Rational Number Worksheet

Most students of mathematics would have heard about the term ‘rational number’ while studying the subject. The word rational is used to denote that makes sense or conveys a logical interpretation followed by a reason.  In math, it is has a different meaning altogether as it is derived from the word ratio. The rational numbers could be defined as the equivalence classes of the quotient set (Z × (Z \ {0})) / ~, where the cartesian product Z × (Z \ {0}) is the set of all ordered pairs (m,n) where m and n are integers, n is not 0 (n ≠ 0), and “~” is the equivalence relation defined by (m1,n1) ~ (m2,n2) if, and only if, m1n2 − m2n1 = 0. Simply put, a rational number is the one that could be expressed as the ratio of integers. An irrational number, on the other hand, is the one that is not rational. Coefficients sometimes would fall under the category of rational numbers owing to the term ‘rational’.  For instance, a rational point would be termed as a point having coordinates with rational coordinates. But the rational curve is not to be misunderstood with the term as it is just a curve having parameters defined by rational functions.

The rational number with decimal expansion would always either begin with the repetition of the digit sequence with the similar finite nature repeatedly or would terminate after a number of digits that are finite. Also, the rational number would convey any kind of termination or repetition of decimals. The rule we just mentioned applies not just to the for the integer base but for the decimal numeral system. The last digits of rational numbers would recur in an indefinite manner if they are expressed in the form of a decimal number like the fraction 10/3 equals the number with decimals like 3.333.

The rational number worksheet is designed to help the students where numbers could be expressed in the form x/y, where y is a non – zero integer and x is any integer. The type of questions asked in the worksheet would include those including the useful results on rational number, negative rational number, positive rational number and rational number ones. The answers to the questions provided in the worksheet are given below to cross check the answers to the questions asked above.

  • Worksheet 1
  • Worksheet 2
  • Worksheet 3

Practise This Question

”Each of Rajat's students either scored distinction in chemistry or physics” is represented by which of the following expressions

X : set of Rajat's students

P : x scored distinction in chemistry

Q : x scored distinction in physics