14 can, for example, be written as a terminating decimal: 0.25. 13 on the other hand, cannot be stated as a terminating decimal since it is a recurring decimal, one that continues indefinitely. In **other terms**, 1/3 is 0.33333 as a decimal. And those three continue on indefinitely. Recurring decimals can be written as repeating decimals by adding "0" between each subsequent term, so 1/3 would then be written as 0.333333333333....

- Which of the following fractions cannot be expressed as a terminating decimal?
- Is the fraction 1/3 equivalent to a terminating decimal?
- is expressed as a terminating decimal?
- What is a never-ending fraction called?
- Which fraction converts to a terminating decimal number?
- How can you determine if a fraction is a terminating decimal?
- Which fraction is an example of a repeating non-terminating decimal?
- Why do you think some fractions have decimals that repeat and some have decimals that terminate?

Answer Expert Approved1/3 is the same as a decimal that does not end. A terminating decimal is one that comes to an end. Some decimals, on the other hand, never stop. This is a non-terminating decimal, sometimes known as a repeating decimal.

A terminating decimal, as the name implies, is a decimal with an end. A number can have more than one terminating decimal, such as 1.5. It may seem counterintuitive at first that a number could have terminations, but this makes sense when you think about how numbers are actually stored in computers. There are only two possible places to store a fractional part of a number: after the decimal point or before it. If there were no way to indicate where a termination should go, then we would need **more digits** than there are atoms in the universe to store **all the possible combinations**.

There are two ways to represent a terminating decimal in computer memory. The most common method is to have the last digit be zero. This is called "terminating" the representation because now there is no further possibility for the value to change. The other option is to use something called a "sign bit". In mathematics and science generally, a sign bit is a bit that indicates whether a number is positive or negative. Computer memories work by indicating which bits are 1's and which are 0's. There are two main methods for storing a sign bit: either as a single 1 followed by all 0's or as a single 0 followed by all 1's.

A non-terminating, non-repeating decimal is a decimal number that never ends, with no set of digits repeating indefinitely. Because decimals of **this sort** cannot be expressed as fractions, they are irrational numbers.

In basic words, each rational number (that is, a fraction) may be expressed as either a terminating decimal or a repeating decimal. Simply divide the denominator by the numerator. You have a terminating decimal if you wind up with a residual of 0. Otherwise, it's a repeating decimal.

For example, the fraction 23/7 has a terminating decimal representation because 2333 is evenly divided by 7. The fraction 514/113 has a repeating decimal representation because 5144 is not evenly divided by 113.

Rational numbers can also be expressed as **repeated fractions**: such as 1 = 1/1 or 4 = 3/1. These are called simple fractions. Also written as 1 = 1/1 or 4 = 4/1. Other examples include 24 = 2/1 + 2/1 + 2/1 or 1000/17 = 5/1 + 5/1 + 5/1.

The best way to think about this is that there are two types of fractions: simple and non-simple. Rational numbers are simply fractions - that is, they are a ratio of two integers. Therefore, they are simple fractions. Exponential fractions are also fractions - that is, they are a power of a base multiplied by a factor. They are non-simple because they contain **multiple factors**. For example, 0.0101020102010..

Examine the prime factors of the denominator when the fraction is in its simplest elementary form to determine whether it will have a terminating or repeating decimal. The decimal point will be terminated if they are made up of 2s and/or 5s. Otherwise, it will repeat.

For example, if you were to divide 1,000 by 7, you would get 14%. Since there are no digits after **the decimal point**, this fraction has **a terminating decimal**. Now, say you divided 0.01 by 7. You would get 0.00007.. Which does not terminate. Fractions with repeating decimals may also have repeating digits within the integer portion of the division as well. For example, if you divided 0.123 by 7, you would get 1.714.... Which means that the digit 3 will also repeat itself once within the integer portion of the division.

In general, fractions with repeating decimals contain numbers with multiple of seven as **their divisors**. For example, 1/7, 2/7, 3/7, 4/7, 5/7, and 6/7 have repeating decimals because they are all multiples of 7.

Fractions that do not have any number with a multiple of seven as its divisor have a terminating decimal.

Non-terminating repeating decimals include 0.12121212121212.. 0.12121212121212ldots 0.12121212121212.. And 1.2354354354354.. 1.2354354354354ldots 1.2354354354354ldots 1.0.

Decimals are fractions having denominators that are powers of 10. Take a look at the decimal: repeating 0.111111 This means that all decimal fractions have denominators that are an exact power of 10. Decimal fractions with terminating digits are similar to **fractional numbers** in that they don't have **any right-hand sides**. For example, 1/7 is equivalent to 0.142857.

Here are some examples of decimal fractions that repeat: 1/2, 1/5, 2/3, 3/8, 4/5, 6/7, 8/9, 9/10. And here are some examples of decimal fractions that terminate: 11/12, 5/6, 7/8, 13/14, 17/18, 19/20.

It's helpful to know that if you divide any decimal by 10 and keep dividing by 10 until the number becomes less than or equal to 1, you will always get a fraction with a denominator that is a power of 10. For example, 1/10 = 0.1. If you divide 0.1 by 10, you'll still get 0.1. This means that anytime you see **a decimal fraction** with many digits after the point, it is equivalent to a repeating decimal.