4th Grade · 4.NBT.A.1

The place value chart in 4th grade

A place value chart is a table with one column for each place: ones, tens, hundreds and so on. In 4th grade, the chart grows to a million, and your child learns the rule that holds it together: each place is worth ten times the place to its right.

What the standard says

The official Common Core wording, quoted exactly. The plain version follows.

4.NBT.A.1 Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.

What it means, in plain words

The place value of a digit is what that digit is worth because of where it sits. In 2,580, the 5 is in the hundreds place, so it is worth 500. The same digit in the tens place would be worth only 50.

A place value chart in 4th grade runs from the ones to the millions: ones, tens, hundreds, thousands, ten thousands, hundred thousands and millions. Every column is worth 10 of the column to its right. Ten ones make a ten, ten tens make a hundred and ten hundreds make a thousand, and the pattern carries on to the top of the chart.

The chart also explains multiplying by 10. Every digit moves one place to the left, so 47 becomes 470. Dividing by 10 moves every digit one place to the right. Many children learn "add a zero", but the chart shows the reason: each digit now sits in a place worth ten times as much.

Your child should be able to:

Name the place and the value of any digit in a number up to 1,000,000
Explain that a digit is worth ten times as much as the same digit one place to its right
Multiply and divide by 10 by moving every digit one place on the chart
Compare the same digit in two places, such as the two 7s in 77,000

Example

In the number 182,465, what is the value of the 8 and what is the value of the 2?

Put the number in the chart: 1 hundred thousand, 8 ten thousands, 2 thousands, 4 hundreds, 6 tens and 5 ones.
The 8 is in the ten thousands place: $8 \times 10{,}000 = 80{,}000$ .
The 2 is in the thousands place: $2 \times 1{,}000 = 2{,}000$ .
The 8 is worth 80,000 and the 2 is worth 2,000.

Example

A store gets 10 boxes with 365 pencils in each box. How many pencils is that?

365 is 3 hundreds, 6 tens and 5 ones.
Multiplying by 10 moves each digit one place left: 3 thousands, 6 hundreds, 5 tens and 0 ones.
$365 \times 10 = 3{,}650$ , so the store gets 3,650 pencils.

Where children usually get stuck

Asked for the value of the 4 in 34,512, your child answers 4.
The child names the digit, not what it is worth. The column decides the worth, and this 4 sits in the thousands place.
What helps. Write the number in a chart with the column names on top. Ask your child to read the digit with its column name, "4 thousands", and then write it as 4,000.
Your child knows $52 \times 10 = 520$ because you "add a zero", but has no idea how to find $520 \div 10$ .
"Add a zero" describes how the answer looks. It says nothing about digits moving to a place worth ten times as much, so the child cannot run it backward.
What helps. Write 52 in a chart, then copy each digit one column to the left on the next row. Do the same in the other direction to divide by 10.
Writing four hundred five thousand thirty, your child puts down 45,030 or 4,530.
A zero holds a place even though it is worth nothing. Without the chart, the empty places are easy to skip.
What helps. Have your child write each digit in its own column of a chart, one box per digit. Every column must hold a digit, so the zeros cannot disappear: 405,030.

Try four practice questions

Real 4th grade questions from our question bank, easiest first. Answer them right here, check each one, and see a worked solution for any question.

