## Topics |
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**1) Explain counting numbers? **

The numbers 1, 2, 3, 4, 5, 6,.... are called counting numbers. These are also known as natural numbers or positive numbers.

**2) Explain rational number? **

A rational number is any number that can be expressed as the quotient or fraction p/q of two integers, with the denominator q not equal to zero.

**3) Explain irrational Number? **

An irrational Number is any real number that cannot be expressed as a ratio p/q, where p and q are integers, with q non-zero, and is therefore not a rational number.

**4) Explain real number? **

A real number is any positive or negative number. This includes all integers and all rational and irrational numbers.

**5) How can we mark the position of π on a number line? **

We know that the perimeter of a circle with diameter 1 units. Now make the perimeter of a circle having diameter 1 unit is π units. Now make a circle having diameter 1 using a thin wire or draw a circle of diameter. 1 on a sheet of paper and take its perimeter using a thread. Now place one end of the wire or the thread on 0 and spread it on the line and the point where its other end touches the line is the position of π.

**6) What is the length of AB in the following figure? **

In this right angled triangle, AB^{2} = BC^{2} - AC^{2 }

= 5^{2} - 3^{2 }

= 25 - 9 = 16

AB = √16 cm = 4 cm

**7) How many numbers are there between 0 and 1? **

There is no counting number between 0 and 1. But there are fractions such as 0.1, 0.2, 0.3---- and 0.9 between 0 and 1. Again between 0 and 0.1 there are 0.01, 0.02, 0.03,.... and 0.09. Also we can find out 0.001, 0.002, 0.003..... and 0.009 between 0 and 0.01. If we proceed like this we get an innumerable (infinite) number of both rational and irrational numbers between 0 and 1. As there are innumerable numbers between 0 and 1 there are infinite number of points on the line between 0 and 1.

**8) Explain absolute value of a number?**

Distance between zero and a number on the number line is the value of the number disregarding its sign. This value is called the absolute value of the number.

**9) Find two numbers x and y for which |x + y| = |x| + |y|.**

Let x = 3 and y = 7

|3 + 7| = |10| = 10

|3| + |7| = 3 + 7 = 10

**10) Verify whether the following are true:**

a) |7 + 5| = |7| + |5|

b) |22 + 8| = |22| + |8|

a) L.H.S = |7 + 5| = |12| = 12

R.H.S = |7| + |5| = 7 + 5 = 12

ie, |7 + 5| = |7| + |5| is true.

b) L.H.S = |22 + 8| = |30| = 30

R.H.S = |22| + |8| = 22 + 8 = 30

ie, |22 + 8| = |22| + |8| is true.

**11) Check whether the following are true:**

a) |-12 - (-4)| = |-12| - |-4|

b) |-6 + (+4)| ≠ |-6| + |4|

a) L.H.S = |-12 - (-4)| = |-12 + 4| = |-8| = 8

R.H.S = |-12| - |-4| = = 12 - 4 = 8

ie, |-12 - (-4)| = |-12| - |-4| is true.

b) L.H.S = |-6 + (+4)| = |-6 + 4| = |-2| = 2

R.H.S = |-6| + |4| = 6 + 4 = 10

ie, |-6 (+4)| ≠ |-6| + |4| is true.

**12. Find the value of |38 - (8)| ? **

|38 - (8)| = |38 - 8| = |30| = 30

**13) Write the absolute value for the following. a) |-327| b) |486| **

a) |-327| = 327

b) |486| = 486

**14) Find the distance between 4 and 9 .**

Distance between 4 and 9 = |4 - 9| = |-5| = 5.

**15) Find the value of x for the following: |x + 2| = 3**.

We can write |x + 2| as |x - (-2)|

|x - (-2)| = 3

That is the distance between x and -2 is 3. x can be 3 unit to the right or left of -2 , 3 unit to the right of -2 is +1 and 3 unit left of -2 is -5

∴ x = 1 and -5

**16) Find the value of x for the following : |x - 3| = |x -5|**

Distance from 3 to x and distance from 5 to x are equal. That is the position of x is in the middle of 3 and 5 .

**17) Mark given numbers on the number line and check whether the distance between them is equal to the number got by subtracting the smaller from the larger. 2, -6.**

Larger = 2, Smaller = -6

Distance = 2 - -6 = 8

lsmaller - larger l

=| -6 - 2 | =|-8| = 8

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Std 9

Kerala (English Medium)

## Practice in Related Chapters |

New Numbers |

Polygons |

Simplification |

Rational numbers |

Circles |

Area |

Prisms |

Statistics |

Pairs of Equations |

Real Numbers |

Similar Triangles |

Polynomials |

Fractions |