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Comparing two-digit numbers Knowledge-Based Study

Math · Number Sense & Operations · Math · Counting & Place Value

Math topic explanations on Comparing two-digit numbers.

Study notes

  1. What Is a Two-Digit Number?

    A two-digit number is formed by two digits: the tens digit on the left and the ones digit on the right.

    For example, in the number 47:

    • The digit 4 is in the tens place and represents 4 tens, which equals 40.
    • The digit 7 is in the ones place and represents 7 ones, which equals 7.

    Understanding the value of each digit is the foundation for comparing two-digit numbers accurately.

    The Language of Comparison

    When comparing two numbers, we use mathematical symbols to describe their relationship:

    • > (greater than): The value on the left is larger than the value on the right (for example, 65 > 32).
    • < (less than): The value on the left is smaller than the value on the right (for example, 28 < 51).
    • = (equal to): Both values are exactly the same (for example, 44 = 44).

    A helpful tip is to remember that the open mouth of the symbol always points toward the larger number.

    Starting with the Greatest Place Value

    Always compare the digits with the greatest place value first. In two-digit numbers, this means looking at the tens place.

    Consider comparing 72 and 58:

    1. Identify the tens digits: In 72, the tens digit is 7. In 58, the tens digit is 5.
    2. Compare the tens digits: Since 7 tens are greater than 5 tens (7 > 5), the number with more tens is greater.
    3. Write the comparison: 72 > 58.

    Important Note: If the tens digits are different, you do not need to look at the ones digits at all.

    When the Tens Are the Same

    If two numbers have the exact same tens digit, the decision moves to the ones place.

    Consider comparing 63 and 68:

    1. Look at the tens digits: Both numbers have 6 in the tens place (60 = 60).
    2. Because the tens digits are equal, compare the ones digits: 63 has 3 ones, while 68 has 8 ones.
    3. Compare the ones digits: Since 3 is less than 8 (3 < 8), 63 is less than 68.
    4. Write the comparison: 63 < 68.

    Worked Examples

    Let us practice with two common scenarios:

    Example 1: Comparing 39 and 81

    • Tens digits: 3 and 8.
    • Since 3 < 8, we conclude immediately: 39 < 81.

    Example 2: Comparing 95 and 91

    • Tens digits: Both are 9.
    • Ones digits: 5 and 1.
    • Since 5 > 1, we conclude: 95 > 91.

    Summary Checklist

    1. Check the tens digits first.
    2. If one is larger, that number is greater.
    3. If they are identical, compare the ones digits.
    4. If both the tens and ones digits match, the numbers are equal (=).