1Warm-up
A student wants to choose every division equation that equals 10. The table below shows the equations and whether the student selected each one.
Equation Selected by student?
$\displaystyle 800 \div 80$
Yes
$\displaystyle 480 \div 480$
Yes
$\displaystyle 250 \div 25$
Yes
Select the statement that best describes the student's work.
A
The student selected $480 \div 480$ , but this equation equals $100$ , not $10$ .
B
The student selected $800 \div 80$ , but this equation equals $100$ , not $10$ .
C
The student's choices are all correct.
D
The student selected $480 \div 480$ , but this equation equals $1$ , not $10$ .
Show the answer and how to solve it
The student incorrectly selected $480 \div 480$ . This equation equals $1$ , not $10$ , because any number divided by itself equals $1$ . The other $2$ selections ( $800 \div 80$ and $250 \div 25$ ) are correct.
1. 1To check the student's work, find the quotient of each equation in the table.
2. 2Compute each quotient by comparing place values.
3. 3Two of the equations equal $10$ : $800 \div 80$ and $250 \div 25$ . In each one, the dividend is exactly one place value bigger than the divisor.
4. 4The equation $480 \div 480$ does NOT equal $10$ . The dividend and divisor are identical — any number divided by itself equals $1$ , not $10$ .
5. 5The student selected $480 \div 480$ as if it equals $10$ , but it actually equals $1$ . The other $2$ selections are correct, so the option that names the $480 \div 480$ selection with the quotient of $1$ is the best description of the work.
Common mistake. A common mistake is to assume that any pair of numbers sharing a leading digit has a quotient of $10$ . For $480 \div 480$ , the dividend and divisor are identical — dividing any number by itself always gives $1$ , not $10$ .
The idea underneath. A quotient is exactly $10$ when the dividend is one place value bigger than the divisor. For example, $80$ is one place bigger than $8$ , and $250$ is one place bigger than $25$ . When a number is divided by itself, the quotient is always $1$ — not $10$ .
2On level
Drag a line from each group of 10 on the left to the single unit on the right that has the same value.
Connect each item on the left to its match on the right.
Group of 10
Single unit
10 ones
10 tens
10 hundreds
1 hundred
1 thousand
1 one
1 ten
Use Tab to navigate between items. Click or tap a card to select it, then click or tap a card on the opposite side to create a match. You can also drag a card or its connector dot to a card on the opposite side.
Show the answer and how to solve it
The matches are: 10 ones equals 1 ten, 10 tens equals 1 hundred, and 10 hundreds equals 1 thousand. The choice '1 one' is left unmatched.
1. 1Look at each group of 10 on the left. For each one, find the single unit on the right that has the same value. Whenever you bundle 10 of any unit, they make 1 of the next larger unit.
2. 2When you put 10 ones together, they bundle into 1 ten. So '10 ones' matches '1 ten'.
3. 3When you put 10 tens together, they bundle into 1 hundred. So '10 tens' matches '1 hundred'.
4. 4When you put 10 hundreds together, they bundle into 1 thousand. So '10 hundreds' matches '1 thousand'.
5. 5The choice '1 one' is left unmatched. There is no group of 10 that equals 1 one -- 1 one is a single unit, not a bundle of 10.
Common mistake. A common mistake is matching '10 ones' to '1 one' because both contain the word 'one.' Remember that 10 ones bundle together to make a larger unit -- 1 ten -- not just 1 of the same kind.
The idea underneath. Each place in our number system is 10 times bigger than the place to its right. Whenever you collect 10 of any unit, they bundle into 1 of the next larger unit.
3On level
Kai looked at the number in the place-value chart below.
Thousands
4
Hundreds
4
Tens
3
Ones
0
Kai says, "The 4 in the thousands place is 10 times the 4 in the hundreds place."
Select the statement that best describes Kai's claim.
A
Kai reversed which 4 is 10 times the other.
B
Kai is correct.
C
Kai treated both 4s as if they had the same value.
D
Kai used 100 times instead of 10 times for adjacent places.
Show the answer and how to solve it
The $4$ in the thousands place ( $4{,}000$ ) is $10$ times the $4$ in the hundreds place ( $400$ ). Kai's claim matches this, so Kai is correct.
1. 1Look at the chart. The number $4{,}430$ has a $4$ in the thousands place and a $4$ in the hundreds place. Find the value of each $4$ .
2. 2Compare the two values. $4{,}000$ is $10$ times $400$ , so the $4$ in the thousands place is $10$ times the $4$ in the hundreds place.
3. 3Kai's claim says the $4$ in the thousands place is $10$ times the $4$ in the hundreds place — exactly what is true. Kai is correct.
Common mistake. A common mistake is reversing which place has the greater digit value. Here the claim has it right: the larger (left) place is $10$ times the next place to the right.
The idea underneath. Each place to the left is worth $10$ times the place to its right. So the same digit in a higher place is always $10$ times its value in the next place to the right.
4Stretch
Drag a phrase into each blank to complete the equations.
Tap or click a tile to drop it into the highlighted blank, or tap an empty blank first to choose a different one. Tap a filled blank to send its tile back.
10 ones =
1 thousand =
10 tens =
1 one
1 ten
1 ten thousand
10 hundreds
1 hundred
1 million
Tap an item to place it in the next empty slot, or drag it to a specific slot. With a keyboard: select an item with Enter or Space, then select a slot to place it. Press Delete or Backspace on a slot to remove an item.
Show the answer and how to solve it
The completed equations are: $10\text{ ones} = 1\text{ ten}$ , $1\text{ thousand} = 10\text{ hundreds}$ , and $10\text{ tens} = 1\text{ hundred}$ . Each place value is $10$ times the place to its right.
1. 1These equations mix two directions: 10 of one place value equal 1 of the next-larger place value, and 1 of a place value equals 10 of the next-smaller place value.
2. 2Group 10 ones together to make 1 ten.
3. 3One thousand is made up of 10 hundreds.
4. 4Group 10 tens together to make 1 hundred.
Common mistake. A common mistake is choosing '1 one' for the '10 ones =' frame because it mentions ones, rather than recognising that 10 ones group into 1 ten. Always move up one place when grouping 10, or move down one place when splitting 1.
The idea underneath. In our base-ten system, every group of 10 in one place makes 1 in the next place up, and every 1 in a place is made of 10 of the next-smaller place. Both directions follow the same pattern.

Equation	Selected by student?
$\displaystyle 800 \div 80$	Yes
$\displaystyle 480 \div 480$	Yes
$\displaystyle 250 \div 25$	Yes