Definition:

Comparing numbers means determining which of two numbers is larger or smaller. To compare numbers up to one million, we look at the value of each digit starting from the highest place (hundred thousand, ten thousand, thousands, hundreds, tens, and ones). We compare digits place-by-place, starting with the largest place value.

Example 1:

Compare 452,783 and 478,921.

Solution:

• Start by looking at the hundred thousand places:
  • The first number has 4 in the hundred-thousandth place.
  • The second number also has 4 in the hundred-thousandth place.
  • Since they are the same, move to the next place (ten thousand).
• Look at the ten thousand places:
  • The first number has 5 in the ten thousand places.
  • The second number has 7 in the ten thousand places.
  • Since 7 is greater than 5, 478,921 is greater than 452,783.

Solution: 452,783 < 478,921.

Example 2:

Compare 872,530 and 872,305.

Solution:

• Start with the hundred thousand places:
  • Both numbers have 8 in the hundred thousandth place, so move to the next place.
• Look at the ten thousand places:
  • Both numbers have 7 in the ten thousand places, so move to the next place.
• Look at the thousands of places:
  • Both numbers have 2 in the thousands place, so move to the next place.
• Look at the hundreds of places:
  • The first number has 5 in the hundreds place.
  • The second number has 3 in the hundreds place.
  • Since 5 is greater than 3, 872,530 is greater than 872,305.

Solution: 872,530 > 872,305.

Example 3:

Compare 600,456 and 605,123.

Solution:

• Start with the hundred thousand places:
  • Both numbers have 6 in the hundred-thousandth place, so move to the next place.
• Look at the ten thousand places:
  • The first number has 0 in the ten thousand places.
  • The second number has 0 in the ten thousand places as well, so move to the next place.
• Look at the thousands of places:
  • The first number has 0 in the thousands place.
  • The second number has 5 in the thousands place.
  • Since 5 is greater than 0, 605,123 is greater than 600,456.

Solution: 600,456 < 605,123.

Example 4:

Compare 950,000 and 945,678.

Solution:

• Start with the hundred thousand places:
  • Both numbers have 9 in the hundred-thousandth place, so move to the next place.
• Look at the ten thousand places:
  • The first number has 5 in the ten thousand places.
  • The second number has 4 in the ten thousand places.
  • Since 5 is greater than 4, 950,000 is greater than 945,678.

Solution: 950,000 > 945,678.

Example 5:

Compare 234,567 and 234,569.

Solution:

• Compare each place value from left to right.
• All digits are the same until the one's place:
  • The first number has 7 in one place.
  • The second number has 9 in the ones place.
  • Since 9 is greater than 7, 234,569 is greater than 234,567.

Solution: 234,567 < 234,569.

Why it matters:

Comparing numbers up to one million helps students develop number sense and understand the value of large numbers. It is essential for solving real-life problems, like analyzing data or managing budgets. This skill strengthens critical thinking and decision-making abilities.

By practicing comparing numbers up to one million, you can solve real-world problems quickly!

Let’s practice and evaluate your work together by comparing numbers.