# 5th Class Mental Ability Numbers Number System

Number System

Category : 5th Class

Number System

Learning Objectives

• Numbers
• Number System
• Hindu-Arabic Numeral System
• International System of Numeration
• Roman Numeral
• Rule of Ordering in Mathematics-BODMAS
• Fraction

Numbers

Numbers are mathematical symbols by which we express date, time, distance, position, quantity etc.

We use ten symbols (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) to write any number.

Like 346562232, 3465452155, 4003444656 etc.

Numbers System

Number system deals with the study of different types of numbers. In this chapter, we will study about the categorization of different types of numbers.

Numbers Types

Numbers are classified according to their type. The first type of numbers we ever learned about: the counting numbers or the natural numbers and the next type of numbers is whole numbers.

• Natural Numbers: The counting numbers (1, 2, 3, 4, . . . . .) are called natural numbers.
• Whole Numbers: Natural numbers including zero (0, 1, 2, 3, 4,.....) are called whole numbers.
• Even and Odd Numbers: Numbers which are divisible by 2 are called even numbers. For example, 2, 4, 6, 8, 10,..... etc.

Numbers which are not divisible by 2 are called odd numbers. For example, 1, 3, 5, 7, 9, 11, .....etc.

• Prime and Composite Numbers: Whole numbers which have only two factors 1 and the number itself are called prime numbers. For example, 2, 3, 5, 7, 11 etc.

Whole numbers which have at least one factor other than 1 and the number itself are called composite numbers. For example, 4, 6, 8, 9, 12 etc....

• Twin Primes: Two prime numbers are called twin primes if there are only one composite number between them. For example, pair of twin primes between 1 and 20 are: (3, 5); (5, 7); (11, 13) and (17, 19).
• Integers: A negative number is a real number that is less than zero, which represents opposite. Integers are set of whole numbers and negative numbers.

For example,....... 5, - 4, - 3, - 2, - 1, 0, + 1, + 2, + 3, + 4, + 5,......

• Successor and Predecessor of a Number: Successor of a number is obtained by adding 1 to the number. For example, successor of 243 is 243 + 1 = 244.

Predecessor of a number is obtained by subtracting 1 from the number. For example. The predecessor of 243 = 243 - 1 = 242.

Hindu-Arabic Numeral System

Hindu-Arabic Numeral System is also known as Indian System of Numeration. This system is based on the following place value chart.

Place Value Chart

 Period Kharabs Arabs Crores Lakhs Thousands Ones Place Ten Kharab (T-KH) 1000000000000 Kharab (KH) 100000000000 Ten Arab (T-A) 10000000000 Arab (a) 10000000000 Ten Crores (T-C) 100000000 Crores (c) 100000000 Ten Lakhs (T-L) 1000000 Lakhs (L) 100000 Ten Thousands (T-TH) 1000 Thousands (TH) 1000 Hundred (H) 100 Tens (T) 10 Ones (O) 0

International System of Numeration

International system of numeration is widely used in the most part of the world. The following table shows the place value chart for international System of Numeration:

 Period Billion Millions Thousands Ones Place Hundred billions Ten billions Billions Hundred millions Ten millions Millions Hundred thousands Ten thousands Thousands Hundred Tens Ones

Points to Remember

• If 1 is added to the largest one digit number, two digit number, three digit number, and go on, we get the smallest two digit number; three digit number, four digit number, respectively.

For example, 9 + 1 = 10; 99 + 1 - 1000; 999 + 1 - 10000; 9999 + 1 = 100000

• One hundred crore or 1000000000 is equal to one kharab in Hindu-Arabic Numeral System.
• Thousand $\times$ Thousand = 1 Million, and Thousand $\times$ Thousand $\times$ Thousand = 1 Billion.

Thousand $\times$ Thousand $\times$ Thousand $\times$ Thousand - 1 Trillion, or we can say Thousand Billions make 1 Trillion.

