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Q. Diffrence between Rational and Irrational Numbers?
Ans.
A number which is not rational is called irrational. The word "irrational" sounds not quite right...as though the numbers were "wrong in some way. As a matter of fact, many early mathematicians like Pythagoras were unwilling to accept that such numbers could exist. Nowadays, irrational numbers are accepted as perfectly "proper."
Some examples of irrational numbers are:
• Square roots of whole numbers that aren't perfect squares; for example,
• Decimal numbers that don't repeat or terminate. Some examples of this type of number are Π ≡ 3.14159... and e ≡ 2.71828...
• There are many other examples. In fact, there are "more" irrational numbers than rational numbers.
How do you know when a number is irrational? That can be difficult. If you can write a number as a fraction., then it must be rational, but if you can't write a number as a fraction, then maybe you just haven't thought of the right fraction yet! To know for sure that a number is irrational, you would have to prove that it can't be written as a fraction.
Figure shows noise results for a prototype van measured on a rolling road. The vehicle had a four-cylinder-in-line engine. The engine speed was varied in 3rd gear from just above
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1. Suppose n ≡ 7 (mod 8). Show that n ≠ x 2 + y 2 + z 2 for any x, y, z ε Z. 2. Prove ∀n ε Z, that n is divisible by 9 if and only if the sum of its digits is divisible by 9.
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Consider the following multiplication in decimal notations: (999).(abc)=def132 ,determine the digits a,b,c,d,e,f. solution) a=8 b=6 c=8 d=8 e=6 f=7 In other words, 999 * 877 = 8
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