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Q: Can every repeating fraction be represented as a decimal?
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Can every fraction be represented as a decimal?


Can every rational fraction be written as a repeating decimal?

Any rational number is either a repeating decimal, or a terminating decimal.

Why every rational number can be represented by either a terminating decimal or a repeating decimal?

That is the definition of a rational number.

Every terminating or repeating decimal represents a rational number and can be changed to a what?

Every rational number can be expressed as a fraction

Does every fraction have an equivalent decimal?

Yes, it may be a repeating decimal, such as 1/3 = 0.33333.... or 1/11 = 0.090909.... or something longer such as 1/7 = 0.142857142857142857.... where the '142857' is the repeating part. But every rational number (eg. fraction) can be mapped to a corresponding decimal equivalent.

Can every decimal be represented as a fraction?

No because irrational numbers can't be expressed as fractions

Can every rational number be represented by a terminating decimal?

No, a rational number, expressed as decimal, is either a terminating decimal, such as 1/4 = 0.25, or a repeating decimal, such as 1/7 = 0.142857 142857 142857 ...

What is the approximate of each irrational?

Every irrational number can be represented by a non-terminating non-repeating decimal. Rounding this decimal representation to a suitable degree will provide a suitable approximation.

What is meaning of repeating decimals?

If I understand your question, you want to know the meaning of the phrase "repeating decimal". It just means an infinite decimal expansion (a decimal with infinitely many digits) in which, from some point on, the same digit or group of digits just keeps repeating forever. Every rational number (fraction) has a decimal that either terminates (in which case it can be considered to be a repeating decimal in which the digit 0 keeps repeating; 1/2 = 0.5 = 0.5000000000...) or repeats. An irrational number has a decimal expansion that never repeats. For example, 1/3 = 0.33333333333...; 1/7 = 0.142857142857142857...; 1/30 = 0.03333333333.... and is often represented with a line above the repeating number

Does all the numbers have to repeat in order to be a rational number?

For a number to be rational you need to be able to write it as a fraction. To answer your question, it must repeat as a decimal or else terminate which can be thought of as repeating zeroes. Further, every repeating decimal can be written as a fraction and you can find the fraction by using the formula for the sum of an infinite geometric series.

Is every rational number a repeating decimal?

No. A rational number is any terminating numeral. A repeating decimal is irrational.

Can a non-terminating decimal be a non-repeating decimal?

Yes. Every irrational number has a non-terminating, non-repeating decimal representation.

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