DOWNLOAD MOBILE APPLICATION TO LEARN MORE: REAL NUMBERS CLASS 10 CBSE
DOWNLOAD MOBILE APPLICATION TO LEARN MORE: REAL NUMBERS CLASS 10 CBSE
1. EUCLID’S DIVISION ALGORITHM
a = b × q + r
where a is dividend, b is divisor, q is quotient and r is remainder.
:: dividend = Divisor × Quotient + Remainder in equation (i) if r = 0, then b would be the HCF of a and b.
2. NATURAL NUMBERS
Counting numbers like 1,2,3,4,5,6,7,8, …………………. are called natural numbers.
3. WHOLE NUMBERS
All natural numbers together with 0, are called whole numbers. So 0, 1, 2, 3, 4, 5, 6, 7, 8, ………… are whole numbers.
It is noted that 0 is the smallest whole number and every natural number is a whole number
4. INTEGERS
The collection of all natural numbers, negative of natural numbers and ‘0’ is called integers, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, …………………….
5. RATIONAL NUMBERS
6. IRRATIONAL NUMBER
A number which can neither be expressed as a terminating decimal nor as a non-terminating repeating decimal is called an irrational number.
Note: An irrational number cannot be written in the form p/q
7. THE FUNDAMENTAL THEOREM OF ARITHMETIC
Statement: Every composite number can be expressed as a product of primes and this decomposition is unique, apart from the order in which prime factors occur.
That is given by any composite number there is one and only one way to write (factor) it as a product of primes, as long as we are not particular about the order in which primes occur So, we regard 3 × 7 × 11 × 13 as same as 7 × 11 × 3 × 13 or any other possible order in which these primes are written.
(i) HCF is the highest common factor. It is also known as greatest common divisor (GCD) .
(ii) LCM is the least common multiple.
(iii) The properties of HCF and LCM of two positive integers a and b are:
• HCF (a, b) × LCM (a, b) = a × b
DOWNLOAD MOBILE APPLICATION TO LEARN MORE: REAL NUMBERS CLASS 10 CBSE
Table of Contents
REAL NUMBERS CLASS 10 CBSE
(d) none of these
2. The decimal expansion of the rational number
(a) one decimal place
(b) two decimal places
(c) three decimal places
(d) four decimal places
3. For given positive integers a and b, there exist unique whole numbers q and r such that :
(a) a = bq + r 0 ≤ q < b
(b) a = bq + r, 0 ≤ r ≤ b
(c) a = bq + r, 0 ≤ r < b
(d) none of these
4. If the HCF of 26 and 65 is expressed in the form 26x – 65 then value of x is :
(a) 1
(b) 2
(c) 3
(d) 4
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6. If HCF (a, b) = 12 and a × b = 1800 , then LCM (a, b) is equal to :
(a) 3600
(b) 900
(c) 150
(d) 90
7. The least number that is divisible by all the numbers from 1 to 10 is:
(a) 10
(b) 100
(c) 504
(d) 2520
8. If m is the HCF of 56 and 72 satisfying m = 56x + 72 y, then values of x and y are:
(a) 3 and 4
(b) – 4 and 3
(c) 4 and – 3
(d) – 4 and -3
9. The greatest number which divides 445, 572 and 699 leaving remainders 4, 5 and 6 respectively is :
(a) 63
(b) 70
(c) 60
(d) 58
10. There are 32 students in section A and 36 students in section B of class X of a school, then the minimum number of books required for the library so that they can be distributed equally among the students of section A or section B is:
(a) 278
(b) 288
(c) 298
(d) 268
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