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The World of Numbers
Chapter summary, hard words and model exam answers for Class 9 Hindi.
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Maths · CBSE Class 9
Summary
Natural numbers count objects. Adding zero gives whole numbers. Adding negative numbers gives integers, which help represent loss, debt, temperature below zero and positions to the left of zero.
A rational number can be written as p/q, where p and q are integers and q is not zero. Fractions, integers, terminating decimals and recurring decimals are rational.
Between any two rational numbers, there is always another rational number. You can use the average, or rewrite the fractions with a larger common denominator.
An irrational number cannot be written as p/q. Its decimal expansion continues forever without ending and without a repeating block. Examples include sqrt(2) and pi.
Rational and irrational numbers together form the real numbers. The real number line has no gaps: every real number has a point, and every point has a real number.
A terminating decimal is rational. A non-terminating recurring decimal is also rational. A non-terminating, non-recurring decimal is irrational.
Hard words & meanings
| natural number | A counting number such as 1, 2, 3 and so on |
| integer | A whole number that may be positive, negative or zero |
| rational number | A number expressible as p/q, where q is not zero |
| irrational number | A number that cannot be expressed as p/q |
| dense | Having another number between any two chosen numbers |
| recurring decimal | A decimal in which a digit or block repeats forever |
| real number | Any rational or irrational number on the number line |
Model exam answers, grammar & audio
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