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Yes, because a fraction a/b where a and b are integer, and b is different than 0, is a rational number which are whole numbers or decimal numbers, where the decimal part is finite or repeating blocks. Conversely, decimals that do not repeat or terminate cannot be represented as a fraction. For example, in a right isosceles triangle with side a and hypotenuse (square root of 2)a, we can't represent as a fraction [(square root of2)a]/a (hypotenuse/side), because will have an irrational number (square root of 2).
Here is one fun thing to know about repeating decimals. If you look at the repeating decimals formed by taking 1/n, where n is a Prime number that is not 2 or 5, you will see that the length of the (smallest choice of) the part that repeats [i.e., 3, not 333, for 0.3333...] is: 1.always less than or equal to n-1, 2. equal to n-1 only for some of these prime numbers. 3. always a divisor of n-1.
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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
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 ...
