Place Value

โฑ 8 minโœ๏ธ Quiz at the end

What is Place Value?

Place value is the value of a digit based on its position in a number. The same digit means different things in different positions.

The number 333 has three 3s โ€” but each one has a different value: 300, 30, and 3. This is the power of our place value system.

Key Terms

  • Digit: one of the symbols 0โ€“9 used to write numbers
  • Place value: the value a digit has because of where it sits in a number
  • Expanded form: writing a number as a sum of each digit times its place value
  • Standard form: the normal way of writing a number (e.g. 43,265)

The Place Value Chart

MillionsHundred-thousandsTen-thousandsThousandsHundredsTensOnes
1,000,000100,00010,0001,000100101

Each column is 10 times the value of the column to its right.

In the number 3,742:

  • 3 is in the thousands place โ†’ value = 3,000
  • 7 is in the hundreds place โ†’ value = 700
  • 4 is in the tens place โ†’ value = 40
  • 2 is in the ones place โ†’ value = 2

Decimal Place Values

Place value extends to the right of the decimal point too:

Ones.TenthsHundredthsThousandths
1.0.10.010.001

In 2.049:

  • 2 is in the ones place
  • 0 is in the tenths place
  • 4 is in the hundredths place
  • 9 is in the thousandths place

Expanded Form

Writing a number in expanded form shows each digit's value separately:

  • 43,265 = 40,000 + 3,000 + 200 + 60 + 5
  • 3,506 = 3,000 + 500 + 0 + 6 = 3,000 + 500 + 6
  • 2.049 = 2 + 0.04 + 0.009

Notice that zero-value digits can be skipped in expanded form but must be included as placeholders in the standard number.

Worked Example

Write 70,000 + 400 + 8 as a standard number.

  • Seventy-thousands column: 7
  • Ten-thousands: 0 (placeholder needed)
  • Thousands: 0 (placeholder needed)
  • Hundreds: 4
  • Tens: 0 (placeholder needed)
  • Ones: 8

Answer: 70,408

Comparing Numbers

To compare two numbers, line up the digits by place value and look at the highest place first:

47,821 vs 47,912:

  • Both have 4 ten-thousands and 7 thousands โ€” equal so far
  • Hundreds: 8 vs 9 โ†’ 9 is greater
  • So 47,912 > 47,821

Ordering and the Role of Zero

Zero acts as a placeholder โ€” without it, 3,042 would look like 342, completely changing its value. Never drop a zero from the middle of a number.

When ordering numbers:

  1. Count the digits โ€” more digits means a larger number (in whole numbers)
  2. If the digit count matches, compare from the leftmost digit

Why Place Value Matters

Place value is the foundation for:

  • Reading and writing large numbers accurately
  • Comparing and ordering numbers
  • Performing addition, subtraction, multiplication, and division correctly
  • Understanding decimals and their sizes
  • Rounding to various degrees of accuracy

Common Mistakes to Avoid

  • Dropping placeholder zeros: 3,042 is NOT the same as 342
  • Confusing the digit with its value: In 4,700, the digit 7 has a value of 700, not 7
  • Misreading decimal places: 0.3 is three tenths, NOT three hundredths
  • Forgetting commas group in threes: 1,000,000 (one million) not 10,00,00

Tips and Tricks

  • Use a place value chart when you are unsure โ€” write each digit in its column
  • To multiply by 10, shift every digit one place to the left (do not just "add a zero")
  • To divide by 10, shift every digit one place to the right
  • When reading large numbers, group digits in threes from the right: 4,327,891
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