People use place value every day, consciously and unconsciously. Whether you're counting money, measuring the weight of something, or just adding two numbers, you use place value to do it.
It's one of the most fundamental principles of mathematics, which is why it's one of the first things children learn in school.
It is incredibly important to understand as it forms the knowledge through which we interact with numbers in our daily lives. But what is that?
That's what we're going to explore in this article. We explain what a place value is, why it's important, and how to use it.
What is a place value?
Place value can be defined as the value that a digit has depending on its position in the number. Each digit in a number has a place value, but is relative to its position for that number. To explain this with an example, let's look at the numbers 375 and 1238. The number 3 is present in both numbers, but has a different meaning because the placement of the digit in the number has changed.
At 375, the 3 stands for 300 and its place is in the hundreds place. On the other hand, for 1238 the 3 represents 30 and its place value is in the tens place. As you may have noticed, the place value system moves to base 10, which means that when a digit's value goes beyond 9, it shifts to the next place value. One of the best ways to visualize position values is with a place value chart.
What is a place value chart?
Place value tables are a great tool for understanding how to find the place value of each digit in a given number. You start with the right column and the place value increases by 10 as you move to the left. On the other hand, position values decrease by 10 as you move to the right.
Typically, a place value chart will go from the ones column, then the tens column, to the hundred millions column, as this will cover most of the numbers you will encounter in your calculations. Below is an example of what a place value chart looks like
| a hundred million | ten million | millions | hundred thousand | ten thousand | hundreds | dozens | Some |
How do you use a place value chart?
To use a place value chart, simply enter your number in the columns from right to left. This allows you to see the correct place value of a digit of any number. Let's take the three-digit number 375 again.
| a hundred million | ten million | millions | hundred thousand | ten thousand | miles | hundreds | dozens | Some |
| 3 | 7 | 5 |
The digit 3 is in the hundreds place, so it has a place value of 300. The digit 7 is in the tens place, which means it has a place value of 70. Finally, the number 5 is in the tens place. units, resulting in a place value of 5.
If we use the same digits but create a new number, the position value of the digit would also change. Suppose we have the number 753. By inserting the new number into the place value chart, we can see its new place value.
| a hundred million | ten million | millions | hundred thousand | ten thousand | miles | hundreds | dozens | Some |
| 7 | 5 | 3 |
The number 7 is now in the hundreds place, so it has a place value of 700. The 5 is now in a tens place, so it has a place value of 50. Finally, the number 3 is now in the ones place and therefore , it has a place value of 3.
To see how it looks for a larger number, let's use the example of 62,981. We can follow the same steps as in the previous two examples and insert the number from right to left in the position value chart.
| a hundred million | ten million | millions | hundred thousand | ten thousand | miles | hundreds | dozens | Some |
| 6 | 2 | 9 | 8 | 1 |
The number 6 is in the thousands place, giving it a value of 60,000. Then the digit 2 is in the thousands place, which means it has a place value of 2000. The number 9 is in the hundreds place, giving a place value of 900. The digit 8 is in the tens column, meaning it has a place value of 80. And finally, the digit 1 is in the units column, so it has a place value of 1.
To make sure you have a good understanding of place values, we have two practical questions that you need to answer.
- In which number does the digit 2 represent the place value 200?
- 8.932
- 420
- 25.361
- 3.241
- In which number does the digit 8 represent 80?
- 38
- 851
- 83
- 728.609
The correct answer to question 1 is 3241. This is because the digit 2 is put in the hundreds place, giving it a place value of 200.
The correct answer to question 2 is 83. This is because the number 8 is in the tens place, i.e. it has a place value of 80.
What is a decimal value?
