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Understanding Place Value (With Examples)

Key Concepts

  • Introduction to place value understanding
  • Numbers through one million
  • Place value relationships

Generalize Place Value Understanding 

Numbers through one million 

A place value chart can help us find and compare the place value of the digits in numbers through millions. The place value of a digit increase by ten times as we move left on the place value chart and decreases by ten times as we move right.  

Numbers through one million place value

Example 1: 

An example of drawing the place value chart can help find the place value of a number in millions. 

Example 1: 

In 3287263, 3 is in the millions place,  and its place value is 3000000,  

2 is in hundred thousand’s place, and its place value is 200000, 

8 is in ten thousand’s place, and its place value is 80000, 

7 is in thousand’s place, and its place value is 7000, 

2 is in the hundred’s place, and its place value is 200, 

6 is in the ten’s place, and its place value is 60, 

3 is in one’s place, and its place value is 3. 

Example 2: 

The place value of digits in numbers can also be represented using base-ten blocks and can help us write numbers in their expanded form.  

Here is how the number 13548 can be represented using base-ten blocks.  

Example 2: 

Place Value Relationships 

Relationship Between the Places: Moving to The Left  

Place Value Relationships 

Notice the value of the base 10  blocks on the far right have a value of 3. Observe what happens each time we move to the left. 

The value of the blocks is 10  times greater than the previous set of blocks. Thus, the value of 3 is 10   times greater as well. 

  • When we move one place to the left from the ones place (3), the tens place (30) is 10  times greater than the ones place. 
  • Moving one place to the left from the tens place (30), the hundreds place (300) is 10  times greater than the tens place. 
  • When we move one place to the left from the hundreds place (300), the thousands place (3,000) is 10  times greater than the hundreds place. 

Relationship Between The Places: Moving To The Right  

Place Value Relationships 

Now, notice the value of the base is10 blocks on the far left have a value of 3,000. 

Each time we move to the right, the value of the blocks is one tenth of the previous set of blocks. Thus, the value of the 3 is one-tenth of the previous value. 

  • When we move one place to the right from the thousands place (3,000), the hundreds place (300) is one-tenth of the thousands place. Think: 3,000/10 = 300. 
  • Moving one place to the right from the hundreds place (300), the tens place (30) is one-tenth of the hundreds place. Think: 300 /10 = 30. 
  • When we move one place to the right from the tens place (30), the ones place (3) is one-tenth of the tens place. Think: 30 /10 = 3. 

Exercise:

  1. Write the number 27349811 in the place value system. Also, write it with commas and in
    words.
  2. In the number 783425, write the digit that is in
    (a) Hundreds place (b) Hundred thousand place
    (c) Ten thousands place (d) Ones place
  3. Expand the numbers representing the place value of each digit.
    • 799
    • 56788
    • 101000
    • 1119
  4. Place value of 2 in 123456? Also, expand the number.
  5. Place value of the digit 6 in the number 496524.
  6. Difference between the place value of 5 and 3 in the number 80523?
  7. Sum of place values of the digits 7 and 9 in the number 694725?
  8. Write the place values of all the digits of the number 254103.
  9. Identify the digit in the thousands place of 254813.
  10. Write the number 21399 in expanded form.
  11. Write an example of a number that would include 2 commas.
  12. Write 25,482 using number names.
  13. Write a number in which the value of the 3 is ten times greater than the value of the 3
    in 135,864.
  14. Place elementary school in raising money. They raise $90 a week. How long will it take them to raise $900?
  15. Mia says 5,555, all the digits have the same value. Is Mia correct? Explain.
  16. In 2016, the world’s oldest tree was 5,066 years old. Write the number that is one hundred
    more using number names.
  17. Write the number 294,160 in expanded form.
  18. Write the number names of 331,872.
  19. Write the number for the expanded form: 900000 + 50000 + 1000 + 500 + 20 + 2.
  20. Identify the digit in the thousands place of 254813.

What we have learnt:

  • Understand how to represent million’s place value in place value chart.
  • Learned how to read and recognize numbers according to number position.
  • Read and write numbers through one million in expanded form with numerals and using number names.
  • Recognize that a digit in one place has ten times the value of the same digit in the place to its right.

Concept Map:

Concept Map: 

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