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VashtiMaiden
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Can someone pls help me on "rational and Irrational numbers". Esp. on Decimals. I can't classify if it is rational or irrational.
lurflurf said:for decimal form a useful fact is
a real nummber x is rational if and only if its decimal expansion at some point repeats.
JohnDuck said:Little off-topic, but here goes: I'm curious, is this not true in some integer base?
Rational numbers are numbers that can be expressed as a ratio of two integers, while irrational numbers cannot be expressed as a ratio and have non-repeating, non-terminating decimal expansions.
A number can be determined to be rational or irrational by trying to express it as a fraction. If it can be written as a fraction, then it is rational. If not, then it is irrational.
No, not all square roots are irrational numbers. Some square roots, such as the square root of 4, can be expressed as rational numbers.
Irrational numbers are important in mathematics because they help to bridge the gap between rational numbers and real numbers. They allow for more precise calculations and help to explain certain mathematical concepts.
Yes, irrational numbers can be approximated by rounding the decimal representation to a certain number of digits. However, the approximation will never be exact since irrational numbers have infinite non-repeating decimals.