Can an integer be an irrational number?

Answer 1

Irrational numbers cannot be expressed as fractions. Integers can be expressed as fractions. (ex: 3/3 or 6/6)

Answer 2

No. A rational number is of the form a/b where a and b are integers, so by definition, an integer cannot be an irrational number.

Answer 3

Hi, I see you have two questions posted about the different number sets and I thought an illustration may help clear it up for you:

Reals
/       \
Q    Q/R
|
Z
|
N

Where:
N = "natural numbers", e.g. 1,2,3..., i.e. positive whole numbers, not including 0

Z = "integers", e.g. ...-2,-1,0,1,2,..., i.e. positive and negative numbers, including 0

Q = "rational numbers", e.g. 2/3, 0, -3,... i.e. any number, positive or negative, that can be represented as a fraction, including 0

Q/R = "irrational numbers", e.g. sqrt(2), pi, e, phi,... i.e. any number that can NOT be represented as a fraction

Reals = "real numbers", e.g. sqrt(2), 2/3, -1, 0, 2, ... i.e. any number listed above

The basic idea of the figure I gave you is that any set contains within itself the set below it. So all natural numbers are integers, all integers are rational and all rationals are real. The opposite isn't true - not all rationals are integers (some are though) just as not all reals are natural.

Hope that helps!

Answer 4

A rational number can be expressed as the fraction of two integers. So consider an odd integer k, then k = r/s is rational if r and s are integer. You can quickly convince yourself that you can find two even integers that yield k. If k is even, it is even easier since every even integer is a multiple of 2. So integers are rational numbers

Answer 5

No. Every integer n can be written as n/1, the quotient
of 2 integers, so it is rational.

Answer 6

Straightforward answer, no. Irrational numbers are those which cannot be expressed as whole fractions. Every Integer can simply be expressed as a fraction with itself as numerator and one as denominator.

Answer 7

No

Answer 8

no

Answer 9

No.