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When fractions with the denominators of 2 4 8 16 32 produce terminating decimals fractions with the denominators 6 12 18 24 produce repeating decimals why?
Wiki User
∙ 9y ago
Decimal numbers are based on powers of 10. The only factors of 10 are 2 and 5. Any denominator of the form 2^x*5^y will divide 10^x or 10^y - whichever is larger.
In the above example, the first set of denominators are all of the form 2^x and so will divide 10^x. So all fractions will have decimal expressions with x decimal digits (assuming you start with the fraction in simplified form).
The second set of denominators include 3 as a factor and so none of these denominators can be expressed as 2^x*5^y and so none of them are a factor of 10^z for any z.
All that may sound complicated. At its simplest, the rule is that if the only prime factors of the denominator are 2 and 5, then you will get a terminating decimal. Anything else and you won't.
Wiki User
∙ 9y ago
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Is 0.16 repeating irrational?
No, no repeating decimal is irrational. All repeating decimals can be converted to fractions. They are, however, non-terminating.
Numbers that cannot be expressed as terminating or repeating decimals?
irrational numbers
What is the difference between a terminating and a repeating decimal?
A terminating decimal reaches an end after a finite number of digits whereas a repeating decimal, after a finite number of digits, has a string of decimals (also of finite length) that repeats forever. Thus 1.2356 is a terminating decimal. 1.456333... is a repeating decimal with the digit 3 repeating an infinite number of times. So also is 23.56142857142857...... where the string 142857 repeats to infinity. In fact, terminating decimals may be viewed as repeating decimals with zero repeating infinitely.
Why are repeating decimals changed to fractions?
There are times when working with fractions is more convenient than working with decimals.
Why is terminating and repeating decimals a rational number?
A rational number is any number that can be expressed as the quotient or fraction p/q of two integers, p and q, with the denominator q not equal to zero. Terminating or repeating decimals are the result of this.
Is 0.16 repeating irrational?
No, no repeating decimal is irrational. All repeating decimals can be converted to fractions. They are, however, non-terminating.
What can rational numbers be expressed as?
fractions or decimals
What are 5 examples of non terminating repeating decimals?
terminating decimals repeating decimals
What are the different kinds of decimal?
terminating decimals non terminating decimals repeating decimals non repeating decimals
Are terminating and repeating decimals irrational numbers?
Terminating and repeating decimals are rational numbers.
What is it called when fractions terminating repeating decimals integers and percents called?
They are called rational numbers
How fractions are related to repeating decimals and terminating decimals?
Fractions are related to repeating decimals in the sense that a fraction can be represented as a repeating decimal if the denominator has prime factors other than 2 or 5. For example, 1/3 can be represented as 0.3333..., with the 3s repeating infinitely. Terminating decimals, on the other hand, are fractions that have denominators which are powers of 10. For example, 1/4 can be represented as 0.25, which terminates after two decimal places.
Can all terminating decimals be written as fractions?
All terminating decimals can be written as fractions.
What are signs for decimals?
terminating decimals and repeating decimals
Is decimals ratios?
Terminating and repeating decimals are.
Are repeating decimals and terminating decimals the same?
No.
What are non-terminating and non-repeating decimals called?
They are called terminating decimals.
