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Is Irrational numbers can never be precisely represented in decimal form Why is this?
They don't stop.
Why can't irrational numbers ever be precisely represented in a decimal form?
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.
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 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.
What kind of decimal numbers are irrational number?
Decimal numbers that can't be expressed as fractions are irrational numbers
Is Irrational numbers can never be precisely represented in decimal form Why is this?
They don't stop.
Why can't irrational numbers ever be precisely represented in a decimal form?
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.
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.
What kind of decimal numbers are irrational number?
Decimal numbers that can't be expressed as fractions are irrational numbers
What kind of decimal numbers are irrational numbers?
They are the decimal numbers that can't be expressed as fractions.
Can an irrational number be expressed as a terminating decimal?
No, irrational numbers can't be expressed as a terminating decimal.
What does non-terminating irrational decimal mean?
All irrational numbers have decimal representations which are non-terminating.
What are the irrational numbers?
Irrational numbers are numbers that cannot be expressed as a ratio of two integers or as a repeating or terminating decimal.
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.
Can an irrational number be a decimal if so give an example?
Irrational numbers are decimal numbers that can't be expressed as fractions. An example is the square root of 2
Why cant irrational numbers be represented in decimal form?
But irrational numbers are decimals that can't be expressed as fractions
How is the decimal of an irrational number different from the decimal of a rational number?
The difference is that rational numbers stay with the same numbers. Like the decimal 1.247247247247... While an irrational number is continuous but does not keep the same numbers. Like the decimal 1.123456789...
