3rd Class Mathematics Numbers Number Sense and Numeration

Number Sense and Numeration

Introduction

Everything is counted by numbers. Numbers are the symbolic representation of counted objects. Categorized of numbers are basically dependent on their factors and divisibility.

Types of Number

Natural Numbers

Counting numbers are known as natural numbers.

For example, natural numbers (N) = {1, 2, 3, 4, 5 ?.. infinite}

Whole Numbers

Counting numbers including 0 are known as whole numbers.

For example, whole numbers (W) = {0, 1, 2, 3, 4?. infinite}

Prime Numbers

Those numbers having two factors 1 and the number itself are called prime numbers.

For example, prime numbers (P) = {2, 3, 5, 7, 11, 13 etc.}

Twin Numbers

Two numbers with difference of 2 are called twin primes.

For example: {3, 5}, {5, 7}, {11, 13} etc.

Note:

2 is even prime number.

Composite Numbers

Numbers having more than two factors, 1 and the number itself, are called composite numbers.

For example: {4, 6, 8, 9, 10 etc.}

Even Number

Numbers which are exactly divisible by 2 are called even numbers.

For example: {2, 4, 6, 8, etc.}

Odd Numbers

Numbers that are not exactly divisible by 2 and leaves remainder are called odd numbers.

For example: {1, 3, 5, 7 etc.}

•           Example

Quotient of division of a number is an odd number. Which one of the following is correct about the dividend if divisor is greater than I?

(a) Dividend is an even number

(b) Dividend is a composite number

(c) Dividend is a prime number

(d) All the above

(e) None of these

Ans.     (d)

Explanation: Quotient can be odd number for even, composite and prime number.

•           Example

If area of a circle C1 is full of natural numbers, which one of the following is correct about the area of circle C2?

(a) Circle C2 is full of prime numbers

(b) Circle C2 is full of composite numbers

(c) Circle C2 is full of even numbers

(d) All the above

(e) None of these

Ans.     (d)

Operation on Numbers

Expanded form of every number is written according 10 tire place value of digits. For example, form of number \[56434=5\times 10000+6\times 1000+4\times 100+3\times 10+4\]

Face Value

Face value of every number is the number itself. For example; face value of 5 in numeral 4356 is 5 itself and value of 4 in 4536 is 4.

Place Value

Place value of digits of a number is their position in the number. For example, place value of 2 in 54276 is 200. Place value of 5 in 5674 is 5000.

Successor

Successor of every number is just after the number. For example, successor of 17 is 18. Successor of a number is obtained by adding 1 to the number.

Predecessor

Predecessor of every number is just before the number. For example, predecessor? of 67 is 66. Predecessor of a number is obtained by subtracting 1 from the number.

Ascending Order

Arrangement of the numbers from smallest to greatest is called the ascending order of the numbers. For example, ascending order of 45, 67, 21, 34 is 21 < 34 < 45 < 67.

Descending Order

Descending order is the arrangement of numbers in decreasing order For example, descending order of 50, 45, 23, 12, 22 is 50 > 45 > 23 > 22 > 12.

Rounding Counting Numbers to Nearest Ten

Rounding counting number 23763 to nearest 10 is 23760. So unit digit is mostly changed while rounding counting numbers to nearest ten. Sometimes, tens digit may also be changed. For example, rounding of 458 to nearest 10 is 460.

Comparison of Place Value of Indian and International Number System

Number Pattern

Numbers can be arranged in different patterns.

Look at the following examples where numbers are arranged in pattern:

1, 4, 7, 10, 13.

In the given pattern difference between the numbers is 3. Adding 3 to previous number next number in the above pattern is obtained.

•           Example

Arrange the following capacity of packing materials in ascending order

Which one of the following is correct about their ascending order?

(a) Pouch < Tin < Gallon < Bottle

(b) Bottle < Pouch < Tin < Gallon

(c) Tin < Gallon < Bottle < Pouch

(d) All the above

(e) None of these

Ans.     (a)

Explanation: Since millilitres < centilitres < litres and 1 centilitre = 10 millilitres and 1 litre = 10 decilitres. Therefore, option (a) is correct.

•           Example

There are 235 holes on a metal plate. If every row has 5 holes then the total row of holes on the plate is a/ an:

(a) Composite number                                         (b) Even number

(c) Prime number                                                (d) all the above

(e) None of these

Ans.     (c)

          Explanation: Total number of rows on plate \[=\frac{235}{5}=47\] and 47 is a prime number.