Place Value Word Problems
Learn
Word problems help you use place value in real-life situations. In this lesson, you will read stories and use what you know about hundreds, tens, and ones to solve them.
Steps to Solve Word Problems
- Read the problem carefully - What is being asked?
- Find the important numbers - Circle or underline them
- Think about place value - Which digits are in hundreds, tens, ones?
- Solve the problem - Use what you know about place value
- Check your answer - Does it make sense?
Key Words to Look For
- "How many hundreds..." - Look at the hundreds digit
- "What is the value of..." - Find the digit and multiply by its place
- "Write in expanded form..." - Break the number apart
- "Which number is greater..." - Compare place by place, starting with hundreds
Examples
Let's solve some word problems together.
Example 1: The Book Collection
The school library has 456 books. How many hundreds of books are there?
Solution:
Step 1: Find the number - 456
Step 2: Look at the hundreds digit - it's 4
Step 3: There are 4 hundreds of books (or 400 books in the hundreds place)
Example 2: Comparing Stickers
Emma has 372 stickers. Jake has 381 stickers. Who has more stickers?
Solution:
Step 1: Compare hundreds - Both have 3 hundreds (equal)
Step 2: Compare tens - Emma has 7 tens, Jake has 8 tens
Step 3: 8 tens is more than 7 tens
Jake has more stickers (381 > 372)
Example 3: Building a Number
Maria has 5 hundred-dollar bills, 2 ten-dollar bills, and 7 one-dollar bills. How much money does she have in all?
Solution:
5 hundreds = 500
2 tens = 20
7 ones = 7
500 + 20 + 7 = $527
Practice
Solve these word problems using place value. Remember to read carefully!
Problem 1: A toy store has 238 toys on the shelves. How many tens are in 238?
Show Hint
Look at the middle digit. That tells you how many tens.
Show Answer
There are 3 tens in 238. The tens digit is 3, which represents 30.
Problem 2: Ben collected 514 baseball cards. His sister collected 509 cards. Who collected more cards?
Show Hint
Both numbers have 5 hundreds and 0 tens. Compare the ones.
Show Answer
Ben collected more cards. 514 > 509 because when hundreds and tens are equal, 4 ones is more than 9... wait! Actually, 509 has 0 tens and 9 ones, while 514 has 1 ten and 4 ones. 1 ten (10) is more than 9 ones, so 514 > 509. Ben collected more.
Problem 3: A farmer has 6 boxes with 100 apples each, 4 bags with 10 apples each, and 3 loose apples. How many apples does the farmer have?
Show Hint
6 boxes of 100 = 6 hundreds. 4 bags of 10 = 4 tens. 3 loose = 3 ones.
Show Answer
600 + 40 + 3 = 643 apples
Problem 4: What is the value of the digit 7 in the number 275?
Show Hint
The 7 is in the tens place. Multiply 7 by 10.
Show Answer
The value of the 7 is 70 (7 tens = 70).
Problem 5: The cafeteria served 382 lunches on Monday and 391 lunches on Tuesday. On which day did they serve more lunches?
Show Hint
Compare hundreds first, then tens, then ones.
Show Answer
Tuesday (391 lunches). Both have 3 hundreds, but 391 has 9 tens while 382 has only 8 tens.
Problem 6: A school has 700 students. Write this number in expanded form showing hundreds, tens, and ones.
Show Hint
700 has 7 hundreds, 0 tens, and 0 ones.
Show Answer
700 = 700 + 0 + 0 (or simply 700 + 0). There are 7 hundreds, 0 tens, and 0 ones.
Problem 7: Lily has 4 hundred-blocks, 0 ten-sticks, and 8 unit cubes. What number did she build?
Show Hint
4 hundreds = 400. The middle digit will be 0.
Show Answer
408
Problem 8: A store sold 629 pencils in September. How many hundreds of pencils is that?
Show Hint
The hundreds digit tells you how many groups of 100.
Show Answer
6 hundreds (which equals 600 pencils)
Problem 9: Two friends are comparing their seashell collections. Mia has 456 shells and Noah has 465 shells. Who has more? Explain how you know.
Show Hint
Compare from left to right: hundreds, then tens, then ones.
Show Answer
Noah has more (465 > 456). Both have 4 hundreds, but Noah has 6 tens while Mia has only 5 tens.
Problem 10: Write a three-digit number that has 2 in the hundreds place, 5 in the ones place, and 0 in the tens place. What is the number?
Show Hint
Put each digit in its correct place: hundreds-tens-ones.
Show Answer
205
Problem 11: A zoo has 318 birds. If you add 2 more tens of birds, how many birds will the zoo have?
Show Hint
Adding 2 tens means adding 20. What is 318 + 20?
Show Answer
338 birds. 318 + 20 = 338 (the tens place changes from 1 to 3)
Problem 12: Sam says that the 3 in 305 is worth more than the 3 in 530. Is Sam correct? Explain.
Show Hint
Think about what place each 3 is in. Then find the value of each.
Show Answer
Yes, Sam is correct! In 305, the 3 is in the hundreds place (value = 300). In 530, the 3 is in the tens place (value = 30). 300 is greater than 30.
Check Your Understanding
Make sure you can answer these questions before moving on.
Question 1: When comparing two three-digit numbers, which place should you compare first?
Show Answer
Always compare the hundreds place first. If they are equal, then compare tens. If tens are also equal, compare ones.
Question 2: Why is the digit 5 worth more in 500 than in 50?
Show Answer
In 500, the 5 is in the hundreds place (5 x 100 = 500). In 50, the 5 is in the tens place (5 x 10 = 50). The hundreds place is worth 10 times more than the tens place.
Next Steps
- Practice finding place value in numbers you see every day (house numbers, page numbers, scores)
- Create your own word problems for a friend or family member
- Move on to the Common Mistakes lesson to avoid errors
- If needed, review the Guided Practice lesson for more support