Can a decimal of this form be expressed as a finite number of figures?
repeating decimal
Practice makes perfect
We want to complete the following sentence.
A(n) is a decimal in which a digit or digits repeat endlessly.
We are asked to complete it with one of the terms from the given box.
We want to know which of these is a decimal in which a digit or digits repeat endlessly. When a digit or digits repeat endlessly in a decimal, it means that it cannot be expressed as a finite number of figures.
lcl
0.3333333 ... & ⇔ & 0.3
5.8144144 ... & ⇔ & 5.8144
0.9999999 ... & ⇔ & 0.9
We call a number of this type a repeating decimal. Now, we can complete the given sentence.
A repeating decimal is a decimal in which digit or digits repeat endlessly.
Extra
Terminating Decimal
Note that the term repeating decimal sounds similar to the term terminating decimal from the box. Recall the definition of a terminating decimal.
Terminating Decimal
A terminating decimal is a decimal that ends in repeating zeros.
We can see that the difference between a repeating decimal and a terminating decimal is that a terminating decimal can be expressed as a finite number of figures. Let's take a look at a few examples of terminating decimals.
lcl
1.25000 ... & ⇔ & 1.25
5.175000 ... & ⇔ & 5.175
0.5000 ... & ⇔ & 0.5
