People use place value every single day, both consciously and subconsciously. Whether you’re counting money, measuring the weight of something, or just adding two numbers together, you’re using place value to do so.
It is one of the most fundamental principles in mathematics, which is why it is one of the first things children are taught at school.
It is incredibly important to understand since it forms the knowledge through which we interact with numbers in our day-to-day lives. But what is it?
That’s what we’ll explore in this article. We’ll explain what place value is, why it is so important, and how to use it.
Place value can be defined as the value a digit has depending on its position in the number. Every digit in a number has a place value, but it will be relative to its position for that number. To explain this using an example, let’s take a look at the numbers 375 and 1,238. The number 3 is present in both numbers but has a different place value since the location of the digit in the number has changed.
For 375, the 3 represents 300, and its place value is in the hundreds place. On the other hand, for 1,238, the 3 represents 30, and its place value is in the tens place. As you may have noticed, the place value system moves in base-10s, meaning if a digit’s value goes beyond 9, it then moves to the next place value. One of the best ways place values can be visualized is through a place value chart.
What is a place value chart?
Place value charts are a great tool for understanding how to find the place value of each digit in a given number. You start the column from the right, and the place value increases by 10 the further left you move. Conversely, the place values decrease by 10 as you move to the right.
Typically, a place value chart will go from the ones column, then to the tens column, all the way up to the hundred millions column since this will cover the majority of numbers you will encounter in your calculations. Below is an example of what a place value chart looks like
| Hundred Millions | Ten Millions | Millions | Hundred Thouands | Ten Thouands | Hundreds | Tens | Ones |
How is a place value chart used?
To use a place value chart, simply input your number into the columns starting from right to left. This will allow you to see the correct place value of a digit of any given number. Let’s use the three-digit number 375 again.
| Hundred Millions | Ten Millions | Millions | Hundred Thousands | Ten Thousands | Thousands | Hundreds | Tens | Ones |
| 3 | 7 | 5 |
The 3 digit is in the hundreds place and therefore has a place value of 300. The 7 digit is in the tens place, which means it has a place value of 70. Finally, the 5 digit is in the ones place, which results in a place value of 5.
If we used the same digits but created a new number, the digit’s place value would also change. Suppose we have the number 753. By inputting the new number into the place value chart, we can see their new place values.
| Hundred Millions | Ten Millions | Millions | Hundred Thousands | Ten Thousands | Thousands | Hundreds | Tens | Ones |
| 7 | 5 | 3 |
The 7 digit is now in the hundreds place, which means that it has a place value of 700. The 5 is now a tens digit, making it have a place value of 50. Lastly, the digit 3 is now in the ones place and therefore has a place value of 3.
To see how this looks for a bigger number, let’s use the example of 62,981. We can follow the same steps as we did for the previous two examples and input the number into the place value chart from right to left.
| Hundred Millions | Ten Millions | Millions | Hundred Thousands | Ten Thousands | Thousands | Hundreds | Tens | Ones |
| 6 | 2 | 9 | 8 | 1 |
The 6 digit is in the then thousands place, giving it a place value of 60,000. Next, the digit 2 is in the thousands place, which means it has a place value of 2,000. The 9 digit is in the hundreds place, resulting in a place value of 900. The 8 digit is in the tens column, meaning it has a place value of 80. And lastly, the 1 digit is in the ones column and therefore has a place value of 1.
To ensure you’ve understood place values correctly, we have two practice questions for you to answer.
- In which number does the digit 2 represent a place value of 200?
- 8,932
- 420
- 25,361
- 3,241
- In which number does the digit 8 represent a place value of 80?
- 38
- 851
- 83
- 728,609
The correct answer to Question 1 is 3,241. This is because the digit 2 is placed in the hundreds place, giving it a place value of 200.
The correct answer to Question 2 is 83. This is because the digit 8 is placed in the tens place, which means it has a place value of 80.
Now that we understand what the place value is and how to use the place value chart, we can use it to find the place value of decimal numbers. As a place value chart increases from ones to millions, the inverse happens after the decimal point. The place value goes from tenths all the way down to millionths, becoming 10 times smaller at each place value. The place value chart would look as follows:
| Ones | Decimal Point | Tenths | Hundredths | Thousandth | Ten Thousandth | Hundred Thousandth | Millionths | Ten Millionths |
Suppose we have the number 0.51893. We can input the numbers into the chart to determine what their place value is, but instead of moving from right to left as we have done previously, with decimal numbers you move from left to right. Let’s see this in practice.
| Ones | Decimal Point | Tenths | Hundredths | Thousandth | Ten Thousandth | Hundred Thousandth | Millionths | Ten Millionths |
| 0 | . | 5 | 1 | 8 | 9 | 3 |
The whole number 0 is before the decimal point. Therefore it is in the ones place and has a place value of 0. The digit 5 comes after the decimal point, positioning it in the tenths place, which means it has a place value of 0.5. The digit 1 is positioned in the hundredths place, giving it a place value of 0.01. Next, is the digit 8 which is in the thousandth place, therefore having a place value of 0.008. Then we have the digit 9 in the ten thousandths place, resulting in a place value of 0.0009. Finally, we have the digit 3, which is in the hundred thousandth place. This digit has a place value of 0.00003.
Understanding the place value of a number is beneficial for various reasons. It can help us understand the value of each digit in a number and thus the value of the entire number. This is known as number sense and forms the foundation upon which we develop all our math skills. We may instinctively know that 65 is greater than 35, but understanding place values teach us why this is the case.
This knowledge is crucial when it comes to completing all types of mathematical calculations and is a requirement for simple things such as adding and subtraction, as well as just knowing how to write numbers.
Place values also help us when rounding up and down as they will identify which digit we need to look at when rounding to the nearest ten, hundred, thousand, etc. This is also relevant for decimal point numbers since rounding decimal numbers is a large part of calculations, such as when dealing with fractions.
Another added benefit of knowing place values is the ability to work with digits in the tens of millions. It may be straightforward to deal with two-digit numbers or a number with three digits. However, when you’re dealing with seven or eight-digit numbers, it can be tricky to dissect and break it down. Place value principles make this easier as you know the value of each digit in the number and can add, subtract, multiply, or divide accordingly.
- What is the place value of 6 in the number 63
The correct answer to this question is 60 since the digit 6 is in the tens place.
- What is the place value of 1 in the number 4,159
The correct answer to this question is 100 since the digit 1 is in the hundreds place
- What is the place value of 9 in the number 719,255
The correct answer to this question is 9000 since the digit 9 is in the thousands place.
- What is the place value of 8 in the number 6.983?
The correct answer to this question is 0.08 since 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 since the digit 2 is in the tenths place.
Many people often get confused with place value and face value as they assume the two to be the same, but they’re not. As we’ve explained in this article, the 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 digit never changes. To explain this using an example, suppose we have two numbers, 517 and 59, and we are looking at the place value and face value of the digit 5.
The place value of 5 is 500 in 517 and 50 in 59. This is because it is located 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, irrespective of its position.
