Place Value Word Problems

A step-by-step guide to solving place value word problems

Here’s a step-by-step guide to solving place value word problems:

1. Read the problem carefully and identify the given information: In a place value word problem, you are usually given a number or a set of numbers, along with some specific information about the digits or their positions. Read the problem carefully, identify the given information, and make sure you understand what the problem is asking you to find.
2. Identify the place value of the digits: The place value of a digit determines the value of the digit based on its position in the number. Identify the place value of the digits that are given or asked for in the problem. For example, if the problem involves finding the value of the hundreds place or the thousands place, make sure you know what these places are and how to calculate their values.
3. Write the number in expanded form: Expanded form is a way of writing a number as the sum of its digits multiplied by its place values. Write the number in expanded form to help you visualize the value of each digit in the number.
4. Perform the necessary operations: Once you have identified the given information and the place values of the digits, perform the necessary operations to solve the problem. This may involve adding, subtracting, multiplying, or dividing the digits to find the answer.
5. Check your answer: After you have completed the problem, double-check your work to make sure your answer makes sense and is consistent with the problem. You can also verify your answer by using estimation or by working the problem backward.

The Absolute Best Book for 4th Grade Students

By following these steps, you should be able to solve place value word problems with greater ease and accuracy.

Basic Mathematics for Beginners 2026 The Ultimate Step by Step Guide and A Comprehensive Basic Math Refresher

Download

$27.99 Original price was: $27.99.$17.99Current price is: $17.99.

Example 1:

The problem asks for a number that has 6 thousand, several hundreds that is 2 less than the number of thousands, several tens that is 1 more than the number of hundreds, and several ones that is 3 more than the number of thousands. What is this number?

Solution: The thousands digit is 6, so the number looks like 6 _ _ _.

 The hundreds digit is 2 less than the thousands digit: 6 − 2 = 4. The tens digit is 1 more than the hundreds digit: 4 + 1 = 5. The ones digit is 3 more than the thousands digit: 6 + 3 = 9.

So, it’s 6459.

The Best Math Books for Elementary Students

Five Kinds of Place Value Story Problems, Solved

Most place value word problems fit one of these five patterns. Each one is solved below.

1. Value of a digit. A stadium holds 48,362 fans. What is the 8 worth? The 8 is in the thousands place, so it is worth 8,000.
2. Build a number from clues. A 4-digit number has 3 thousands. The hundreds digit is twice the thousands digit. There are no tens. The ones digit is 1 less than the hundreds digit. Thousands = 3, hundreds = 6, tens = 0, ones = 5, so the number is 3,605.
3. Bundles of hundreds and tens. Ms. Lee has 4 boxes of 100 pencils, 13 packs of 10 and 6 loose pencils. That is 400 + 130 + 6 = 536 pencils. Notice that 13 tens regroup into 1 hundred and 3 tens.
4. The ten-times rule. In 5,550, how many times greater is the 5 in the hundreds place than the 5 in the tens place? 500 ÷ 50 = 10, so it is 10 times greater. Each place is worth ten times the place to its right.
5. Rounding. A town has 26,481 people. Rounded to the nearest thousand, look at the hundreds digit, 4. It is less than 5, so round down to 26,000.

Using a Place Value Chart for Number Riddles

Riddles with several clues get much easier when you draw a chart before doing any math.

1. Draw one box for each place the number has, labeled from left to right, for example thousands, hundreds, tens, ones.
2. Fill in any digit the problem gives you directly first.
3. Use the clues that compare digits next, working from a known digit to an unknown one.
4. Write a 0 in any place the problem says is empty.
5. Read the number aloud, then reread every clue and check it against your chart.

For the example at the top of this page, the chart starts with 6 in the thousands box. Then hundreds = 6 − 2 = 4, tens = 4 + 1 = 5, and ones = 6 + 3 = 9, so the number is 6,459.

Frequently Asked Questions

How do you solve place value word problems?

Read each clue, draw a place value chart, and fill it in from the largest place down. Then check every clue against your number. Try this one: a number has 4 thousands, 0 hundreds, a tens digit 3 more than the thousands digit, and 2 ones. The tens digit is 4 + 3 = 7, so the number is 4,072.

What are place value word problems for 4th grade?

In 4th grade, place value word problems use whole numbers up to 1,000,000 and the idea that a digit is worth 10 times what it would be one place to the right. For example: in 652,000, what is the 6 worth? It sits in the hundred thousands place, so its value is 600,000. Students also compare, round and write numbers in expanded form.

What are place value word problems for 5th grade?

Fifth grade place value problems add decimals to thousandths. A typical question asks for the value of a digit, such as the 8 in 3.582, which is in the hundredths place and worth 0.08. Others compare places: the 4 in 0.4 is worth 10 times the 4 in 0.04. Students also multiply and divide by 10, 100 and 1,000.

What is an example of a place value story problem?

A store has 3 boxes of 100 pencils, 14 packs of 10 pencils, and 6 loose pencils. How many pencils is that? The boxes give 300 and the packs give 140, so the total is 300 + 140 + 6 = 446. Notice that 14 tens regroup into 1 hundred and 4 tens, which is why the hundreds digit becomes 4, not 3.

How do you write numbers in word form for place value problems?

Read the number in groups of three digits, saying the period name after each group except the last. For 405,230, the first group is 405 thousand and the second is 230, so the word form is four hundred five thousand, two hundred thirty. Never say “and” for whole numbers, since “and” marks a decimal point in word form.