A decimal in which some digits after the decimal point repeat infinitely. The digits repeat their values at regular intervals and the infinitely repeated part is not zero.
A decimal with a finite number of digits. Terminating numbers can be written as fractions, which means that they are rational numbers.
The next logical step is to consider some examples of repeating and terminating decimals.
Repeating Decimal Numbers
Terminating Decimal Numbers
Number
Notation
Fraction
Number
Fraction
0.666666...
0.6
2/3
0.5
1/2
1.454545...
1.45
16/11
1.53
153/100
This table helps us to write the given fraction as a decimal number. But first, recall that 2 5 means 2÷ 5. That means we will divide the numerator by the denominator. Let's do it!
We found that 25 written as a decimal is 0.4. In this case, our decimal has a finite number of digits. This means that our fraction has terminating decimals.
We want to determine whether the given fraction has repeating or terminating decimals. First, we can write the given fraction as a decimal number. To do so, recall that 7 45 means 7÷ 45. Therefore, we will divide the numerator by the denominator. Let's do it!
Notice that the pattern starts to repeat itself after a few steps. This means that the decimal is a repeating decimal. We can write it using bar notation. Remember, the bar goes over the decimal part that repeats itself.
0.155555... = 0.15
We found that 745 written as a decimal is 0.15. In this case, the digits in our decimal repeat infinitely. This means that our fraction has repeating decimals.
We want to determine whether the given fraction has repeating or terminating decimals. First, we can write the given fraction as a decimal number. To do so, recall that 5 99 means 5÷ 99. Therefore, we will divide the numerator by the denominator. Let's do it!
We can see that the pattern starts to repeat itself after a few steps. This means that the decimal is a repeating decimal. We can write it using bar notation. Remember, the bar goes over the decimal part that repeats itself.
0.050505... = 0.05
We found that 599 written as a decimal is 0.05. In this case, the digits in our decimal repeat infinitely. This means that our fraction has repeating decimals.
We want to determine whether the given fraction has repeating or terminating decimals. First, we can write the given fraction as a decimal number. To do so, recall that 27 250 means 27÷ 250. Therefore, we will divide the numerator by the denominator. Let's do it!
We found that 27250 written as a decimal is 0.108. In this case, our decimal has a finite number of digits. This means that our fraction has terminating decimals.
