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A.3 Understand and convert place values

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What is place value?

Place value tells the value of a digit based on its position in a number. Each place is ten times greater than the place to its right.

Example:
  • In the number 3.482:
  • 3 is in the thousands place → value: 3,000
  • 4 is in the hundreds place → value: 400
  • 8 is in the tens place → value: 80
  • 2 is in the ones place → value: 2
Note

A digit’s value changes when it moves to a different place in the number.

Understanding place value relationships

Each place is related to the next by a factor of ten. A digit in one place is ten times the value of the same digit in the place to its right, and one-tenth the value of the same digit in the place to its left.

Example:
  • In the number 560:
  • The 5 in the hundreds place (500) is ten times the value of a 5 in the tens place (50).
  • The 6 in the tens place (60) is ten times the value of 6 in the ones place (6).
Note

Thinking in groups of ten makes it easier to understand how numbers grow or shrink when digits shift places.

How to convert between place values

To convert between place values, you multiply or divide by ten. Moving a digit to the left makes it ten times greater. Moving a digit to the right makes it one-tenth as great.

Examples:
  • 40 tens = 4 hundreds (because 40 × 10 = 400)
  • 3 hundreds = 30 tens (because 300 ÷ 10 = 30)
  • 70 ones = 7 tens (because 70 ÷ 10 = 7)
Note

A quick check: if the number gets bigger, you multiplied by ten; if the number gets smaller, you divided by ten.

Reading and writing numbers using place value

Breaking a number into thousands, hundreds, tens, and ones helps you understand and explain its value. This is called writing a number in expanded form.

Example:
  • 3,742 in expanded form:
  • 3,000 + 700 + 40 + 2
  • This shows the value of each digit clearly.
Note

Expanded form helps you see how each place contributes to the total number.

Using place value to compare numbers

You can compare numbers by looking at the highest place value first. The number with the greater digit in the largest place is the greater number.

Example:
  • Compare 4,256 and 4,196:
  • Thousands place: both have 4
  • Hundreds place: 2 hundreds vs. 1 hundred → 4,256 is greater
Note

Always compare digits from left to right, starting with the greatest place value.