Identifying Place Values Within Numbers Lesson

Place value is the value of a digit based on its position in a number. Each digit in a number has a specific place value, which is determined by its position from the right side of the number. Place values are determined by the position determined from right to left, and are in powers of 10.

Here’s a quick breakdown of place values:

Ones (1): The rightmost digit represents the ones place.

Tens (10): The digit to the left of the ones represents the tens place.

Hundreds (100): The digit to the left of the tens represents the hundreds place.

Thousands (1,000): The digit to the left of the hundreds represents the thousands place.

Ten Thousands (10,000): The digit to the left of the thousands represents the ten thousands place.

Hundred Thousands (100,000): The digit to the left of the ten thousands represents the hundred thousands place.

This pattern continues for larger numbers. Each place value is ten times the value of the place to its right.

For example, in the number 623,457:

Place Value Breakdown of 623,457
  • The digit 7 is in the ones place.
  • The digit 5 is in the tens place.
  • The digit 4 is in the hundreds place.
  • The digit 3 is in the thousands place.
  • The digit 2 is in the ten thousands place.
  • The digit 6 is in the hundred thousands place.

Understanding place value is crucial for performing operations like addition, subtraction, multiplication, and division, as it helps in correctly manipulating the digits within a number.

Place value is a concept in mathematics that assigns a value to each digit in a number based on its position or place in the numeral. The value of a digit is determined by its position from the right side of the number, and it is a crucial concept for understanding the numerical system.

In the decimal system, which is the most commonly used numeral system, each place value is a power of 10. For example in the number 3,267, the 6 is in the tens place, therefore it is 6 tens, or 60. Additionally, the 2 is in the hundreds place, therefore it is read as 2 hundreds, or 200.

Place values with decimals follow a similar concept to whole numbers, but they extend to include parts of a whole. In a decimal number, each digit has a specific place value based on its position to the right of the decimal point. The basic place values to the right of the decimal point are powers of 10, but they are fractions of 1.

Here are the key place values to the right of the decimal point:

Tenths (0.1): The first digit to the right of the decimal point represents tenths.

Hundredths (0.01): The second digit to the right represents hundredths.

Thousandths (0.001): The third digit to the right represents thousandths.

Ten Thousandths (0.0001): The fourth digit to the right represents ten-thousandths.

Hundred Thousandths (0.00001): The fifth digit to the right represents hundred-thousandths.

For example, in the number 2.45678:

Decimal Place Value Breakdown of 2.45678
  • The digit 2 is in the ones place.
  • The digit 4 is in the tenths place.
  • The digit 5 is in the hundredths place.
  • The digit 6 is in the thousandths place.
  • The digit 7 is in the ten thousandths place.
  • The digit 8 is in the hundred thousandths place

Bringing it all together to illustrate place values in whole numbers and decimals, let’s look at the chart below.

Complete Place Value Chart

Place values can be expressed in two different ways, for example in the number 352, the 5 could be expressed as 5 tens or 50. To get the 50, we simply multiply the 5 times the column it is in, which was the tens, therefore 5 times 10 is 50.

We can also use place values to write numbers, for example, if we were given the following information about a number, we could express that number with digits. A number has three hundreds, four tens, and two ones.

We would express that number with digits as 342.

Examples

Example 1: Write the place value of the underlined digit, 4,372.

Solution:

Since the 3 is in the hundreds place, the place value of 3 is 3 hundreds, which can equally be expressed as 300, by taking 3 and multiplying it by 100.

3 * 100 = 300, hence the place value of 3 is expressed as 300.

Example 2: Use the given information to express the number with digits. A number has 5 ten thousands, 3 thousands, 8 hundreds, and 6 tens.

Solution:

  • 5 ten thousands would equal 5 times 10,000, so 50,000.
  • 3 thousands equals 3 times 1,000 or 3,000.
  • 8 hundreds equals 8 times 100, or 800.
  • 6 tens equals 6 times 10, which is 60.

Therefore, 50,000 + 3,000 + 800 + 60 = 53,860

Example 3: What is the place value of the 4 in the number 3.2546?

Solution:

Since the digit 4 is in the third position to the right of the decimal, that is the thousandths place. Therefore, it would be 4 thousandths place, this can also be expressed as 4 times 0.001, which equals 0.004.

FAQs on Identifying Place Values Within Numbers

  1. What is a place value?
  • Place value is the value of a digit based on its position in a number. It helps in understanding the numerical system by assigning a specific value to each digit. It also helps in learning how to round numbers.

2. How are place values determined?

    • Place values are determined by the position of a digit from the right side of a number. In the decimal system, each place value is a power of 10.

    3. What are the basic place values in the decimal system?

      • To the left of the decimal point the basic place values are ones, tens, hundreds, thousands, etc. and to the right of the decimal point tenths, hundredths, thousandths, etc., to the right of the decimal point.

      4. How do you find the value of a digit in a specific place?

        • Multiply the digit by its corresponding place value. For example, in the number 326, the value of 3 in the hundreds place is 3 * 100 = 300.

        5. Can place values be applied to decimal numbers?

          • Yes, place values extend to decimal numbers. Each digit to the right of the decimal point has a specific place value based on powers of 10, but in fractional form. These places are the tenths, hundredths, thousandths, and so on.

          6. Why is understanding place value important?

            • Understanding place value is crucial for performing arithmetic operations, working with decimals, and comprehending the structure of numbers. It forms the foundation for various mathematical concepts, for example rounding numbers to certain place values.

            7. What is the place value of zero?

              • The place value of zero is always zero. For example, in the number 3,206, the zero is in the tens place, so we would express this as 0 tens, or 0 times 10, which equals 0. Since zero times any number is always zero, the place value of zero is always zero.