Place Value Word Problems of Multi-Digit Numbers

A place value word problem describes a multi-digit number using clues about its digits instead of showing the number itself. Each clue tells you something about a digit's place, such as "the digit in the hundreds place" or "the tens digit is twice the ones digit." Your job is to read the clues carefully, figure out what each digit is, and then put those digits together in the correct order to form the number.

These problems build directly on knowing what each position in a number is worth. If you need a refresher on how to name and find a digit's place, look back at identifying the place value of a digit before working through the examples below.

Every digit in a multi-digit number has both a place (its position) and a value (what that position is worth). In the number 4,709, the digit 4 sits in the thousands place and is worth 4,000, the digit 7 sits in the hundreds place and is worth 700, the digit 0 sits in the tens place and is worth 0, and the digit 9 sits in the ones place and is worth 9.

Organizing digits this way is exactly what a place value table does, and it is the easiest tool for keeping track of clues as you solve a word problem.

Use this approach for almost any place value word problem:

1. Draw a place value chart with one column for each place mentioned in the problem (ones, tens, hundreds, thousands, and beyond).
2. Read each clue and write the digit it describes into the matching column.
3. If a place is never mentioned, remember it still needs a digit, often a zero, so the number does not lose a place.
4. Read the completed chart from left to right to write the final number.
5. Check your answer using expanded form, adding the value of every digit to make sure it matches the clues.

A number has 4 thousands, 7 hundreds, 0 tens, and 9 ones. What is the number?

Place each digit in its column: 4 in thousands, 7 in hundreds, 0 in tens, 9 in ones. Reading across gives 4,709. Checking with expanded form confirms the answer: \( 4000 + 700 + 0 + 9 = 4709 \).

A four-digit number has a 6 in the thousands place. The digit in the hundreds place is 3 less than the thousands digit. The tens digit is double the hundreds digit. The ones digit is the same as the tens digit. What is the number?

Start with what is given directly: the thousands digit is 6. The hundreds digit is 3 less than 6, so it is \( 6 - 3 = 3 \). The tens digit is double the hundreds digit, so it is \( 3 \times 2 = 6 \). The ones digit matches the tens digit, so it is also 6. Placing these digits in order gives 6,366. Checking with expanded form: \( 6000 + 300 + 60 + 6 = 6366 \), which matches.

Some word problems describe two multi-digit numbers and ask which is greater. Build each number using the steps above, then compare them one place at a time starting with the highest place value. For example, if one number has 5 in the thousands place and another has 4 in the thousands place, the first number is greater no matter what the rest of the digits are, since \( 5000 > 4000 \).

• Confusing a digit's place with its value, such as writing 7 instead of 700 for a digit in the hundreds place.
• Skipping a place value that was not mentioned in the clues instead of filling it with a zero placeholder.
• Misreading similar-sounding words, such as hundreds versus hundredths, or tens versus tenths.
• Placing digits in the wrong order when writing the final number after filling in the chart.

Whenever a word problem feels confusing, redraw the place value chart from scratch and fill it in clue by clue rather than trying to guess the number all at once. Reviewing how to convert between place values can also help when a clue describes one place in terms of another, since many riddle-style problems rely on that same kind of relationship.

Related lessons

• Math 3