Real Numbers Exercise 1-1 , New Complete answers – real numbers from class 10 Most imp questions. Its for SSC Public exams and also for competitive exams like NTSE, RGUKT CET, POLYCET, APRJC etc…

“God made the integers. All else is the work of man”…….…. Leopold Kronecker

Euclid’s division lemma: Given positive integers a, b there exists unique pair of integers q and r satisfying

a = bq +r; 0≤r<b

This result was first published / recorded in book VII of Euclid’s “The Elements” Euclid’s division algorithm is a technique to compute the Highest Common Factor

(H.C.F) of two given numbers.

E.g: HCF of 80 and 130

130 = 80 X 1 + 50

80 = 50 x 1 + 30

50 = 30 X 1 + 20

30 = 20 × 1 + 10

20 = 10 x 2 + 0 and H.C.F = 10

### Real Numbers Exercise 1-1

Euclid’s division algorithm can also be extended to all integers. Numbers which can be expressed in the form p/q, where q # 0 and ‘p and q’ are

integers are called rational numbers; represented by Q.

Q={ p/q ; q is not equal to 0, p,q ∈ Z}

Every rational number can be expressed either as a terminating decimal or as a non-terminating recurring decimal.

Numbers which can’t be expressed in algebraic form i.e in p/q form are called irrational numbers represented by S. You may notice that the first letter of surds is ‘S’

The combined set of rationals and irrationals is called the set of Real numbers; represented by R

R= QUS.

### Real Numbers Exercise 1-1 Here is complete solutions.

## Real Numbers Exercise 1-1

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Real number is easy topic to score in SSC Public examination. So we hope student can practice more and more. We hope our notes will help them.