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Suppose an irrational number can be written precisely in decimal form, with n digits after the decimal point. Then if you multiply the decimal value by 10n you will get an integer, say k. Then the decimal representation is equivalent to k/10n, which is a ratio of two integers and so the number, by definition, is rational - not irrational.
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Is Irrational numbers can never be precisely represented in decimal form Why is this?
They don't stop.
Why can irrational numbers never be represented precisely in decimal form?
Irrational numbers cannot be represented precisely in decimal form because they have non-repeating, non-terminating decimal expansions. Unlike rational numbers, which can be expressed as a fraction of two integers and thus have either a finite or repeating decimal representation, irrational numbers go on infinitely without any repeating pattern. This intrinsic property makes it impossible to write them exactly in decimal form, as any finite or repeating decimal approximation can only be a close estimate, never an exact representation.
Why cant irrational numbers be represented in decimal form?
But irrational numbers are decimals that can't be expressed as fractions
Why irrational numbers can never be precisely repersented in decimal form?
They don't stop.
Why can't irrational numbers represented in decimal form?
They don't stop.
Is Irrational numbers can never be precisely represented in decimal form Why is this?
They don't stop.
Why can irrational numbers never be represented precisely in decimal form?
Irrational numbers cannot be represented precisely in decimal form because they have non-repeating, non-terminating decimal expansions. Unlike rational numbers, which can be expressed as a fraction of two integers and thus have either a finite or repeating decimal representation, irrational numbers go on infinitely without any repeating pattern. This intrinsic property makes it impossible to write them exactly in decimal form, as any finite or repeating decimal approximation can only be a close estimate, never an exact representation.
Why cant irrational numbers be represented in decimal form?
But irrational numbers are decimals that can't be expressed as fractions
Why irrational numbers can never be precisely repersented in decimal form?
They don't stop.
Why can't irrational numbers represented in decimal form?
They don't stop.
Is an irrational number a number that is represented by a nonrepeating decimal?
Yes, However, it is not defined that way. It is defined as a number that cannot be expressed precisely as a ratio of two real numbers (a fraction). But that is equivalent to a non-repeating decimal.
Is the number log 216 an irrational number?
Irrational numbers are precisely those real numbers that cannot be represented as terminating or repeating decimals. Log 216 = 2.334453751 terminates and is therefore not irrational.
Can irrational numbers be decimals?
An irrational number by definition can not be exactly represented by a decimal that terminates or recurs. The moment a decimal terminates, or settles into a repeating pattern, it is rational.
Can every decimal be represented as a fraction?
No because irrational numbers can't be expressed as fractions
Why might you need to be able to estimate an irrational numbers?
Because rational numbers aren't able to be notated precisely in decimal form. They don't stop.
Which of these numbers are irrational number a0.5151.b0.7 c0898898889.?
None of them: they are all rational since they can all be represented as terminating decimal numbers.
Can all real numbers be represented as a decimal?
Yes, except that all irrational numbers will be non-terminating, non-repeating decimals.
