Real Numbers For Class 10th

  • In Class IX we started with real numbers and also defined irrational numbers.
  • We continue our discussion on real numbers in this chapter.
  • We begin with two very important properties of positive integers in Sections 1.2 and 1.3, namely Euclid’s division algorithm and the fundamental theorem of Arithmetic.
  • We already know that every composite number can be expressed as a product of primes in a unique way —this important fact is the Fundamental Theorem of Arithmetic.

This Lesson on Real Number will cover 

  1. Euclid’s Divison Lemma and Algorithm
  2. The Fundamental Theorem of Arithmetic
  3. Concept of Irrational Numbers
  4. Showing Rational Numbers and Their decimal expansion

Happy Learning 😛 

rational number, in Mathematics, can be defined as any number which can be represented in the form of p/q where q ≠ 0

According to Euclid’s Division Lemma if we have two positive integers a and b, then there exist unique integers q and r which satisfies the condition a = bq + r where 0 ≤ r ≤ b.

HCF is the largest number which exactly divides two or more positive integers.

Since 12576 > 4052

12576 = (4052 × 3) + 420

420 is a reminder which is not equal to zero (420 ≠ 0).

4052 = (420 × 9) + 272

271 is a reminder which is not equal to zero (272 ≠ 0).

Now consider the new divisor 272 and the new remainder 148.

272 = (148 × 1) + 124

Now consider the new divisor 148 and the new remainder 124.

148 = (124 × 1) + 24

Now consider the new divisor 124 and the new remainder 24.

124 = (24 × 5) + 4

Now consider the new divisor 24 and the new remainder 4.

24 = (4 × 6) + 0

Reminder = 0

Divisor = 4

HCF of 12576 and 4052 = 4.

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