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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 ...
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.
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.
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 ...
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
What is the fraction for 0.428571429?
The fraction for 0.428571429 is 3/7. This can be determined by recognizing the repeating decimal pattern of 0.428571429, which repeats every 6 digits. By understanding that the repeating decimal can be expressed as a fraction by placing the repeating digits over the same number of nines as the repeating pattern, we can simplify 428571/999999 to 3/7.
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.
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.
