3, the decimal form of 1/3 is 0.333..., which repeats.
3. The decimal form of ab is a whole number.
This statement can be true. If the remainder becomes zero and there is no decimal part, then the decimal representation of ab will be a whole number. For example, when dividing 8 by 4, the decimal form of 8/4 is 2, which is a whole number.
4. The decimal form of ab never repeats or terminates.
This statement cannot be true. The decimal representation of a rational number ab will either terminate (ends in zeros) or repeat eventually. This is because fractions can always be expressed as either terminating or repeating decimals.
Therefore, the statement "The decimal form of ab never repeats or terminates" cannot be true.
So, the correct answer is: The decimal form of ab never repeats or terminates.