Numeral Expanding Up to 99

Every two-digit number is really made of two smaller pieces: a group of tens and a group of ones. Expanding a numeral means splitting it apart to show exactly what those pieces are worth. For example, the number \(47\) is not just "47", it is really \(40 + 7\). Writing it this way is called expanded form, because it "expands" the number into the values that each digit represents.

This idea builds directly on identifying tens and ones in a two-digit number. Once you can tell which digit is in the tens place and which digit is in the ones place, expanding the number is just one more step.

In any two-digit number, the digit on the left tells you how many groups of ten you have, and the digit on the right tells you how many single units, or ones, you have. Take the number \(83\):

• The digit \(8\) is in the tens place, so it stands for \(8\) tens, which is \(80\).
• The digit \(3\) is in the ones place, so it stands for \(3\) ones, which is \(3\).

Putting those two values back together with a plus sign gives the expanded form: \(83 = 80 + 3\).

Follow these steps for any number from \(10\) up to \(99\):

1. Look at the number and find the tens digit (the left digit) and the ones digit (the right digit).
2. Multiply the tens digit by ten to find its true value.
3. Keep the ones digit exactly as it is.
4. Write the two values with a plus sign between them.

For a deeper look at why the tens digit is worth ten times more than it looks, see place values of digits up to 99.

Let's expand \(47\) using the steps above.

• The tens digit is \(4\), so its value is \(4 \times 10 = 40\).
• The ones digit is \(7\), so its value stays \(7\).
• Written in expanded form: \(47 = 40 + 7\).

Expanding also works in reverse. If you are given \(60 + 5\), you can rebuild the standard number by adding the two parts together: \(60 + 5 = 65\). This skill checks that you understand what each digit is worth, not just how to write it, which connects closely to counting the value of a digit up to 99.

Expanded form is more than a way to rewrite a number. It shows exactly how much each digit contributes to the total value, which makes it easier to add, subtract, and compare numbers later on. A number like \(58\) is easy to compare with \(83\) once you can see \(50 + 8\) next to \(80 + 3\), because the tens values make the bigger number obvious right away.

Try expanding these numbers on your own before checking the answers below.

• \(29\)
• \(74\)
• \(91\)

Answers: \(29 = 20 + 9\), \(74 = 70 + 4\), \(91 = 90 + 1\).

Related lessons

• Math 1