1) What is a real number that is not rational?
2) Which two whole numbers are neither prime nor composite?
3) Explain why 1/4 and 1.4 are not equivalent expressions.
2) Which two whole numbers are neither prime nor composite?
3) Explain why 1/4 and 1.4 are not equivalent expressions.
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1. A real number that is not rational is one which is the quotient of two integers where the second one is equal to 0.
An integer is a whole number, it may be positive, negative or the number zero but it must be a whole number. The quotient of two integers means when one integer is divided into the other. For example 3/4, this is a rational number as the second number is not a 0. Something like 5/0 however is an irrational number as the second integer is a zero.
2. A prime number is a number which can only be divided by itself and 1, a composite number is one which can be divided equally amongst itself.
The numbers 1 and 0 are neither prime nor composite as zero cannot be divided by anything and 1 can only be divided by itself.
3. 1/4 and 1.4 are not the same as 1.4 is a decimal, 1/4 is a fraction, if 1/4 were to be made into a decimal it would be 0.25
An integer is a whole number, it may be positive, negative or the number zero but it must be a whole number. The quotient of two integers means when one integer is divided into the other. For example 3/4, this is a rational number as the second number is not a 0. Something like 5/0 however is an irrational number as the second integer is a zero.
2. A prime number is a number which can only be divided by itself and 1, a composite number is one which can be divided equally amongst itself.
The numbers 1 and 0 are neither prime nor composite as zero cannot be divided by anything and 1 can only be divided by itself.
3. 1/4 and 1.4 are not the same as 1.4 is a decimal, 1/4 is a fraction, if 1/4 were to be made into a decimal it would be 0.25
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1) Wants an irrational number. So basically the easiest route to go is the square root of a non perfect square. So sqrt(12) would be good. pi and e are irrational. Rational multiples of these numbers are also irrational.
2). Whole numbers are the set of numbers that are 0 1 2 3 4 ... 0 and 1 are neither prime nor composite.
3. 1/4 is the same as .25 and .25 does not equal 1.4 or 1.4 is the same as 14/10 and 1/4 and 14/10 are not the same.
2). Whole numbers are the set of numbers that are 0 1 2 3 4 ... 0 and 1 are neither prime nor composite.
3. 1/4 is the same as .25 and .25 does not equal 1.4 or 1.4 is the same as 14/10 and 1/4 and 14/10 are not the same.
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sqrt 2, sqrt 7 and pi are irrational for a few examples. 1/4 as a decimal is 0.25 because fractions mean a fraction of one therefore a quarter of one. 1.4 is over one and as a fraction would be 14/10 or 7/5 (simplified)