Rational Numbers are numbers that can be written as a Ratio of integers. When you convert these ratios to a decimal, the decimal either
A. repeats itself
B. terminates itself
i chose a
A and B both are true
1/7 = 0.142857 142857 ...
1/5 = 0.2
When converting ratios of integers to decimals, there are two possibilities: the decimal either repeats itself or terminates.
To understand why, let's consider the definition of rational numbers. Rational numbers are numbers that can be expressed as the ratio of two integers, where the denominator is not zero. For example, 2/3, 5/6, and -4/7 are all rational numbers.
To convert a rational number into a decimal, we perform division. Let's take the example of 2/3:
2 ÷ 3 = 0.666...
In this case, the decimal representation of 2/3 repeats itself. The ellipsis (...) indicates that the decimal pattern continues indefinitely. We represent this decimal as 0.666... or 0.6̅.
Now let's consider another rational number, 5/6:
5 ÷ 6 = 0.833...
Again, the decimal representation of 5/6 repeats itself, so the decimal is 0.833... or 0.8̅3.
On the other hand, some rational numbers result in decimal representations that terminate. In these cases, the division process comes to an end without any repeating decimals.
For example, let's take the fraction 1/4:
1 ÷ 4 = 0.25
In this case, the division process terminated after the second decimal place, resulting in a decimal representation that doesn't repeat. So, the decimal representation of 1/4 is 0.25.
Similarly, the fraction 3/8 can be converted into a terminating decimal:
3 ÷ 8 = 0.375
Here, the division process terminates after the third decimal place, resulting in the terminating decimal representation of 0.375.
In summary, when converting ratios of integers to decimals (rational numbers), the decimal representation can either repeat or terminate. This depends on the specific numerical values involved in the ratio.