Class 9 Maths Ganita Manjari Chapter 3 MCQ – The World of Numbers

Early humans matched one object with another (like pebbles for cows). This method, called one-to-one correspondence, helped them count before numbers or symbols were invented.

ℕ represents natural numbers, which are counting numbers like 1, 2, 3, and so on. These were the earliest numbers used by humans.

The Lebombo bone had notches that likely tracked lunar cycles or time, showing early use of numbers for counting natural events.

These numbers are prime numbers because they have only two factors: 1 and themselves. The Ishango bone shows early knowledge of such patterns.

In the Indus Valley, numbers were essential for trade, using weights and measures to exchange goods accurately.

Śhūnya means zero. It represents nothingness and became an important concept in mathematics through Indian scholars.

Brahmagupta defined zero as a number and gave rules for its use in arithmetic, making it a major mathematical advancement.

Subtracting a number from itself always gives zero. This is one of the fundamental rules defined by Brahmagupta.

Any number multiplied by zero equals zero. This is a basic rule of arithmetic involving zero.

Negative numbers were used to represent debts or losses, while positive numbers represented wealth or gains.

Integers include all whole numbers, both positive and negative, along with zero.

A negative number multiplied by a positive number gives a negative result. So, (–3) × 4 = –12.

The product of two negative numbers is positive. So, (–3) × (–4) = 12.

Fractions represent parts of a whole, such as dividing something into equal parts.

A rational number is any number that can be written as a fraction p/q, where p and q are integers and q is not zero.

3/4 is a rational number because it can be written as a fraction of integers.

Division by zero is not defined in mathematics, so q cannot be zero in a rational number.

Dividing 3 by 8 gives 0.375, which is a terminating decimal.

A repeating decimal has digits that repeat infinitely. In 0.333…, the digit 3 repeats forever.

A rational number terminates if the denominator has only 2, 5, or both as prime factors.

Absolute value gives distance from zero, so it is always non-negative. Thus, |–5/3| = 5/3.

Absolute value represents how far a number is from zero on the number line, regardless of direction.

Rational numbers, like fractions, lie between integers and fill the gaps between them.

Between any two rational numbers, there are infinitely many rational numbers.

√2 cannot be written as a fraction and has a non-repeating decimal, so it is irrational.

Irrational numbers cannot be expressed as a ratio of two integers and have non-terminating, non-repeating decimals.

π is an irrational number with a non-repeating, non-terminating decimal expansion.

Real numbers include all rational and irrational numbers, forming a continuous number line.

Irrational numbers like √2 have decimal expansions that never end and do not repeat.

0.999… is exactly equal to 1. This can be shown using algebra by assuming x = 0.999… and solving.