Now that we understand what a place value is and how to use the place value chart, we can use it to find the place value of decimals. When a place value chart increases from one to a million, the reverse occurs after the decimal point. The place value ranges from tenths to millionths and gets 10 times smaller with each place value. The place value chart would look like this:
| Some | Come | tenth | hundredths | thousandth | ten thousandth | hundred thousandth | Millionstel | ten millionths |
Suppose we have the number 0.51893. We can enter numbers in the table to determine their place value, but instead of going right-to-left as before, decimals go left-to-right. Let's see this in practice.
| Some | Come | tenth | hundredths | thousandth | ten thousandth | hundred thousandth | Millionstel | ten millionths |
| 0 | . | 5 | 1 | 8 | 9 | 3 |
The integer 0 comes before the decimal point. It is therefore in the ones place and has a place value of 0. The digit 5 comes after the decimal point and is therefore in the tenths place, which means that it has a place value of 0.5. The digit 1 is placed in the hundredths place, giving it a place value of 0.01. Next comes the digit 8, which is in the thousandths place, so it has a place value of 0.008. So we have the digit 9 in the ten thousandths place, giving a place value of 0.0009. Finally, we have the number 3, which is in hundred-thousandths. This digit has a place value of 0.00003.
Why is place value important?
Understanding the place value of a number is beneficial for several reasons. This can help us understand the value of each digit in a number and therefore the value of the whole number. This is known as number sense and forms the foundation upon which we develop all of our math skills. We may instinctively know that 65 is greater than 35, but understanding place values teaches us why.
This knowledge is essential for all kinds of mathematical calculations and a prerequisite for simple things like addition and subtraction and knowing how to write numbers.
Position values also help us round up and down, as they identify which digit to consider when rounding to the nearest tens, hundreds, thousands, etc. Calculations, such as handling fractions.
Another added benefit of knowing place values is the ability to work with digits in the tens of millions. It can be easy to deal with two digit numbers or a three digit number. However, when it comes to seven or eight digit numbers, it can be difficult to parse and break them down. The place value principle makes this easier because you know the value of each digit in the number and can add, subtract, multiply, or divide accordingly.
Worked examples of place value
- What is the significance of the 6 in the number 63?
The correct answer to this question is 60 because the number 6 is in the tens place.
- What is the significance of 1 in number 4159?
The correct answer to this question is 100 because the number 1 is in the hundreds place.
- What is the place value of 9 in number 719255?
The correct answer to this question is 9000 because the number 9 is in the thousands place.
- What is the place value of 8 in the number 6983?
The correct answer to this question is 0.08 because the digit 8 is in the hundredths place.
- What is the place value of 2 in the number 515,276?
The correct answer to this question is 0.2 because the digit 2 is in the tenths place.
Are face value and face value the same?
Many people are often confused about position value and face value, assuming the two are the same but they are not. As we explained in this article, place value is the value of a digit depending on its position in the number.
On the other hand, the face value of a digit is the value of the digit itself, regardless of its position in a number. Therefore, the face value of a single digit never changes. To explain this with an example, let's say we have two numbers, 517 and 59, and we look at the place value and face value of the digit 5.
The place value of 5 is 500 in 517 and 50 in 59. That's because it's in a different place in each number.
The face value of 5 in the numbers 517 and 59 is 5. This is because the face value simply describes the value of the digit, regardless of its position.
FAQs
What are place value and examples? ›
Place value can be defined as the value represented by a digit in a number on the basis of its position in the number. For example, the place value of 7 in 3,743 is 7 hundred or 700. However, the place value of 7 in 7,432 is 7 thousand or 7,000.
What is place value short answer? ›What Is Place Value in Math? Place value is the basis of our entire number system. This is the system in which the position of a digit in a number determines its value. The number 42,316 is different from 61,432 because the digits are in different positions.
What is place value explanation for kids? ›Place value is the value of each digit in a number. For example, the 5 in 350 represents 5 tens, or 50; however, the 5 in 5,006 represents 5 thousands, or 5,000. It is important that children understand that while a digit can be the same, its value depends on where it is in the number.
What is place value for Grade 2? ›During second grade, your child is introduced to the concept of using “place value” (the value of where the digit is in the number, based on the location of the digit) in order to add and subtract numbers. At this age, she will likely become stronger at taking numbers apart and putting them back together.
