Place Value and Zeros: Why Children Write the Wrong Number

1 October 2026 · by Larry

You dictate “three thousand and five” and your child writes 3005. Fine. Then you say “four thousand and fifty” and the page says 400050, or 450, or 4500. The sum is not the problem here. The child can add. What has gone wrong is how a number said in words becomes a number written in digits, and the zeros are where it shows.

This is worth a calm look, because a slip like this does not stay in the “numbers” chapter. It follows a child into addition, subtraction, money, rounding and decimals, and it is often mistaken for carelessness.

What is actually going on

In a number like 4,050 every digit has a job that depends on where it sits. The 4 means four thousands, the 0 means no hundreds, the 5 means five tens, and the last 0 means no ones. The zeros are not empty. They are placeholders, and they hold the other digits in their right places. Take them out and 4,050 collapses into 45, which is a completely different size.

Children often learn this slowly, because with small numbers they can get by writing what they hear. Once numbers reach the thousands there are four places to keep track of, and a child who has been “writing what they hear” starts to meet numbers that cannot be written that way.

Five slips, and what each one looks like

1. Writing the number the way it sounds

“Four thousand and fifty” is heard as 4000 and 50, so the child writes 4000 next to 50 and gets 400050. The logic is reasonable: two chunks said, two chunks written. What is missing is the idea that there are exactly four places, and that each one needs a digit, even if the digit is 0.

2. Leaving a zero out

“Three thousand and five” becomes 35, or 305. The child heard “three” and “five”, wrote both and stopped. A quick check: how many digits does a number in the thousands have? It must be four.

3. Adding a zero that is not needed

The opposite slip. A child who has just been told zeros matter puts them in everywhere, and 2,300 becomes 20,300. It is a sign the rule has been learned as a rule, without the picture behind it.

4. Right digits, wrong place

In a question like “what is the digit in the hundreds place of 7,284?” a child answers 7 because it comes first, or 4 because it comes last. Reading a number from the left and knowing which place each digit belongs to are two separate skills. The answer is 2, and the way to get it is to name the places out loud, left to right: thousands, hundreds, tens, ones.

5. Place value and value mixed up

“What is the value of the 5 in 4,050?” The digit is 5, but its value is 50. A child who answers 5 has named the digit and not its value. This matters because the same digit means different amounts in different places, and questions about it come in several forms.

Why it keeps coming back

Place value is the idea underneath most of what comes next. Regrouping when carrying and borrowing is place value in action, which is why carrying and borrowing slips so often turn out to be place-value slips in disguise. A number like 4,002 minus 1,867 forces a child to borrow across a zero, and that is where many children get stuck. They cannot borrow from the hundreds because there is nothing there, and they have not yet seen that the tens place is also empty, so they have to go all the way to the thousands.

The same idea returns when numbers go the other way. Decimals are place value continued past the point, and rounding asks a child to decide which place matters, which is covered in rounding and estimation. A child whose place value is shaky at four digits tends to find all of these harder than they should be.

Commas, spaces and groups of three

Your child may meet the same number written two ways: 4,050 with a comma, and 4 050 with a small space. Both are the same number, and some school books use the space version. It is worth saying so, because a child who has only seen one can be thrown by the other and think it is a different number. Either way the digits sit in groups of three counting from the right, which is a useful trick for long numbers: split them into threes before reading them aloud.

A five-minute check at the kitchen table

Try these four, out loud or on paper. Use numbers with zeros in them, since those are the ones that show the gap.

• Say a number such as “six thousand and forty” and ask your child to write it. (6,040 is what you want.)
• Write 5,008 and ask them to read it aloud.
• Ask: “In 7,284, what is the digit in the hundreds place? What is the value of the 8?”
• Ask which is bigger, 4,050 or 4,500, and why.

If the writing goes wrong and the reading is fine, the trouble is turning words into digits (slips 1 to 3). If the reading stalls as well, the places themselves are not yet clear. If both are right but “value” questions go wrong, it is slip 5, and it is a matter of vocabulary more than understanding.

What helps

• Draw four boxes. Label them thousands, hundreds, tens, ones. Put one digit in each box for every number, with a 0 in any box that has nothing. Writing 3,005 becomes “3 in thousands, 0 in hundreds, 0 in tens, 5 in ones”.
• Use money. Dollar notes make place value physical. Ten $1 coins swap for a $10 note, ten $10 notes swap for a $100 note. Ask your child to build $2,304 from notes and coins, and notice which note they do not need.
• Read numbers in full. “4,050” is four thousand and fifty, not “four oh five oh”. Saying the place names takes a little longer, but it is the thing that connects the sound to the digits.
• Expand it. 4,050 is 4,000 + 50. Writing a number as the sum of its parts shows where each digit belongs, and shows what the zeros are for.
• Count in steps across a zero. 1,998, 1,999, 2,000, 2,001. Counting through the point where the digits all change is one of the best ways to see that the places are linked.

What does not help

• Telling a child to “just remember the zeros”. A rule with no picture gets applied wrongly (slip 3).
• Twenty more sums on the same page. If the place value is not there, more sums are more chances to repeat the slip.
• Treating it as careless. A child who writes 400050 has followed a sensible rule that does not work here, which is a different thing from not trying.

Which numbers a child is expected to handle at each level depends on the school’s own workbook, so check the class first; the MOE primary mathematics syllabus on moe.gov.sg lists the topics by level. StudyLab’s Primary 3 has a topic called Numbers to 10 000 that asks for the digit in a given place, and a few minutes on it now and then is enough. If four-digit numbers feel solid and the trouble shows up mainly in subtraction, the next place to look is carrying and borrowing.