How to explain place value to a child: what each digit is worth, and why one place left means 10 times

By 15Q20M Editorial · Last updated October 10, 2026

Explain place value as what a digit is worth because of where it sits. In 2,700 the 7 is in the hundreds place, so it is worth 700, not 7. Each place is worth 10 times the place to its right, so a digit that moves one place to the left is worth 10 times as much.

How do you explain place value to a child?

Draw a chart on paper with four columns labeled thousands, hundreds, tens, and ones. Then use 2,700, from Day 1, Question 7 of our Grade 4 workbook: "In 2,700, the value of the 7 is ___." Your child does the talking. Read the left column out loud and let them answer before you move on.

That is the whole idea. A digit has two things: the digit itself and the place it sits in. The place decides its value. The 7 in 2,700 is worth 700, and the same 7 in 2,070 would be worth 70. One of the wrong choices for that workbook question is 7, which is the digit with its place left off.

What is the ten-times rule in place value?

Each place is worth 10 times the place to its right. Day 1 opens with a chain that shows it: 8 × 10 = 80, then 80 × 10 = 800, then 800 × 10 = 8,000, then 8,000 ÷ 10 = 800. Ask your child to write each answer in the chart. The 8 moves one column to the left every time it is multiplied by 10, and one column back to the right when it is divided by 10.

Day 1, Question 5 asks the same thing a different way: "4,000 vs 400: the 4 is ___ times as big." The answer is 10, because the 4 in 4,000 sits one place to the left of the 4 in 400. Day 2, Question 10 takes it one step further: multiplying by 100 moves the digits two places to the left, "because 100 = 10 × 10, so it is two ×10 shifts."

Day 2, Question 6 uses the same numbers: it shows a student who says 700 ÷ 70 = 7 and asks for the correct quotient. Ask your child how many tens are in 70 (7) and how many tens are in 700 (70). So the question is how many groups of 7 tens fit into 70 tens, and the answer is 10. You can also check it by multiplying: 70 × 10 = 700.

Watch the direction. Day 1, Question 10 asks which statement about place value is true, and one wrong choice reads "Each place is 10 times the place to its left." Have your child put a finger on the hundreds column and slide it one column left. Thousands is the bigger place, so the place on the left is worth 10 times as much as the place to its right.

Why does the zero matter in place value?

A zero holds a place open so the other digits stay where they belong. Day 3, Question 10 asks: "Why does the 0 in 4,065 matter?" The correct choice says it holds the hundreds place so the 6 stays in the tens place. Take the 0 out and the other digits slide together into 465, which is a different number.

Zeros are also where writing numbers from words can go wrong. Day 3, Question 8 reads "'Sixty thousand, five hundred two' = ___." The answer is 60,502, and the wrong choices are 6,502, 60,520, and 600,502. Day 3, Question 9 asks for seventy-three thousand, forty-eight, which is 73,048. One check covers both: after the thousands comma there are always exactly three digits. "Five hundred two" fills them as 502, and "forty-eight" fills them as 048.

What is expanded form?

Expanded form writes a number as the sum of what each digit is worth. Day 3, Question 7 asks for the expanded form of 4,236, and the answer is 4,000 + 200 + 30 + 6. One wrong choice is 4,000 + 230 + 6. It adds up to 4,236, but it is not expanded form, because 230 lumps the hundreds and tens together. Except for the ones, each part of expanded form is one nonzero digit followed by zeros.

How do you compare large numbers?

First count the digits in each number. Day 4, Question 6 compares 90,500 and 9,050. They use the same nonzero digits, but 90,500 has five digits and reaches the ten thousands place, while 9,050 has four and stops at thousands. So 90,500 is greater. Day 4, Question 10 asks why 9,999 is less than 10,000, and the answer is the same idea: 10,000 has a digit in the ten thousands place and 9,999 does not.

If both numbers have the same number of places, compare digits from the left and stop at the first place where they differ. In Day 4, Question 4, 67,400 and 67,040 match in the ten thousands and thousands places. In the hundreds place it is 4 against 0, so 67,400 is greater. Day 4, Question 2 shows why the first difference is the one that decides: 8,100 is greater than 8,099, even though 8,099 ends in a bigger digit.

What place value mistakes do kids make?

Each wrong answer below comes from a problem in Days 1 to 4 of our Grade 4 workbook: either a made-up student's answer that your child has to fix, or a wrong answer choice. The workbook shows only the wrong answer; the first column adds one likely reason, and there may be others.

One question covers most of these: "Which place is that digit in?" A child who names the place out loud before writing the value has to look at the column first. Several of the wrong answers in the table look like that step was skipped.

What grade do kids learn place value?

In the Common Core, 2nd grade works with hundreds, tens, and ones in three-digit numbers (2.NBT.A.1). In 4th grade the same ideas stretch to whole numbers up to 1,000,000: the ten-times rule (4.NBT.A.1) and reading, writing, and comparing large numbers (4.NBT.A.2). In 5th grade the rule runs in both directions and reaches decimals (5.NBT.A.1), so a digit is also worth 1/10 of what it would be one place to its left.

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