Question

Which of the following statements is false?



If a number is a natural number, then it is rational.

If a number is a whole number, then it is rational.

If a number is a fraction, then it is rational.

If a number is an integer, then it is irrational.

Answer 1

the third one

Answer 2

This is a question to help understand the different kinds of numbers.
Note that we are looking for the ONE \(false\) statement.

All rational numbers can be expressed as a fraction of integers and vice versa.
For example, 5/2, 4.5, 2.33333333... are all rational numbers. (note: 2.33...=7/3)
Some examples of irrational numbers are: \(\pi\), \(\sqrt 2\), \(\sin(60)\), etc.

The counting numbers are called natural numbers, i.e. {1,2,3,...} It is denoted by N. Mathematicians in some countries define natural numbers as {0,1,2,3,....}

Whole numbers are numbers that \(can\) be written without fractions, they are called integers. Whole numbers belong to the set {...-3, -2, -1, 0, 1, 2, 3, ...} and is denoted by Z. Examples are 4, -2, \(\sqrt{49}\), \(\dfrac{240}{12}\), etc.

Fractions are numbers obtained by dividing one number by another, such as \(\dfrac{5}{3}\), \(\dfrac{7}{1}\), \(\dfrac{355}{113}\), \(\dfrac{22}{7}\), etc. Fractions may or may not be reduced to integers.

After reading and understanding the previous notes, reread the question carefully, and you should be able to spot the correct answer, i.e the incorrect statement. Post your answer for a check if you wish.