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No; the only condition for qualyfing as an irrational number is that the same pattern of digits doesn't repeat over and over again, as it does with a rational number. For example, 8/7 is a rational number; the decimal expansion is 1.142857 142857 142857 ... As you see, the same pattern of digits repeats over and over. The number may start with different digits, but if after a while the same pattern repeats again and again, the number is rational.
The following number is irrational: 0.101001000100001000001 ... The pattern doesn't repeat, because a zero is added every time. And, in this example, the decimal expansion doesn't contain any digits other than 0 and 1.
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Can a non-terminating decimal be a non-repeating decimal?
Yes. Every irrational number has a non-terminating, non-repeating decimal representation.
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.
Prove that Pi is an irrational number?
Every rational number has a decimal expansion that either terminates (like 42.23517) or repeats (like 26.1447676767676...)Pi's decimal expansion neither terminates nor repeatsHence, Pi cannot be rational.If we could prove the first two statements, this would constitute a proof that Pi is irrational, but most people cannot provide proof of either. Most proofs on this issue are quite technical, but I'm hoping to return to this question with a suitable answer soon.
Is every rational number a decimal number?
All real numbers have a decimal representation. Rational numbers have decimal representations that terminate or repeat infinitely. Irrational numbers have decimal representations that are non-terminating and non-repeating.
Can Every real number can be expressed as a decimal?
Yes, but most of them (the irrational numbers) will have infinitely long, non-repeating representations.
Is every decimal number an irrational number?
No.
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.
What Is 12.52 rounded 2 decimal points rational or irrational?
Every two-decimal place number is rational.
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.
Prove that Pi is an irrational number?
Every rational number has a decimal expansion that either terminates (like 42.23517) or repeats (like 26.1447676767676...)Pi's decimal expansion neither terminates nor repeatsHence, Pi cannot be rational.If we could prove the first two statements, this would constitute a proof that Pi is irrational, but most people cannot provide proof of either. Most proofs on this issue are quite technical, but I'm hoping to return to this question with a suitable answer soon.
Is every rational number a decimal number?
All real numbers have a decimal representation. Rational numbers have decimal representations that terminate or repeat infinitely. Irrational numbers have decimal representations that are non-terminating and non-repeating.
Can every natural number be irrational?
No. No natural number can be irrational.
Can Every real number can be expressed as a decimal?
Yes, but most of them (the irrational numbers) will have infinitely long, non-repeating representations.
What is a real number is also irrational number?
Every irrational number is a real number.
What will produce an irrational number when multiplied by 0.4?
Every irrational number, when multiplied by 0.4 will produce an irrational number.
Which number can be added to a rational number to explain that the sum of rational number and an irrational number is irrational?
Any, and every, irrational number will do.
