Place Value Worksheets

Introduction

Place value is the foundation for understanding number systems in mathematics. Place value helps in understanding the base 10 number system. Place value worksheet is an important tool to understand the concept, and helps students develop logical, problem-solving and reasoning skills.

Place Value

Each digit in a multi-digit number has a specific position in that number, which is defined by the base 10 number system. When a multi-digit number is written in numerical form, the position of a number can vary from unit to infinity.

Place Value Chart

For a 10-digit number, the following table represents the placement of digits. Place value, in mathematics, describes the value of every digit in a number depending on its position. The positions begin from unit place (ones place). The placement of digits in a number such as units/ones, tens, hundreds, thousands etc. It is done through place value chart.

109

108

107

106

105

104

1000

100

10

1

Most widely used place value charts follow two systems, namely,

• Indian System of Counting

• International System of Counting

Indian System of Counting

The Indian system of number representation is different from the international system. It uses units, tens, hundreds, thousands, lakh, crore, and so on as a place value for digits in a number. The Indian System of place value chart is given below. The first comma is placed after 3 digits starting from the right-hand side, then all the following commas are placed after two digits.

For example, consider a number 534526370, which can be written as 53,45,26,370. Following table helps us better understand the Indian system of counting.

Indian System of Counting
PERIODS	FIGURES	DIGITS
Crores	Ten Crores (TC) 10,00,00,000	9
	Crores (C) 1,00,00,000	8
Lakhs	Ten Lakhs (TL) 10,00,000	7
	Lakhs (L) 1,00,000	6
Thousands	Ten Thousands (TTh) 10,000	5
	Thousands (Th) 1,000	4
Units/Ones	Hundreds (H) 100	3
	Tens (T) 10	2
	Ones (0) 1	1

International System of Counting

In the International numeral system, the order of placement of digits in a number is done in units, tens, hundreds, thousand, ten thousand, hundred thousand, million, ten million, etc. In the International numeral system, the commas are separated after every three digits starting from the right of the number. In this place value chart, the numbers are grouped into periods of ones, thousands, millions, and so on and they are separated by a comma after every 3 digits, starting from the right.

For example, consider a number 534526370, which can be written as 534,526,370. Following table helps us better understand the international system of counting.

International System of Counting
Period	Figures	Digits
Millions	Hundred Million (HM) 100,000,000	9
	Ten Million (TM) 10,000,000	8
	Million (M) 1,000,000	7
Thousands	Hundred Thousand(HT) 100,000	6
	Ten Thousands (TTh) 10,000	5
	Thousands (Th) 1000	4
Units/Ones	Hundreds (H) 100	3
	Tens (T) 10	2
	Ones (0) 1	1

Solved Examples

1.What numbers complete the following: ___ tens + ___ ones = 96.

Solution:

Placing the given number 96 according to place value chart

9	6
tens	ones

From the above chart, 9 tens+6 ones=96.

2. What place does 5 represent in the number 5787?

Solution:

Placing the given number 5787 according to place value chart

5	7	8	7
Thousands	Hundreds	tens	ones

From the chart, we can say that 5 holds the “Thousands” position in place value chart.

3.Draw place-value model for 586.

Solution:

Placing the given number 586 according to place value chart

5	8	6
Hundreds	tens	ones

4.In the number 7963, which digit is in the hundreds place?

Solution:

Placing the given number 7963 according to place value chart

7	9	6	3
Thousands	Hundreds	tens	ones

From the chart we can see that 9 is in the hundreds place.

5.Find the smaller number in the following.

• 9176---- 9716

• 3189----- 3819

Solution:

• Placing the given number 9176 and 9716 according to place value chart

9	1	7	6
Thousands	Hundreds	tens	ones

9	7	1	6
Thousands	Hundreds	tens	ones

As we know that the digit in the thousands is the same, but in the hundreds place 9716 is greater. Therefore, the greater digit is 9716.

• Placing the given number 3189 and 3819 according to place value chart

3	1	8	9
Thousands	Hundreds	tens	ones

3	8	1	9
Thousands	Hundreds	tens	ones

As we know that the digit in the thousands is the same, but in the hundreds place 3819 is greater. Therefore, the greater digit is 3819.

6. Answer the following 3 thousands, 7 hundreds, 2 tens = -------

Solution:

3 thousands = 3000

7 hundreds=700

2 tens= 20

Therefore, 3000+700+20=3720

7. Consider the following numbers 145, 664, 587, 327, 820, and answer the following.

a) A multiple of 5 but not divisible by 10.

Solution:

145 is the number which is multiple of 5 but not divisible by 10.

b) An odd number, whose ones digit is two more than its hundreds digit.

Solution:

The number whose unit digit is two more than the hundreds digit is 587.

c) A number whose hundreds digit is the same as the tens digit.

Solution:

664 is the number whose hundreds digit is the same as the tens digit.

Conclusion

Place value worksheets help to understand the number system and significance of placement of numbers. Place value is the foundation for understanding number systems in mathematics. Place value helps in understanding the base 10 number system. Each digit in a multi-digit number has a specific position in that number, which is defined by the base 10 number system. The placement of digits in a number such as units/ones, tens, hundreds, thousands etc. is done through place value chart. There are two types of systems: Indian System of Counting and International System of Counting.

FAQs

1.Define the place value of zero?

Assuming a number 2046, we can see that at the hundreds place there is 0. So, the place value of zero can be calculated by 0 × 100 = 0. Therefore, the place value of zero is always zero.

2.Why is Place Value in Numbers Important?

Place value of a digit in a number gives the magnitude of that digit.

3.How are place values defined in the Indian system of counting?

The Indian system of counting uses units, tens, hundreds, thousands, lakh, crore, and so on as a place value for digits in a number.

4.How are place values defined in the international system of counting?

Placement of digits in the international system of counting is done in units, tens, hundreds, thousand, ten thousand, hundred thousand, million, ten million, etc.

5.Write any use of place value in defining a number.

Place value can help in determining whether a number is even or odd.