## Number Sense and Numeration

Category : 4th Class

Number Sense and Numeration

Numbers

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

Writing and Reading Numbers

Numbers are written using symbols or digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) called numerals.

For example, 3564 is a numeral in which four digits (3, 5, 6 and 4) are used. In this section, we will study two types of numeration.

(i)     Indian system of numeration.

(ii)    International system of numeration.

Indian System of Numeration

This method of numeration is based on the place value chart. This system is also known as Hindu - Arabic system.

Given below is the Indian place value chart

 Period Kharab Arab Crores Lakhs Thousands Ones Places ten Kharab (T-kh) 1000000000000 Kharab (kh) 00000000000 Ten Arab (T-A) 1000000000 Arab (A) 100000000 Ten Crores (T-C) 10000000 Crores (C) 1000000 Ten lakhs (T-L) 100000 Lakhs (L) 10000 Ten thousands (T-TH) 10000 Thousands (TH) 1000 Hundred (H) 100 Ones (0) 0
•           Example

Name the numeral given in the place value chart.

 Period Arab Crores Lakhs Thousands Ones Places Ten Arab (T-A) (10000000000) Arab (A) 100000000 Ten Crores (T-C) (10000000) Crores (C) (10000000) Ten lakhs (T-C) (1000000) Lakhs (L) (100000) Ten Thousands (TH) (10000) Thousands (TH) (1000) Hundred (H) (100) Ten (T) (10) Ones (O) (0) 3 5 6 4 8 1 7 0 2 9 6

Solution:

Thirty five arab sixty four crore eighty one lakh seventy thousand two hundred ninety six.

International System of Numeration

This system of numeration is widely used in the most part of the world.

Given below is the place value chart of international system

 Period Billions Millions Thousands Hundreds Places Hubdred 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)

In this system of numeration, as shown in the chart, every period has three groups.

The digits under each group are read together with the period.

•            Example

Name the numeral given in the place value chart.

 Period Billions Millions Thousands Ones Places Hundred billions Ten billions Billions Hundred millions Ten millions Millions Hundred thousands Ten thousands Thousands Hundred Tens Ones 2 7 3 0 9 1 7 8 4 5 3 7

Solution:

Two hundred seventy three billions ninety one million seven hundred eighty four thousand five hundred thirty seven.

Face Value of a Digit in Numerals

The face value of the digit in the numeral is the value of the digit itself.

For example, the face value of 5 in the numeral 5234698230 is 5 itself.

Place value

When we multiply the face value of the digit with the value of period, it gives place value.

For example, in the numeral 7854698230 the place value of 7 is$\left( 7\times 1000000000 \right)$, that is, 7000000000.

Expanded From

Expanded form means expansion of any number according to the place value of the digits.

For example,

$7894564122=7\times 1000000000+8\times 100000000+9\times 10000000+4\times 1000000+5\times 100000$

$+6\times 10000+4\times 1000+1\times 100+2\times 10+2\times 1.$

Successor

It is defined as a number which is one more than the given number.

For example, the successor of $54987852456856\underline{23}$ is $54987852456856\underline{24}$

Predecessor

It is defined as a number which is one less than the given number.

For example, the predecessor of $98914363578\underline{95}$ is $98914363578\underline{94}$

•           Example

Find the successor of 98775565886234.

(a) 98775565886233                                           (b) 98775565886236

(c) 98775565886235                                           (d) 98775565886237

(e) None of these

Answer (c)

Explanation: Successor of a number is 1 more than the given number.

•         Example

Find the predecessor of 8276426596265.

(a) 8276426596264                                             (b) 8276426596263

(c) 8276426596262                                             (d) 8276426596261

(e) None of these

Answer (a)

Explanation: Predecessor of a number is 1 less than the given number.

Note:

For finding successor add 1 to the given figure.

For finding predecessor subtract 1 from the given figure.

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