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An irrational number must not have a repeating sequence. If we have a number, such as 0.333333...., we can turn this into a rational number as such.
Let x = 0.333333......, then multiply both sides by 10:
10x = 3.333333......
Now subtract the first equation from the second, since the 3's go on forever, they will cancel each other out and you're left with:
9x = 3. Now divide both sides by 9: x = 3/9 which is 1/3, a rational number equal to 0.3333333....
If a number can be expressed as the ratio a/b, where a and b are integers (with the restriction that b not equal zero), then the number is rational. If you cannot express the number as such, then it is irrational.
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Is the decimal form of an irrational number is a repeating decimal?
No.
Is a decimal form of an irrational number a repeating decimal?
Not necessarily. Remember that the definition of an irrational number is a number that can't be expressed as a simple fraction. 2/3, for example, is rational by that definition even though its decimal form is a repeating decimal. Since irrational numbers cannot be written as fractions, they don't have fraction forms. So basically, numbers with repeating decimals are considered rational. Irrational numbers don't have repeating decimals.
Why can't irrational number be represented as decimal form?
Any terminating or repeating decimal number can be converted easily into the form of p/q: a ratio of two integers. If it can be written in that form then it is rational.
What is the decimal form of 17 square root?
√17 is irrational (a never repeating, never ending) decimal. √17 ≈ 4.1231
What is the square root of 168 in a decimal form?
It is an irrational number and as a decimal number it has no ending
Is the decimal form of an irrational number is a repeating decimal?
No.
Is a decimal form of an irrational number a repeating decimal?
Not necessarily. Remember that the definition of an irrational number is a number that can't be expressed as a simple fraction. 2/3, for example, is rational by that definition even though its decimal form is a repeating decimal. Since irrational numbers cannot be written as fractions, they don't have fraction forms. So basically, numbers with repeating decimals are considered rational. Irrational numbers don't have repeating decimals.
Why can't irrational number be represented as decimal form?
Any terminating or repeating decimal number can be converted easily into the form of p/q: a ratio of two integers. If it can be written in that form then it is rational.
Is The decimal form of an irrational number is a repeated decimal?
No it is not.
What is the decimal form of 17 square root?
√17 is irrational (a never repeating, never ending) decimal. √17 ≈ 4.1231
What is the square root of 168 in a decimal form?
It is an irrational number and as a decimal number it has no ending
Is 0.712 repeating a rational number is a irrational?
0.712 repeating is a rational number because it can be expressed as a fraction in the form of 712/999
What is a rational number in decimal form that has a finite number of digits after the decimal point?
I think it's a repeating decimal.
Is 3.40764076407640764076 rational or irrational?
3.407640764076407640764076(not repeating) is rational. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction. ---- 3.407640764076407640764076 = 3407640764076407640764076/1000000000000000000000000 Which is of the form of one_integer/another_integer so it a rational number. 3.4076... (where the 4076 repeats forever): 3.4076... = 34076/9999 = 34073/9999 Again of the form of one_integer/another_integer so it a rational number. Either way, 3.4076...4076 is a rational number. Decimal numbers that terminate, or go on forever with repeating a sequence of digits are rational. Decimal numbers that go on forever without repeating a sequence of digits are irrational, eg √2.
Repeating decimal definition?
A repeating decimal is a number expressed in decimal form in which, after a finite number of miscellaneous digits, the number continues with a string of a finite number of digits which repeats itself without end.
What are the irrational?
Irrational numbers are a subset of real numbers which cannot be written in the form of a ratio of two integers. A consequence is that their decimal representation is non-terminating and non-repeating.
Can a rational number have a decimal point?
Yes, for example 3/2 can be written as 1.5. All rational numbers have either a decimal expression of finite length or a repetitive pattern, unlike an irrational number, which goes on for ever when written in decimal form, never repeating.
