Place Value

View Notes

Number System:

A number system is a method of representing numbers. It is also known as the numeration scheme, which determines a set of values to describe a quantity. The position of a digit in a number determines the value of the digit in it. For instance, 5 in 350 represents 5 tens, or 50; but 5 in 5,006 represents 5,000. Kids need to know that while the same digit can be present in many numbers, its value depends on where it is in the number.

Place value is most often taught to children through a place value chart as given below.Â

 Ten Millions Millions HundredÂ Thousands Ten Thousands Thousands Hundreds Tens Ones Decimal Point Tenths Hundredths Thousandths 1 2 4 5 6 7 8 9 . 1 2 3

This will also only appear with letters on them to denote Millions, Hundreds of Thousands, Ten Thousand, Thousands, Hundreds, Tens, Ones, Tenths, Hundredths, and so on, per place.

Example

In the number 1329:

• 1 holds the thousands position.

• 3 holds the hundreds position.

• 2 holds the tens position.

• 9 holds the ones position.

More on Place Value

Whole numbers are arranged in groups of three, called periods. Each period features a hundred(s), ten(s) and one(s) position.

Number 123 456 789 below as an example. Here, 8 holds the tens position, 5 holds the ten-thousands position, and so on.

Decimal numbers are also organized in groups of threes called periods. Each period features a ten(th), hundred(th), and thousand(th) position as explained in the below example.

Place Value and the Face Value

The digit's place value is the product of the digit's face value and its place value, while a digit's face value is the digit itself.

In this example, we will calculate the face value and place a value of 6 in 6, 45,100.

The face value of 6 in 6, 45,100 is â€˜6â€™

The place value of the digit is obtained by multiplying the face value of the digit and the value of its place so, the place value of 6 in 6,45,100 is 6 x 1,00,000 = 6,00,000 (6 Lakh).

Â

Expanded Notation:

We express each digit of a number to its position value in an extended form. Let's see the extended 29,1233 number notation.

In three different ways, this can be expanded:

Â Â Â Â 1. Â  2 ten thousands + 9 thousands + 1 hundred + 2 tens + 3 ones

Â Â Â Â Â Â 2. Â  (2 x 10,000) + (9 x 1,000) + (1 x 100) + (2 x 10) + (3 x 1)

Â Â Â Â Â Â 3. Â  20000 + 9000Â  + 100 + 20 + 3

Standard form of 60000+4000+40+6 is 64,046

Â

The Indian System and the International System

Indian System:Â

The first period, consisting of three place values (ones, tens, and hundreds), is one in the Indian system of numeration, starting from the right. There are thousands in the next period, consisting of two-position values (thousands and ten thousand). Lakhs, consisting of two-position values (lakhs and ten lakhs), and then crores and so on is the third cycle from the right. This numeration scheme is often referred to as the Hindu-Arabic system of numeration. To divide the cycles, we use commas, which help us read and write large numbers. The first comma comes from the right after three digits (i.e., after one period) in the Indian scheme, and the next comma comes after the next two digits (i.e., after the thousand periods) and then after every two digits, and so on.

Indian Place Value Chart

 CroresÂ (C) CroresÂ (C) CroresÂ (C) LakhsÂ (L) Thousands(Th) Thousands(Th) Ones Ones Ones Ten crores(TC) CroresÂ (C) Ten Lakhs (TL) Lakhs(L) Ten Thousands (TTh) Thousands (Th) Hundreds(H) Tens(T) Ones(O) 10,00,00,000 1,00,00,000 10,00,000 1,00,000 10,000 1,000 100 10 1

Consider an example of the International Numeration System:

In the Indian numeration scheme,

92357385 = 9,23,57,3855

Likewise, 2930625 will be translated as 29,30,625 in the Indian method of numeration.

The first cycle, consisting of three place values (ones, tens, and hundreds), is one in the International Numeration Scheme, beginning from the right. Thousands belong to the next period, consisting of three place values (one thousand, ten thousand, and one hundred thousand) and then millions and then billions.

International Place Value Chart

 Billions (B) Billions (B) Billions (B) Millions (M) Millions (M) Millions (M) Thousands(Th) Thousands(Th) Thousands(Th) Ones Ones Ones Hundred Billions(HB) Ten Billions (TB) One Billion (B) Hundred Millions(HM) Ten Millions (TM) One Million (M) Hundred Thousands(HTH) Ten Thousand (TTh) Thousands(Th) Hundreds (H) Tens (T) Ones(0) 100,000,000,000 10,000,000,000 1,000,000,000 100,000,000 10,000,000 1,000,000 100,000 10,000 1,000 100 10 1

Comparison of Two Number Systems:

 Crores (C) Crores (C) Crores (C) Lakhs (L) Thousands(Th) Thousands(Th) Ones Ones Ones Ten crores(TC) Crores (C) Ten Lakhs (TL) Lakhs(L) Ten Thousands (TTh) Thousands(Th) Hundreds(H) Tens(T) Ones(O) 10,00,00,000 1,00,00,000 10,00,000 1,00,000 10,000 1,000 100 10 1

 Billions (B) Billions (B) Billions (B) Millions (M) Millions (M) Millions (M) Thousands(Th) Thousands(Th) Thousands(Th) Ones Ones Ones Hundred Billions(HB) Ten Billions (TB) One Billion (B) Hundred Millions(HM) Ten Millions (TM) One Million (M) Hundred Thousands(HTH) Ten Thousands(TTh) Thousands(Th) Hundreds (H) Tens (T) Ones(0) 100,000,000,000 10,000,000,000 1,000,000,000 100,000,000 10,000,000 1,000,000 100,000 10,000 1,000 100 10 1

From above we can conclude that:

100 thousands = 1 lakh

1 million = 10 lakhs

10 millions = 1 crore

100 millions= 10 crores

Place Value for Decimals

Place value of chart looks like a figure below:

Below are some of the mentioned points which need to be captured while reading the writing of any number system.

• Separate the period by using commas when writing a number in the Indian numeral system or the international numeral system.

• In each period, read the number and say the name of the period after each number in the period.

• Skip the time containing zeros at all the locations when reading a number.

1.How to Make a Place Value Chart?

Answer: To form an Indian place value chart, draw 4 columns showing the 4 periods: ones, thousands, lakhs, and crores. Draw sub-columns for each time to display various position values: ones, tens, hundreds, thousands, ten thousand, lakhs, ten lakhs, crores, and ten crores.Â

Â

Similarly, draw 3 columns representing the 3 periods: ones, thousands, and millions, to create an International Place Value Map. Draw sub-columns for each time to display the different values of the place: ones, tens, hundreds, thousands, ten thousand, hundreds of thousands, millions, ten million, hundreds of millions.

Â

For example, the number 26984 is regarded in the Indian place value chart as follows.

Â