- What Is Place Value?
- What Are The Two Types Of Place Value?
- What Is The Importance Of Place Value?
- When Will Your Child Learn About Place Value?
- Chart Of Place Value
- Difference Between Indian and International Place Value Chart
- What Are The Four Operations Of Place Value?
- Place Value With Decimals
- Place Value Vs Face Value
- Activities That Will Help Your Child To Learn About Place Values
- Solved Examples Of Place Value
When you look at a number, you will notice that the entire number, whether big or small, is made up of numeric digits. Each digit, depending on the position it holds in the number, has a value. This value is called ‘place value’ in mathematical terms.
What Is Place Value?
Place value is defined as the value of a digit in a number on the basis of its position (or place) in the number. Place value’s meaning is how much each digit in a number is worth. For example, the number 895 is made up 3 digits, 8, 9 and 5. But considering the place values of these three numbers, it can be said that the number 895 is composed of 800, 90 and 5. This is because the number 8 holds the hundreds place, the number 9 holds the tens place and the number 5 holds the units or ones place.
What Are The Two Types Of Place Value?
You will come across two types of place value systems followed in the world:
1. Indian Place Value
The Indian place value chart is used to find the value of each digit as per the Indian numeral system. In this place value system, a 10-digit number is divided into periods of ones, thousands, lakhs, crores, and so on. These numbers are separated by commas following the rule of 3:2:2. This means starting from the right, the first comma is placed after 3 digits, then the subsequent commas are placed after every 2 digits.
2. International Place Value
The International numeral system is used worldwide in which the digits are counted in this order: ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions, and further. In this place value chart, the numbers are divided into periods of ones, thousands, millions, and so forth. The comma here, comes after every 3 digits, starting from the right.
What Is The Importance Of Place Value?
Imagine that someone is supposed to give you Rs 215. What if they hand you one coin of Rs 2, one coin of Re 1 and one coin worth Rs 5; will that cover the debt? Not really. Because, the digits 2, 1 and 5 in the whole number hold a much larger place value. It is important to learn the concept of place value in math to understand this value.
Knowing the correct value of this number, you would break down this amount as one note worth Rs 200, one note or coin worth Rs. 10 and one coin of Rs. 5.
Place value is important to learn about such calculations. It also helps simplify basic math operations like addition, subtraction, multiplication and division. Thus, children should be taught about numbers and place values at an early stage.
Knowing the digit’s place value also helps children in number recognition, and understanding number names.
When Will Your Child Learn About Place Value?
To start with, pre-schoolers are taught single digit numbers. As they progress to learning two-digit numbers like 10 and above, they need to start understanding the place value of all the digits.
You can teach place value shortly after your child has learnt to count by ones and perform simple addition and subtraction operations, generally around class 1 & 2. A good understanding of place value will be a foundation for your kids to learn more complex mathematical concepts.
Chart Of Place Value
Here is a chart that you can refer to understand the place value system.
1. Indian System Place Value Chart
If you are dealing with Indian data, then the Indian place value chart will be useful for you, especially when dealing with large numbers:
|Thirty Four Lakh
|Fifty Two Thousand
|One Hundred and Nine
2. International System Place Value Chart
When handling international data, you may come across millions and billions. You will need to understand the international place chart for it:
|Three Hundred and Fourty One Million
|Five Hundred And Twenty Eight Thousand
|One Hundred And Seventy Nine
Difference Between Indian and International Place Value Chart
Let’s understand how the numbers are written in numeric as well as words in the Indian vs International place value system.
Eighty three lakh, sixty five thousand, seven hundred and eighty three
Eight million, three hundred and sixty five thousand, seven hundred and eighty three
Three crore, fifty four lakh, seventy two thousand, eight hundred and ninety two
Thirty five million, four hundred and seventy two thousand, eight hundred and ninety two
Forty five thousand, six hundred and thirty nine.
Forty five thousand, six hundred and thirty nine.
Sixty crore, fourteen lakh, thirty two thousand, eight hundred and ten.
Six hundred and one million, four hundred and thirty two thousand, eight hundred and ten.
Five hundred and eighty nine crores, seventy two lakhs, seventeen thousand and forty three.
Five billion, eight hundred and ninety seven million, two hundred and seventeen thousand and forty three.
What Are The Four Operations Of Place Value?
Mathematical calculations with big numbers can prove difficult, but knowledge of the place value system makes it possible to do these easily. Let us understand how to perform the four mathematical operations using the place value system.
A sum like 842 + 531 would be tricky to do straight away; we certainly can’t start taking 531 leaps on a number line. That’s where partitioning and place value come in to make things easier. We can split complicated questions into simpler calculations by breaking up the numbers and taking each place value in turn.
