# 5th Class Mathematics Numbers Number Sense and Numerations

Number Sense and Numerations

Category : 5th Class

Number Sense and Numerations

Numbers

Numbers are mathematical symbol 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 62232, 52155, 40034 etc.

Number 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.

Natural Numbers

Counting starts with 1 and continue till infinite. Counting numbers are called natural numbers.

For example, 1, 2, 3, 4, 5, 6, 7 ................ etc.

Whole Numbers

When 0 is included with natural numbers, they are called whole number. In other words "Natural numbers together with zero are called whole numbers."

For example, 0, 1, 2, 3, 4, 5, 6, 7 ................ etc.

Integers

Integers are the collection of whole numbers and negative of natural numbers.

For example,

$-5,\text{ }-4,\text{ }-3,\text{ }-2,\text{ }-1,\text{ }0,\text{ }+\text{ }1,\text{ }+\text{ }2,\text{ }+\text{ }3$, $~+\text{ }4,\text{ }+\text{ }5,\text{ }+\text{ }6,\text{ }+\text{ }7\text{ }...........$ etc.

System of Numeration

Mathematical notation of numbers is called numeration. Let us know about two types of numeration.

(A) Indian system of numeration

(B) International system of numeration

Indian System of Numeration

It is a positional decimal number system. Look at the following place value chart

International System of Numeration This system is applied in whole world. The following place value chart shows the international system of numeration.

Place are value of a digit in a number is the position it occupies according to the place value chart.

• Example:

Find the place value of 5 in the number 568232.

Solution: 500000

Face value

Face value of a number is the number itself.

• Example:

Find the face value of 3 in the number 453282.

Solution: 3

Successor

The number which comes just after a number is called successor of that number.

• Example:

Find the successor of 4444.

Solution: $4444+1=4447$

Predecessor

Predecessor of a number just comes before the number.

• Example:

Find the predecessor of 4444.

Solution: $44441=4443$

Roman Numeral

Roman numerals represent the numbers using alphabetical symbols.

The seven alphabetical symbol, 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 for Using Symbols

Rule1: When a symbol is repeated, its value is multiplied as many times as the symbol is repeated.

• Example:

$II=2\times 1=2$

$XXX=3\times 10=30$

Rule 2: The symbols I, X, C, M can be repeated in a roman numeral.

• Example:

$CCC=3\times 100=300$

$MM=2\times 1000=2000$

Rule 3: The symbols V, L, and D can not be repeated.

• Example:

$DD=2\times 500=1000$

But 1000 is represented by symbol M.

Therefore, the above expression is not correct.

Rule 4: If a symb01 of smaller value is right to the symbol of greater values are added.

• Example:

$LV=50+5=55$

$DC=500+100=600$

Rule 5: If a symbol of smaller value is left to the symbol of greater value, their difference is the resulting value.

• Example:

$VL=50-5=45$

$CD=500-100=400$

Rule 6: If a symbol of smaller value comes between two symbols of larger value, its value is subtracted from the value of the symbol, which is right to it.

• Example:

$XIV=10+5-1=14$

$DXC=500+10010=590$

Look at the following table:

 I 1 XXI 21 XLI 41 LXI 61 LXXXI 81 II 2 XXII 22 XLII 42 LXII 62 LXXXII 82 III 3 XXIII 23 XLIII 43 LXIII 63 LXXXIII 83 IV 4 XXIV 24 XLIV 44 LXIV 64 LXXXIV 84 V 5 XXV 25 XLV 45 LXV 65 LXXXV 85 VI 6 XXVI 26 XLVI 46 LXVI 66 LXXXVI 86 VII 7 XXVII 27 XLVII 47 LXVII 67 LXXXVII 87 VIII 8 XXVIII 28 XLVIII 48 LXVIII 68 LXXXVIII 88 IX 9 XXIX 29 XLIX 49 LXIX 69 LXXXIX 89 X 10 XXX 30 L 50 LXX 70 XC 90 XI 11 XXXI 31 LI 51 LXXI 71 XCI 91 XII 12 XXXII 32 LII 52 LXXII 72 XCII 92 XIII 13 XXXIII 33 LIII 53 LXXIII 73 XCIII 93 XIV 14 XXXIV 34 LIV 54 LXXIV 74 XCIV 94 XV 15 XXXV 35 LV 55 LXXV 75 XCV 95 XVI 16 XXXVI 36 LVI 56 LXXVI 76 XCVI 96 XVII 17 XXXVII 37 LVII 57 LXXVII 77 XCVII 97 XVIII 18 XXXVIII 38 LVIII 58 LXXVIII 78 XCVIII 98 XIX 19 XXXIX 39 LIX 59 LXXIX 79 XCIX 99 XX 20 XL 40 LX 60 LXXX 80 C 100 D 500 M 1000

Note: A symbol can not be repeated more than 3 times.

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