How do you find the place value? ›We can find the place value of a digit by finding how many places the digit is to the right or left of the decimal point in a number. If it is n places to the left of the decimal point, we multiply the digit by 10^(n - 1) to get the digit's place value.
How do you teach place value to Grade 2? ›- Use Base Ten Blocks. Base ten blocks offer a visual and manipulative mechanism to help second grade students understand the concept of place value. ...
- Expanded Form Fun Facts. ...
- Dicey Place Value. ...
- Place Value Clothesline Race.
- writing the number in word form.
- writing the number in digit form.
- recording the place value of each digit.
- writing the number in expanded form.
- creating a number pattern starting with the given number.
- representing the number with beads on an abacus.
- writing a number greater than the given number.
A place value chart is a table that is used to find the value of each digit in a number based on its position, as per the numeral system. In order to identify the worth of different digits in a number accurately, we place the given number in the place value chart so that the place value of each digit is seen.
What is the place value of 6 in 64? ›Let us look at the digit 6 in the number 64. It is in the tens place of the number. So, the place value of 6 is 60.
What is the place value of 12? ›For two-digit numbers, there is the TENS place and the ONES place. Let's take a closer look at the place value for the number 12. The 1 is in the TENS place, and the 2 is in the ONES place. That's because the number 12 is made up of 1 ten and 2 ones.
What is the difference of place value and value? ›
The major difference between place value and face value is that the place value deals with the position of the digit, and the face value represents the actual value of a digit. The number system is available and is essential for characterising the digits into groups of tens, hundreds and even thousands.
How do you write a place value lesson plan? ›- Call students together as a group.
- Inform the students that they will be learning about place value, or a number's position.
- Inform students that each number represents a hundreds, tens, or ones place.
- To motivate and activate the students, play the Place Value Song.
Before digging into place value using two-digit numbers, your students should have a solid foundation of numeracy, addition, and subtraction skills up to ten.
What is value example in math? ›For instance: If we consider a number 45. Here the digit 4 is in the tens column. Hence, the face value of the digit 4 will be 4 or four. The value refers to the worth of each digit depending on where it lies in the number.
What is place value and face value for grade 4? ›Place value is the value represented by a digit in a number according to its position in the number. Face value is the actual value of a digit in a number. To get the place value of a number, we multiply the digit value with its numerical value.
How do you write place value for kids? ›The order of place value of digits of a number of right to left is units, tens, hundreds, thousands, ten thousand, a hundred thousand, and so on. Let us understand with the help of an example, say 7231468, and see the below figure for the place value of each digit.
What is the place value of point? ›The place value of a decimal number is recognised according to the position of the dot or decimal point. The first digit to the right of the decimal point indicates the number of tenths and the second digit to the right indicates the number of hundreths. For example, 0.7 can be written as 710 as a fraction.
What is the place value of 24? ›If I am reading your question correctly, you are asking what the place value for 24 is, right? Because there is 1 in the hundreds place, 3 in the tens place, and 4 in the ones place.
What is the place value of 14? ›So in the number 14, there is one ten and four ones—10 + 4 = 14. If we change that 1 to a 2, we get 24, or twenty-four. The number 2 in the tens place tells us there are two tens. Each place value is 10 times larger than the place value to the right of it.
What is the place value of 84? ›The first digit is the tens' place. It tells you that there are 8 tens in the number 84. The right digit is the ones' place which is 4 in this example. Therefore, there are 8 sets of 10, plus 4 ones in the number 84.
What is a starter activity for place value? ›
Place Value Starters:
Balloon Bursting Buttons: Use only the 1, 5 and 0 keys on a calculator to make given totals. Big Order: Estimate or calculate then put the large numbers in order of size. Figuratively Speaking: Write the numbers written as words using digits.
Place value helps us make decisions that are used in our daily lives ex) costs, weight, distances, time etc. Our number system is based on a Base Ten system. Base ten means our number system has a base of ten. We group our numbers by clusters of ten.
Why is it important to teach learners place value? ›Place value is one of the key concepts in mathematics. Understanding place value (or not understanding it) will follow students through their mathematics journey. Without this understanding, students often struggle with regrouping, adding and subtracting multi-digit numbers, and more difficult computations.
