NCERT Maths Solutions for Class 10 Real Numbers & Rational Numbers

Rational Numbers

We will understand the few terms related to the number system-

Natural Numbers – All the counting numbers 1, 2, 3,4 …., etc are known as natural numbers.

Whole Numbers – All counting numbers together with 0 form the collection of whole numbers
Thus 0,1,2,3,4,5….etc are whole numbers.

Integers – All counting numbers, negatives of counting numbers and 0 forms the collection form the collection of integers.

Thus -1,-5, 0, 5 6….etc are all integers.

Rational Numbers –The number of the form p/q, where p and q are integers and q is not equal to 0 are called rational numbers.

Rational Numbers in Decimal forms – Every rational number when expressed in decimal form is expressible either in terminating or in non-terminating repeating decimal form.

To find out whether a given rational number is a terminating or repeating decimal

Let x be a rational number whose simplest form is p/q, where p and q are integers and q is not equal to 0 then,

X is a terminating decimal only q is of the form (2m * 5n )for some non-negative integers m and n
X is a non-terminating repeating decimal if q is not equal to (2m * 5n)

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For the practice of Rational and Irrational number, click on NCERT Class 10 Maths

Few Solved examples-

Example: – Without actual division show that each of the following rational numbers is a non-terminating repeating decimal.

1)17/90

90 = (2*3*3*5)

Out the above none of the numbers are factors of 17

So, 17/90 is in the simplest form.

NCERT Solutions for Class 10 Maths available.

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