• 1 Million (1000000) = 10 Lakh

10 Million (10000000) = 1 Crore

1 Billion (1000000000) = 1 Arab

100 Billion (10000000000) = 1 Kharab

1 Trillion (1000000000000) = 10 Kharab

Roman Numeral

Roman numerals represent the numbers using alphabetical symbols.

The seven alphabetical symbols, which are used in Roman system of numeration, and their values are as follows:

 Symbols I Value 1 V 5 X 10 L 50 C 100 D 500 M 1000

Rules of Ordering in Mathematics-BODMAS

Brackets: There are three types of brackets:

(i) Small brackets (Parentheses), which is denoted by ( ).

(ii) Middle brackets (Braces), which is denoted by { }.

(iii) Big brackets (Brackets), which is denoted by [ ].

When we use brackets, it is customary to put [ ] outermost, then { } and then

( ) innermost symbols first. For example, $[\{\left( 4+5 \right)\times ~6\}+7\left] = \right[\{9~\times 6\}+7\left] = \right[54+7]=11$.

BODMAS: When a single expression contains many mathematical operations then BODMAS rules are used for the simplification of the expression. The word BODMAS has been arranged according to the priority of the operations. The BODMAS acronym is for:

• Brackets (part of a calculation inside brackets always come first)
• Orders (numbers involving powers or sequence roots)
• Division ($\div$)
• Multiplication ($\times$)
• Subtraction (-)

Recall that 'of is replaced by multiplication (x). Correct order for numbers in operations is: () {} []$\div$$\times$ or ‘of’ + -

Fractions

Fraction is a number, which is used to represent the part of a whole. It is expressed, in the form of $\frac{P}{Q}$ where P and Q are natural numbers. The upper part of the fraction is called numerator and the lower part is called denominator. For example, $\frac{5}{9}$ is a fraction, where 5 is numerator and 9 is denominator.

1. A prime number just before the predecessor of 19 is:

(a) 19                            (b) 18

(c) 17                            (d) 23

(e) None of these

Explanation: Predecessor of 19 = 19 - 1 = 18.

18 is not a prime number and just before 18 is 17.

1. Sixteen crore sixteen lakh sixteen thousand six hundred and sixteen is:

(a) 16, 16, 16, 616

(b) 1, 61, 61, 61, 616

(c) 1, 61, 61, 61, 61, 616

(d) 6, 16, 16, 616

(e) None of these

Explanation: Sixteen crore sixteen lakh sixteen thousand six hundred and sixteen

$=1\times ~100000000+6~\times 10000000+1\times ~1000000+6~\times 100000+1\times ~10000$

$+6~\times 1000+6\times ~100+1~\times 10+6~\times 1=161616616=16, 16, 16, 616$.

1. Roman numeral for the greatest three digit even number is:

(a) CMXCVIII                 (b) CMLXXXIX

(c) CMXXVIII                             (d) CMLXVIII

(e) None of these

Explanation: The greatest three digit even number == 998.

$=900+90+8=\left( 1000100 \right)+\left( 10010 \right)+8=\text{CM+XC+VIII = CMXCVIII}$.

1. Find the value of 6 + 2[3 + 5 {28 - 12 (12 - 10)}].

(a) 56                            (b) 52

(c) 53                            (d) 58

(e) None of these

Explanation: On applying BODMAS, we get,

$=6+2[3+5\{2812\times ~2\}\left] =6+2 \right[3+5\left\{ 2824 \right\}\left] =6+2 \right[3+5~\times 4]$

$=6+2\left[ 3+20 \right]=6+2\times ~23=6+46=52$.

1. What mixed fraction does represents the sum of fractions represented by given shaded parts?

(a) $2\frac{1}{4}$         (b) $1\frac{1}{8}$

(c) $2\frac{3}{4}$         (d) $1-\frac{3}{8}$

(e) None of these

Explanation: Here, fraction represented by shaded parts is as follow:

Hence, the required mixed fraction = $\frac{3}{4}+\frac{1}{2}+1$

= $\frac{3\times 1+1\times 2+1\times 4}{4}=\frac{3+2+4}{4}=\frac{9}{4}=2\frac{1}{4}$

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