In mathematics, place value explains the worth of each digit in a number based on its position. These locations begin at the location of the unit. Ones/units, tens, hundreds, thousands, ten-thousands place, and so on are the order of place value of digits in a multi-digit number from right to left. Keep reading to learn what place value is as well as effective place-value model methods to get top grades!
What is place value?
The value of each digit in a number is called place value. A number may have two digits that are similar yet have distinct values, which is determined by the digit’s position in the number.
The value of a digit is determined by its location in a number, such as ones, tens, hundreds… all the way to infinity! The place value of 5 in 3,458, for example, is 5 tens, or 50. The place value of 5 in 5,781, on the other hand, is given as 5 thousand or 5,000.
The following is a place value number line that will help you for future calculations:
Thousands – Hundreds – Tens – Units – POINT –– Tenths – Hundredths – Thousandths
Everything left to the POINT is a whole number, and everything right to the POINT is a decimal.
For example: What are the place values of 2,471?
- 2,473
- 2 x 1000 = 2000 or, 2 thousands
- 4 x 100 = 400 or, 4 hundreds
- 7 x 10 = 70 or, 7 tens
- 3 x 1 = 3 or, 3 units
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What is the difference between value and place value?
The major difference between value and place value is that place value assigns a digit’s value based on its position in a number, whereas value assigns a digit’s real value. A number’s value is fixed and cannot be modified. However, its place value varies depending on the digit’s location.
Here are key differences between value and place value:
- The value of a digit in a number based on its position in the number is known as place value. The true value of a digit in a number is called face value.
- To find a number’s place value, multiply the digit value by its numerical value. Because 5 is in the tens place, the place value of 5 in the number 452 is 50. A digit’s value (or face value) is the number itself. The face value of 4 in the number 452, for example, is 4.
- The place value of a number is determined by the digit’s position in the number. The face value is unaffected by the digit’s position in the number.
- A digit’s place value is always a single digit and the place value of each subsequent digit to the left increases by one digit. A number’s face value is always a single digit.
Why is place value important?
Place value, despite its basic definition, can be a difficult concept to grasp for young students. It’s important because it is one of the first abstract mathematical concepts children learn. It serves as a basis for regrouping, multiple-digit multiplication, and other operations in the decimal system, as well as a springboard for learning about other base systems. In real life, money and finance are extremely dependent on place value.
If you receive $50 but a toy costs $500, according to face value, both have a value of 5, but place value tells you that one is hundreds whilst the other is tens. Here is an example, if someone was to ask, “How big is the Milky Way Galaxy?” you could write “1,000,000,000,000,000,000,000 meters” which is incredibly difficult to understand, or you could write the scientific notation: 1 x 1021 meters which translates to the face value 1 multiplied by the place value of 21 zeros which is a sextillion!
This notation, which harnesses place values, allows scientists to work with incredibly big or immeasurably small numbers with ease. The idea of place value is likely the most fundamental in elementary and middle-grade school mathematics. Almost all mathematical concepts are built on a foundation of place value knowledge!
How do you write place value?
- The number 2,965 contains the digit 2. This 2 is the first number on the sequence and the fourth digit from the right. It is located in the thousands spot. As a result, it has a place value of 2,000. This is how you write place value. We write 2 as 2,000 by adding three zeros to its right. The number after 2 has three digits to the right of the thousand-place.
- The number 2,965 contains the digit 9. This 9 is in the hundreds position. The number 9 is the third position from the right in the sequence. The number has two digits on the right side. We write the number 9 and add two zeros to the right. As a result, the number’s place value for 9 is 900.
- At the tenth position, the number 2,965 contains the digit 6. The number 6 is the second from the right in the sequence. The number has one extra digit to its right. We write 6 and add a zero to the right of it. As a result, the number’s place value for 6 is 60.
- In the number 2,965, there is a 5 at one’s spot in the extreme right. As a result, it has a place value of 5. As such, 2965 can be expressed as 2 thousand, 9 hundred, 6 tens, and 5 units. You could also express it as 2000 + 900 + 60 + 5 in an expanded form.
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How to find the place value in decimal numbers
Using a decimal point, a decimal number system is utilized to express whole numbers and fractions simultaneously. Between the total number and the fractional part is the decimal point. The first digit after the decimal point represents the tenth place which can be expressed as 1/10. Therefore, in 125.7 the place value of .7 is 7/10.
While the whole number system follows the typical place value chart of ones, tens, hundreds, and so on, the numbers to the right of the decimal point have a tiny variance in place value. Place values begin with tenths and progress through hundredths, thousandths, and so on as we move to the right after the decimal.
The one-tenth (1/10th) position is the first to the right of the decimal, followed by 1/100, and so on. For decimal numbers, look at the place value number line below.
Thousands – Hundreds – Tens – Units – POINT – Tenths – Hundredths – Thousandths
1000 – 100 – 10 – 1 – . – 1/10 – 1/100 – 1/1000
Place Value Practice Questions
What are the place values of 9,721?
- The number 9,721 contains the digit 9. This 9 is the number’s fourth digit from the right. It is located in the thousandth spot. As a result, it has a place value of 9,000. We write 9,000 by adding three zeros to the right of it.
- The digit 7 is present in the 9,721. This 7 is in the hundredth position. The number 7 is the third number from the right in the sequence. The number has two digits on the right side. We write the number 7 and add two zeros to the right. As a result, the number’s place value for 7 is 700.
- At the tens position, the number 9,721 contains the digit 2. The number 2 is the second from the right in the sequence. On the number, there is one additional digit to the right. We write 2 and add a zero to the right of it. As a result, the number’s place value for 2 is 20.
- The digit 1 is at the one’s place in the number 9,721 on the far right. As a result, it has a place value of 1. As such, 9,721 can be expressed as 9 thousand, 7 hundred, 2 tens, and 1 unit.
What are the place values of 2,940?
- The first number 2,940 contains the digit 2. This 2 is the number’s fourth digit on the left. It is located in the thousands spot. As a result, it has a place value of 2,000. We write 2,000 by adding three zeros to the right of it.
- The second digit 9 is present in the 2,940. This 9 is in the hundreds column. The number 9 is the third from the right in the sequence. The number has two digits on the right side. We write the number 9 and add two zeros to the right. As a result, the number’s place value for 9 is 900.
- At the tens position, the number 2940 contains the digit 4. The number 4 is the second from the right in the sequence. On the number, there is one additional digit to the right. We write 4 and add a zero to the right of it. As a result, the number’s place value for 4 is 40.
- The digit 0 is at one’s place in the number 2940 on the far right. As a result, it has a place value of 0. As such, 2940 can be expressed as 2 thousand, 9 hundred, 4 tens, and 0 units.
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