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B.1 Compare numbers - up to ten thousands

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What does it mean to compare numbers?

Comparing numbers means looking at two numbers to decide which is greater, which is smaller, or if they are equal.

Examples:
  • 7,532 is greater than 6,849
  • 4,210 is less than 4,905
  • 8,340 is equal to 8,340
Note

We use symbols to compare: > means greater than, < means less than, and = means equal to.

How do we compare numbers?

When comparing numbers, always start with the leftmost digit (the largest place value). Move to the right until you find a difference.

Steps:
  • Look at the digits in the ten-thousands place first.
  • If they are the same, compare the thousands place.
  • If they are still the same, compare the hundreds, tens, and ones.
  • Stop when you find a difference.
Note

The first place value with different digits tells you which number is greater.

Examples of comparing numbers

Let’s look at how to compare numbers up to the ten-thousands place value.

Examples:
  • 12,450 < 13,025 (compare the ten-thousands digit: 1 and 1 are equal, compare thousands: 2 and 3 β†’ 2 is less)
  • 9,876 > 9,769 (compare thousands: 9 and 9 are equal, hundreds: 8 and 7 β†’ 8 is greater)
  • 7,004 = 7,004 (all digits match)
Note

Always write the comparison symbol pointing toward the smaller number, like an arrow that points to the least value.

Using place value charts

A place value chart helps line up numbers by place so you can compare them more easily.

Example:
  • Number 1: 14,352 β†’ Ten-thousands: 1 | Thousands: 4 | Hundreds: 3 | Tens: 5 | Ones: 2
  • Number 2: 13,947 β†’ Ten-thousands: 1 | Thousands: 3 | Hundreds: 9 | Tens: 4 | Ones: 7
  • Compare: Ten-thousands are equal (1 and 1). Thousands: 4 is greater than 3, so 14,352 > 13,947.
Note

Place value charts prevent mistakes when comparing larger numbers with many digits.