# 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 346562232, 34654521155, 4003444656 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, -4, -3, -2, -1, 0, +1, +2, +3, +4, +5, +6, +7 ........... 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

 Period Kharab Arab Crores Lakhs Thousands Ones Places Ten Kharab (T-kh) 1000000000000 Kharab (kh) 100000000000 Ten Arab (T-A) 10000000000 Arab (A) 10000000000 Ten Crores (T-C) 100000000 Crores (C) 10000000 Ten Lakhs (T-L) 1000000 Lakhs (L) 100000 Ten thousands (T-TH) 10000 Thousands (TH) 1000 Hundred (H) 100 Tens (T) 10 Ones (0) 0
•                Example

Name the number, indicated in the place value chart:

 Period Kharab Arab Crores Lakhs Thousands Ones Places Ten Kharab (T-kh) 1000000000000 Kharab (kh) 100000000000 Ten Arab (T-A) 10000000000 Arab (A) 1000000000 Ten Crores (T-C) 100000000 Crores (C) 10000000 Ten Lakhs (T-L) 1000000 Lakhs (L) 100000 Ten thousands (T-TH) 10000 Thousands (TH) 1000 Hundred (H) 100 Tens (T) 10 Ones (0) 0 1 4 0 2 6 5 2 1 0 3 2 5 3

Solution:

Fourteen kharab two arab sixty five crore twenty one lakh three thousand two hundred fifty three.

International System of Numeration

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

 Period Trillions Billion Million Thousands Ones Places Hundred Trillion (100000000000000) Ten Trillions (10000000000000) Trillions (1000000000000) Hundred billions (100000000000) Ten billions (10000000000) Billions (1000000000) Hundred millions (100000000) Ten millions (10000000) Millions (1000000) Hundred thousands (100000) Ten thousands (10000) Thousands (1000) Hundred (100) Tens (10) Ones (0)
•           Example:

Name the number indicated in the place value chart.

 Period Trillion Billions Million Thousands Ones Places Hundred Trillions (100000000000000) Ten Trillions (10000000000000) Trillions (1000000000000) Hundred billions (100000000000) Ten billions (10000000000) Billions (1000000000) Hundred millions (100000000) Ten million (10000000) Millions (10000000) Hundred thousands (100000) Ten thousands (10000) Thousands (1000) Hundred (100) Tens (10) Ones (0) 5 4 6 5 6 8 0 2 2 0 6 5 2 1 5

Solution:

Five hundred forty six trillion five hundred sixty eight billion twenty two million sixty five thousands two hundred fifteen.

Place Value

Place 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 646568232.

Solution: 500000

Face Value

Face value of a number is the number itself.

•           Example:

Find the face value of 3 in the number 451453282.

Solution: 3

Successor

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

•             Example:

Find the successor of 5456446.

Solution: 54564446 + 1 = 54564447

Predecessor

Predecessor of a number just comes before the number.

•           Example:

Find the predecessor of 4665655416.

Solution: 4665655416 ? 1 = 4665655415

Roman Numeral

Roman numerals the number using alphabetical symbols.

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

 Symbols Value I 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 symbol of smaller value is right to the symbol to greater value, their values are added.

•            Example:

$LV=50\times 5=55$

$DC=500\times 100=600$

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

$XIV=10+5-1=14$

$DXC=500+100-10=590$

Look at the following table:

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

Note: A symbol cannot be repeated more than 3 times.

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