Number Sense and Numerations

**Category : **4th Class

** Number Sense and Numerations**

**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

**Example**

Name the numeral given in the place value chart.

**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

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.

**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 \[(7\times 1000000000),\]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__23__ is 54987852456856__24__

** **

**Predecessor**

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

**For example**, the predecessor of 98914363578__95__ is 98914363578__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 or 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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