Select Page

Rational and Irrational Numbers

Rational and Irrational Numbers

Rational Numbers

Any number that can be expressed in the form \\frac{p}{{q}}  where p, q are integers and q \\neq  0 is called a rational number. p is called the numerator and q the denominator of the rational number.

Any integer can be expressed as a rational number. For example, 5 can be written as \\frac{5}{1}  in the rational form.

The numbers \\frac{4}{-5},\\frac{6}{4},\\frac{-11}{-9},\\frac{8}{1},\\frac{-7}{-1},\\frac{0}{-3},… are all rational numbers

All fractions are rational numbers. All integers are also rational numbers. There are many rational numbers which are neither fractions nor integers.

Rational numbers can also be represented on the number line.

Example: Which of the following is (are) rational number(s)?

2, \\frac{1}{3}\\sqrt{2}, -9, \\frac{-5}{12}}

It can be seen that apart from\\sqrt{2}, all other numbers can be written in the form\\frac{p}{q}}.

So, except\\sqrt{2}, all the given numbers are rational numbers.

Irrational Numbers

All numbers which are not rational are called irrational numbers, which means all the numbers that cannot be put in the form  \\frac{p}{q}} where p, q are integers and q \\neq  0 are called ‘irrational numbers’.

Any rational number will be a terminating decimal or a repeating decimal. For example, \\frac{7}{8}} = 0.875(terminating decimal)

\\frac{5}{12} = 0.41666…(repeating decimal)

An irrational number is a decimal that is neither terminating nor repeating.

The square roots of 2, 3, 5, 6, 7, 8 are all irrational numbers.

Example: Which of the following is NOT irrational?

  1. \\sqrt{2}
  2. \\sqrt{7}
  3. \\sqrt{16}
  4. \\sqrt{8-4}

 

\\sqrt{2}  and  \\sqrt{7} are irrational numbers.

\\sqrt{16} = 4, which is a rational number.

\\sqrt{8-4} = \\sqrt{4} = 2, which is also a rational number.

So, \\sqrt{16} and  \\sqrt{8-4} are NOT irrational numbers.

CHECK POINT

1. Is 0.31 311 3111… an irrational number?

2. Identify the rational numbers: 21π, \\sqrt{83}, \\frac{10}{7}.

3. Which of the following is an irrational number?
   rational2
4. Is 0 a rational number?

5. Which list contains only rational numbers?

rational3

Answer key
  1. Yes
  2. \\frac{10}{7}
  3. π
  4. 0 is a rational number because we can write it as\\frac{0}{1} ,\\frac{0}{-4}, which implies that 0 is a rational number.
  5. (A)

 

Give Your Child The eTutorWorld Advantage

Research has proven that personal online tutoring not just cements school learning, it helps build student confidence. eTutorWorld provides the best K-12 Online Tutoring Services so you can learn from the comfort and safety of your home at an affordable cost.

Be it an exam, class test or a quiz, eTutorWorld’s Math, Science and English tutors are responsible for your academic progress. Meet your personal coach at your convenient day and time to get help for Grade 3-12 Math, Science and English subjects and AP, SAT, SSAT and SCAT Test Prep help and test practice. All our tutors are graduates and bring with them years of teaching experience to the tutoring lessons.

Our ‘Learning by Design’ methodology makes sure that each student is at the center of the teaching-learning process. All tutoring sessions start with a question to the student ‘What do you want to learn today?’ Hence, tutors diagnose your skills and recognize your requirements before the actual tutoring happens. Post every tutoring session, an individualized worksheet is emailed to the student to assimilate learned concepts. Regular formative assessments are used to evaluate a student’s understanding of the subject.

The state of the art technology used is stable, user friendly and safe. All you need is a computer or a tablet and an internet connection. The easy-to-use web conferencing software requires a one time download, using which the student can talk and chat to the tutor, annotate on an interactive shared whiteboard or even share documents, assignments or worksheets.

All tutoring sessions are recorded and made available for a month so you can review concepts taught.

Email or call our support team with any issues or questions – we are here for you 24X7.

Also, download free printable math and science worksheets in pdf format and solve SCAT and SSAT Practice Tests online. Sign up for a Free Trial Lesson Today!

Thousands have taken the eTutorWorld Advantage – what are you waiting for?

 

 

© 2019 eTutorWorld - Online Tutoring and Test Prep | All rights reserved