Common Mistakes in Place Value
Learn
Everyone makes mistakes when learning something new. In this lesson, we will look at the most common mistakes students make with place value and learn how to avoid them.
Mistake #1: Confusing the Digit with Its Value
The Mistake: Saying the 4 in 456 is just "4"
The Truth: The digit 4 in 456 is worth 400 (4 hundreds), not just 4!
How to Avoid: Always ask yourself, "What PLACE is this digit in?" Then multiply the digit by its place value.
Wrong: "The 4 in 456 is 4"
Right: "The 4 in 456 is in the hundreds place, so its value is 400"
Mistake #2: Forgetting About Zero
The Mistake: Writing 307 as "37" or reading 507 as "fifty-seven"
The Truth: Zero is a placeholder! It holds a place even when there are none of that value.
How to Avoid: Always write three digits for three-digit numbers. Zero matters!
Wrong: 205 = 2 + 5 = 7
Right: 205 = 200 + 0 + 5 = 205
Mistake #3: Comparing Numbers by Looking at the Biggest Digit
The Mistake: Thinking 199 > 200 because 9 is bigger than 2
The Truth: You must compare from LEFT to RIGHT, starting with the hundreds place.
How to Avoid: Always start comparing at the hundreds place. The leftmost digit matters most!
Wrong: 189 > 201 because 8 and 9 are bigger than 0 and 1
Right: 201 > 189 because 2 hundreds > 1 hundred
Mistake #4: Mixing Up Expanded Form
The Mistake: Writing 347 as 3 + 4 + 7
The Truth: In expanded form, each digit must be multiplied by its place value.
How to Avoid: Remember: hundreds digit x 100, tens digit x 10, ones digit x 1
Wrong: 347 = 3 + 4 + 7 = 14
Right: 347 = 300 + 40 + 7
Mistake #5: Reading Numbers Backwards
The Mistake: Reading 234 as "four hundred thirty-two"
The Truth: We read numbers from LEFT to RIGHT, just like words.
How to Avoid: Point to the hundreds place first (left side), then move right.
Wrong: 521 read as "one hundred twenty-five"
Right: 521 read as "five hundred twenty-one"
Examples
Let's look at some problems and identify the mistakes.
Example 1: Find the Mistake
Student answer: "In 672, the 7 equals 7."
What's Wrong: The student confused the digit with its value.
Correct Answer: In 672, the 7 is in the tens place, so it equals 70.
Example 2: Find the Mistake
Student answer: "309 in expanded form is 30 + 9."
What's Wrong: The student forgot the hundreds and treated 30 as one number.
Correct Answer: 309 = 300 + 0 + 9 (3 hundreds, 0 tens, 9 ones)
Example 3: Find the Mistake
Student answer: "298 is greater than 310 because 9 and 8 are bigger than 1 and 0."
What's Wrong: The student compared the wrong digits. You must start with hundreds!
Correct Answer: 310 > 298 because 3 hundreds > 2 hundreds
Practice
Find and fix the mistakes in these problems.
Problem 1: A student says, "The number 504 has no tens, so it's really just 54." Is this correct? Explain.
Show Hint
Does zero in the tens place mean we can ignore it?
Show Answer
This is INCORRECT. The zero is a placeholder. 504 means 5 hundreds, 0 tens, and 4 ones. Without the zero, we would write 54, which is a completely different number (fifty-four, not five hundred four).
Problem 2: Which is correct? "The 5 in 358 equals 5" OR "The 5 in 358 equals 50"
Show Hint
What place is the 5 in?
Show Answer
"The 5 in 358 equals 50" is correct. The 5 is in the tens place (5 x 10 = 50).
Problem 3: Fix this expanded form: 429 = 4 + 2 + 9
Show Hint
Multiply each digit by its place value.
Show Answer
429 = 400 + 20 + 9
Problem 4: A student claims 178 > 219 because "7 and 8 are bigger than 1 and 9." Is this correct?
Show Hint
Which place should you compare first?
Show Answer
This is INCORRECT. 219 > 178 because 2 hundreds is greater than 1 hundred. Always compare hundreds first!
Problem 5: Circle the correct reading of 603: "sixty-three" or "six hundred three"
Show Hint
How many hundreds are there? Don't forget the zero!
Show Answer
"Six hundred three" is correct. 603 has 6 hundreds, 0 tens, and 3 ones.
Problem 6: A student writes: "740 = 700 + 4". What did they forget?
Show Hint
What is the value of the 4? And what about the ones place?
Show Answer
They wrote 4 instead of 40 (the 4 is in the tens place, so it's worth 40). Also, they forgot the ones: 740 = 700 + 40 + 0
Problem 7: Is 199 or 200 greater? Explain using place value.
Show Hint
Compare hundreds first: how many hundreds in each?
Show Answer
200 is greater. 200 has 2 hundreds while 199 has only 1 hundred. Even though 199 has 9s, 2 hundreds beats 1 hundred every time!
Problem 8: Fix this mistake: "850 in expanded form is 8 + 50"
Show Hint
The 8 is in the hundreds place. What is 8 hundreds?
Show Answer
850 = 800 + 50 + 0 (The 8 is worth 800, not 8)
Problem 9: True or False: In 444, all three 4s have the same value.
Show Hint
Each 4 is in a different place. What is each place worth?
Show Answer
FALSE! The first 4 = 400 (hundreds), the second 4 = 40 (tens), the third 4 = 4 (ones). They look the same but have different values!
Problem 10: A student compared 305 and 350 and said they are equal because they have the same digits. Is this right?
Show Hint
Do the digits have the same value if they are in different places?
Show Answer
INCORRECT! 305 and 350 are NOT equal. In 305: 3 hundreds + 0 tens + 5 ones = 305. In 350: 3 hundreds + 5 tens + 0 ones = 350. The position of each digit matters! 350 > 305.
Problem 11: Fix this comparison: "489 > 501 because 489 has bigger digits"
Show Hint
Look at the hundreds place first. Which number has more hundreds?
Show Answer
The comparison is WRONG. 501 > 489 because 5 hundreds is greater than 4 hundreds. Always compare from left to right, starting with hundreds!
Problem 12: A student writes that 270 has "2 hundreds, 7 ones, and 0 tens." What mistake did they make?
Show Hint
Check the order: hundreds, tens, ones (left to right).
Show Answer
They mixed up tens and ones! The correct breakdown is: 2 hundreds, 7 TENS, and 0 ONES. The middle digit is always tens, and the rightmost digit is always ones.
Check Your Understanding
Answer these questions to make sure you understand common mistakes.
Question 1: What is the most important thing to remember when comparing three-digit numbers?
Show Answer
Always compare the hundreds place first! The number with more hundreds is always greater, no matter what the other digits are.
Question 2: Why is zero important in place value?
Show Answer
Zero is a placeholder. It holds a place to show there are none of that value. Without zero, numbers like 305 would be confused with 35, which are very different numbers!
Next Steps
- Review any mistakes you have made in previous lessons
- When checking your work, look for these common errors
- When you feel ready, take the Unit Quiz to test your skills
- Remember: making mistakes helps you learn! The key is to understand why they happen.