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Chapter Analysis
Intermediate24 pages • EnglishQuick Summary
The chapter on Number Systems explores a variety of mathematical concepts such as rational and irrational numbers, the representation of these numbers on the number line, and the laws of exponents. It delves into the definitions and properties of rational numbers, including their decimal expansions as either terminating or repeating. The chapter also covers irrational numbers, characterized by non-terminating, non-repeating decimals, and examines operations with real numbers.
Key Topics
- •Rational numbers and their properties
- •Irrational numbers
- •Decimal expansions of real numbers
- •Operations on real numbers
- •Laws of exponents for real numbers
- •Representation of real numbers on the number line
Learning Objectives
- ✓Understand the difference between rational and irrational numbers.
- ✓Represent various types of numbers on the number line.
- ✓Learn and apply the laws of exponents.
- ✓Perform arithmetic operations with real numbers.
- ✓Rationalize the denominators of fractional expressions.
Questions in Chapter
Is zero a rational number? Can you write it in the form p/q, where p and q are integers and q ≠ 0?
Page 5
Find six rational numbers between 3 and 4.
Page 5
Write the following in decimal form and say what kind of decimal expansion each has: (i) 36/100 (ii) 1/11
Page 14
Additional Practice Questions
Express 0.333... as a fraction.
easyAnswer: Let x = 0.333... Then 10x = 3.333... So, 10x = 3 + x, solving gives x = 1/3.
Find an irrational number between 1/7 and 2/7.
mediumAnswer: An example of such a number is 0.150150015000150000..., which is non-terminating non-recurring.
Rationalise the denominator of 1/(2 + √3).
hardAnswer: Multiply and divide by the conjugate: (1/(2 + √3)) * ((2 - √3)/(2 - √3)) = (2 - √3)/(4 - 3) = (2 - √3).