For example, we can work out this addition problem by adding the ones, the tens and the hundreds, then putting it all together. 2 + 1 = 3, 40 + 30 = 70 and 800 + 500 = 1300, making the total 1373. Place value makes multi-digit calculations easier with manageable chunks.
Subtraction works in a very similar way, for 842 – 531 we can take away the numbers by their place value. So, 2 – 1 = 1, 40 – 30 = 10 and 800 – 500 = 300. Then, we have our answer, 311.
Multiplication and division have a few more steps for numbers this large, as we need to times or divide the whole number by the entirety of the other number, not just the ones by the ones or the tens by the tens. But, let’s look at an example with a 3-digit number and a 1-digit number to see how the same idea applies.
We can break down 972 × 3 into 900 × 3 = 2700, 70 × 3 = 210 and 2 × 3 = 6. Adding these together gives us 2916.
972 ÷ 3 works the same way. 900 ÷ 3 = 300, and 70 ÷ 3 = 20, with ten left over to add to the final sum. 10 + 2 = 12, and 12 ÷ 3 = 4. When we add those up, we get 324.
Place value is vital for children to use the four operations with large numbers. It lets them follow easier steps to reach their answer. There are useful ways to make this even easier, including the column method for addition, subtraction and multiplication, and the bus stop method for division. All of them rely on looking at the different digits in turn, and understanding how their place value affects the overall result.
Place Value With Decimals
Decimal numbers can also be called fractions or mixed numbers where the denominators have the powers of ten. In a number with a decimal point, all the digits to the left of the decimal point represent a whole number. Conversely, all digits to the right of the decimal represent the parts. As we go towards the right after the decimal point, the place value of the digits becomes 10 times less than it’s face value.
The very first digit on the right of the decimal point denotes tenths i.e. 1/10. The next place to its right becomes ten times smaller, called the hunderdths i.e. 1/100 and so on.
Place Value Vs Face Value
While place value is the value of a digit assigned due to its position, face value is a concept that much simpler to understand.The face value of a digit is simply the value of the digit itself. In other words, the face value tells us the actual value of the independent digit.
Hence, the face value of a digit never changes irrespective of it’s position in the number. Whereas, the place value of the digit changes with the change in the position.
For instance, the face value of 2 in both the numbers 273 and 723 is 2. Whereas, the place value of 2 is 200 in 273 and 20 in 723.
Activities That Will Help Your Child To Learn About Place Values
Here are some ways to teach your child about place value with games and activities that you can do at home:
1. Making Bundles of Tens Activity
Making Bundles of Tens Activity is excellent for helping students conceptualize the change in place value as a number becomes a 10 for students from Kindergarten to second grade.
Children will be presented with 8 problems where they will be required to find the number of bundles of 10s and the leftover ones of a specific number. Learning to bundle numbers helps students become more familiar with the property of numbers, and learn how larger numbers can break down into smaller numbers.
2. Medicine Box and Dice Game
Take a medicine box which has individual compartments for every day of the week. Put small dice in it. Close the lids and shake the box to reveal the numbers on the dice. Now, imagine the compartments of the box to hold place values. Read the number on the dice accordingly. This fun game will be a good practice for learning the place value system. You can choose to use as many dice as you want, depending on whether your child is well-versed with two, three, or more digits, up to seven. You can make this a competitive game where children shake the dice in turns to see who rolls the highest number.
3. Spaghetti and Fruit Loops Game
A fun game to play while your meal is being prepared. Get three long pieces of uncooked spaghetti and lots of fruit loops. Ask someone to name a random three digit number in words, eg. “three hundred and forty two”. Now, you need to identify the digits in the hundreds, tens and units place and string your spaghetti accordingly. Add two fruit loops to the units, four to the tens, and three to the hundreds.
4. Number Hunt
Take a walk with your child around the neighbourhood. Look for one-, two-, three-digit numbers and have your child read them out loud. You may want your child to record the numbers that he or she sees. Discuss each number and ask how many ones, tens, or hundreds are in the number. What is the largest number you can find? What is the smallest number?
5. Playing Cards
Here is a game that children can play with number cards. Keep a pile of cards in the centre, and let each child pull up 7 cards. Now, the child must create the highest 3-digit number possible using the deck at hand by showing the three cards. The child with the highest value cards wins the round. The next round starts by drawing three more cards to complete the deck of 7.
Solved Examples Of Place Value
Here are some questions and examples of place value system with their solutions.
1. What is the place value of 6 in the number 86,527?
Solution: The place value of 4 in 86,527 is 6000 (six thousand).
2. Write 412,394 in words using the place value system.
Solution: Four hundred twelve thousand three hundred and ninety-three.
3. Write the following numbers in figures and in expanded form:
- Ten thousand two hundred and thirty-three
Solution: 10,233 = 10,000 + 200 + 30 + 3
- Nine thousand four hundred and eighty-five
Solution: 9,485 = 9,000 + 400 + 80 + 5