Class 10 Exam > Class 10 Notes > Math Solutions (Exercise 1.4) - Real Numbers, Class 10, Mathematics
Math Solutions (Exercise 1.4) - Real Numbers, Class 10, Mathematics PDF Download
NCERT Math Solutions (Exercise 1.4)
(Page 17)
Q1: Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion:
Solution:
The denominator can be written in the form 5m. Hence, this decimal expansion is terminating.
Since the denominator is of the form 2m so, this decimal expansion is terminating.
Since the denominator can not be written in the form 2m × 5n and it also contains other factors 7 and 13, so its decimal expansion will be non-terminating repeating type.
As the denominator is of the form 2m × 5n so, the above decimal expansion is terminating.
Since the denominator can not be written in the form 2m × 5n and it has 7 as its factor so, the decimal expansion of is non-terminating repeating.
The denominator is of the form 2m × 5n therefore, it is a terminating decimal expansion.
Since the denominator is not of the form 2m × 5n, and it also contain another factor 7 so, the above decimal expansion is non-terminating repeating.
The denominator can be written in the form 2m × 5n. Hence, the above decimal expansion is terminating.
Since the denominator is of the form 2m × 5n so, the above decimal expansion is a terminating one.
Since the denominator is not of the form 2m × 5n and also contains 3 as its factors so, the above decimal expansion is non-terminating repeating.
Q2: Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions.
Solution:
Q3: The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If they are rational, and of the form p/q, what can you say about the prime factor of q?
Solution:
(i) 43.123456789
This number has a terminating decimal expansion. So, it is a rational number of the form p/q and q is of the form
(ii) 0.120120012000120000 …
The given decimal expansion is non-terminating and non-recurring. Therefore, it is an irrational number.
Since the given decimal expansion is non-terminating, so it is a rational number of the form p/q and q is not of the form 2m x 5n i.e., the prime factors of q will also have a factor other than 2 or 5.
FAQs on Math Solutions (Exercise 1.4) - Real Numbers, Class 10, Mathematics
| 1. What are real numbers? |  |
Ans. Real numbers are a set of numbers that include rational and irrational numbers. They can be represented on a number line and include all possible values, from negative infinity to positive infinity.
| 2. What is the difference between rational and irrational numbers? | |
Ans. Rational numbers can be expressed in the form of p/q, where p and q are integers and q is not equal to zero. Irrational numbers cannot be expressed in this form and cannot be represented as terminating or repeating decimals.
| 3. How are real numbers used in mathematics? | |
Ans. Real numbers are used in a variety of mathematical concepts, including algebra, geometry, and calculus. They are used to represent quantities such as distance, time, and weight, and are essential in solving equations and calculating measurements.
| 4. What are the properties of real numbers? | |
Ans. The properties of real numbers include commutative, associative, distributive, identity, and inverse properties. These properties are used in solving equations and performing mathematical operations.
| 5. How are real numbers related to the Pythagorean theorem? | |
Ans. The Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides, involves the use of real numbers to calculate distance and length. Real numbers are used to represent the sides of the triangle and the distance between points.
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