What is place value standard form? ›When a whole number is written using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9, it is said to be in standard form. The position of each digit determines the digit's place value . A place value chart names each place value.
What is the place value of 5 in 3,254,710? ›so location value of 5=5×10000=50000.
What is the place value of 8 in 48? ›Using the place value chart we identify the place for each digit in the given number and write the numbers in words. For 48 we see that the digits in units = 8, tens = 4.
What is the place value of 6 in 126? ›The next digit is six, which we write in the ones column. The question asks us to find the value of the six in 126. Six digit is worth six ones.
What is the place value of 2 in 1234? ›In the number 1234, 4 is in the units place, 3 is in the tens place, 2 is in the hundreds place and 1 is in the thousands place.
What is the place value of 6 and 9? ›We write 9 and put two zeroes to its right. So, the place value of 9 in the number is 900. We write 6 and put one zero to its right. So, the place value of 6 in the number is 60.
What is the place value of 100? ›The digit 1 is in the hundreds place. Its value is 100 . The digit 9 is in the tens place. Its value is 90 .
What are the different place value of the number? ›
The place value of every one-digit number is the same as and equal to its face value. (i) Place value and face value of 1, 2, 3, 4, 5, 6, 7, 8 and 9 are 1, 2, 3, 4, 5, 6, 7, 8 and 9 respectively. (ii) The place value of zero (0) is always 0.
What is the place value and value of 64? ›The number 64 has 4 in the ones place and 6 in the tens place.
What is value in math grade 1? ›Place values tell us how much each digit in a number is worth. Digits on the left (👈) have a bigger place value. Digits at the Ones place count as 1 each. Digits at the Tens place count as 10 each. For example, 24 has 2 Tens and 4 Ones.
What is the value of 4 in 45? ›For instance: If we consider the number 45. Here digit 4 is in the tens column. Hence, the value of the digit 4 will be i.e. 40 or forty.
What is place value example of 9? ›9 represents 9 ones. If you observe, the digit 6 is in the hundreds place, so it represents 6 hundreds or 600. 9 is at the tens place, which represents 9 tens or 90. So, the place value of 9 is 90.
What is the place value of 4 in 1234? ›In the number 1234, 4 is in the units place, 3 is in the tens place, 2 is in the hundreds place and 1 is in the thousands place.
What is the place value of 5 in 57? ›For a two-digit number, the place value tens digit is 10 times the digit, For example, the place value of 5 in number 57 is 5 x 10 = 50, and the place value of the one-digit is 7 x 1 =7.
What is the place value of 6 in 645? ›Since 6 is in the hundreds place, the place value of 6 in 645 is 6 hundreds. This means the place value of 6 is expressed as 6 × 100 = 600. Example 2: A number has 4 thousands, 7 hundreds, and 8 tens.
What is the place value of 9 in 579? ›| Places | Hundreds | Ones |
|---|---|---|
| Digits | 5 | 9 |
| Multipliers | 100 | 1 |
| Place Values | 500 | 9 |
Expert-Verified Answer
The place value of 4 in 42 is 40. Step-by-step explanation: The given number is 42. Here, 4 is in tens place and 2 is in once place.
What is the place value of 123? ›
We discussed the ones place and tens place. If we take a look at a three-digit number like 123, we would need to add another column called the hundreds column. The number 123 is made up of 1 Hundred, 2 Tens, and 3 Ones. You can also write this as 1 x 100 + 2 x 10 + 3 x 1 which equals 132.
What is the place value of 9 in 296? ›In English words, the number 296 is written as “Two hundred ninety-six”. Using the place values of the number 296, we can quickly convert the number into words. For example, the number 6 is in one's place, 9 is in ten's place, and 2 is in 100's place.
What is the place value of 9 in 79? ›| Places | Tens | Ones |
|---|---|---|
| Digits | 7 | 9 |
| Multipliers | 10 | 1 |
| Place Values | 70 | 9 |