Numbers to Ten Thousand: Place Value and Rounding

Imagine stacking ten hundred-blocks. Together they make one big thousand-block. You can count a large amount by counting these groups.

Build bigger groups

Our ten digits are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. We use them to write every whole number. Each time you collect ten of one group, you can trade them for the next bigger group.

With base-ten blocks, a small cube shows one. A rod shows ten, a flat shows one hundred, and a big cube shows one thousand. Ten rods make a flat. Ten flats make a big cube.

One thousand is 10 hundreds. You could also build it with 100 tens or 1,000 ones. Ten tens make only one hundred, so you need ten groups of those to reach one thousand.

Read the blocks

A tray holds 3 big cubes, 5 flats, 2 rods and 6 small cubes. Start with the biggest blocks:

• 3 big cubes are 3 thousands: 3,000.
• 5 flats are 5 hundreds: 500.
• 2 rods are 2 tens: 20.
• 6 small cubes are 6 ones: 6.

Together they make 3,526. A place value chart keeps these groups in order.

Trade a group of ten

Suppose you have 4 thousands and 12 hundreds. Trade 10 of the hundreds for another thousand. You now have 5 thousands and 2 hundreds: 5,200. No blocks were added or taken away. You changed how they were grouped.

Reach ten thousand

Count in thousands: 1,000; 2,000; 3,000; 4,000; 5,000; 6,000; 7,000; 8,000; 9,000; 10,000.

After 9 thousands comes 10 thousands. Trade those for 1 ten thousand. This needs a new chart column, just left of thousands.

10,000 is the first five-digit number. It holds 100 hundreds or 1,000 tens. The four zeros keep the empty places open.

The two 6s in 6,164 look alike. One is worth 6,000, and the other is worth 60. Their places tell you their values.

Digit, place and value

A digit is one symbol from 0 to 9. Its place tells you which group it counts. Its value tells you how much that group is worth.

Start on the right when you name the places: ones, tens, hundreds, thousands. For 4,352, the chart shows:

To find the value of the 3, first find its place. It is in hundreds, so it means 3 hundreds, or 300. Saying “3” names the digit, but the question asks what it is worth.

The same digit in different places

In 7,777, the four 7s have these values: 7,000; 700; 70; 7. Each 7 is worth ten times the 7 just to its right. Seven hundreds are ten groups of seven tens.

You can find a nonzero digit’s value by writing zeros after it. Use one zero for each place to its right. In 6,218, the 6 has three places to its right, so its value is 6,000.

Keep an empty place open

Zero is a placeholder. It shows an empty place and keeps the other digits where they belong.

In 4,035, the hundreds place is empty. The 3 is in tens and is worth 30. If you erase the zero, you get 435. Now the 4 is worth 400, and the 3 is worth 30. The whole number is much smaller.

Compare 4,305 with 4,035. Both use 4, 3, 0 and 5. In the first number, the 3 is worth 300. In the second, it is worth 30. Moving it one place right makes its value ten times smaller.

Solve a number puzzle

“My thousands digit is 5. My hundreds digit is 0. My ones digit is 3. My tens digit is twice my ones digit.”

Fill a chart one place at a time. Put 5 in thousands, 0 in hundreds and 3 in ones. Twice 3 is 6, so put 6 in tens. The number is 5,063. Read it back as 5 thousands, no hundreds, 6 tens and 3 ones.

You can write the same number with digits or with words. A chart helps you move between the two without losing any zeros.

Read thousands first

Standard form uses digits: 6,481. Word form uses words: “six thousand, four hundred eighty-one.”

Read the thousands first. Then read the last three digits together. Write number names without “and”: “three hundred fifty-two.” You may hear someone say “three hundred and fifty-two.” That names the same amount.

Use a hyphen for two-word numbers from twenty-one to ninety-nine, such as “forty-seven.” Notice the spelling of “forty.”

A comma helps you spot the thousands. Count three digits from the right and put the comma before them: 6,481. You may also see a four-digit number without it, such as 6481. Years are written without a comma, as in 2026.

Write the places you hear

Try “five thousand, three hundred six.”

1. Put 5 in thousands.
2. Put 3 in hundreds.
3. No tens are named, so put 0 in tens.
4. Put 6 in ones.

The number is 5,306. The zero is quiet when you speak, but it has a job when you write.

Listen for missing groups

“Seven thousand, eight” has no hundreds or tens. Write 7,008. It has four digits, with 8 in the ones place.

“Six thousand, forty” has no hundreds or ones. Write 6,040. “Two thousand, fifteen” has no hundreds. Its last two digits are 15, giving 2,015.

Do not join full pieces of digit writing together. For “four thousand, twenty,” fill four places: 4, 0, 2, 0. The answer is 4,020. Writing “400020” would make a much bigger number.

From the least to the greatest

The least four-digit number is 1,000: “one thousand.” The greatest is 9,999: “nine thousand, nine hundred ninety-nine.” One more gives 10,000: “ten thousand.”

Digits and words are two ways to show an amount. Blocks, charts, sums of parts and number lines can show that same amount too.

The digits in a number each have a value. Expanded form shows those values joined by plus signs. You can use the parts to build the number again.

Show each digit’s value

Start with 4,352. Name each part: 4 thousands, 3 hundreds, 5 tens and 2 ones. This is unit form because it names the groups.

Now write what each group is worth:

4,352 = 4,000 + 300 + 50 + 2

That is expanded form. Each part comes from one digit’s value. The 5 gives 50 because it counts tens.

Leave zero parts out

For 7,008, the hundreds and tens are empty. Their values are both zero. You can leave them out of the sum:

7,008 = 7,000 + 8

For 5,060, only thousands and tens have a nonzero value:

5,060 = 5,000 + 60

The zeros stay in standard form to hold the places open. Expanded form does not need a separate zero part.

Put the parts back together

What number is 3,000 + 400 + 9? Put 3 in thousands, 4 in hundreds and 9 in ones. There is no tens part, so put 0 in tens. The number is 3,409.

The parts may arrive in a different order. For 50 + 4,000 + 2 + 300, sort them by place. They still make 4,352. Adding the parts in a new order keeps the total the same.

Do not write the whole parts side by side. For 6,000 + 200 + 7, place each digit in its column. The answer is 6,207, with zero tens.

Find a missing part

Look at 6,000 + ? + 40 + 7 = 6,247. Thousands, tens and ones are already there. The 2 hundreds are missing. Their value is 200, so that is the missing part.

You can also draw a part-whole model. Put 2,815 in a circle for the whole. Link it to four parts: 2,000; 800; 10; 5. Adding all four parts rebuilds 2,815.

You can split a number in more than one way. The parts can change, but they must still add to the same whole.

Choose where to split

4,352 = 4,000 + 352. You could also write 3,000 + 1,352. The second split moves 1,000 from the first part into the second part.

Another split is 4,000 + 200 + 152. You do not have to use just one part for each place.

Trade without changing the total

Regrouping means trading equal amounts between places. Trade 1 thousand for 10 hundreds, or trade 10 tens for 1 hundred.

4 thousands and 3 hundreds make 4,300. Trade one thousand for ten hundreds. You now have 3 thousands and 13 hundreds. Both ways still make 4,300.

Try 3 thousands, 14 hundreds and 2 tens:

1. Trade 10 of the 14 hundreds for 1 thousand.
2. Join that thousand to the other 3 thousands.
3. Keep the 4 hundreds and 2 tens left over.

You have 4 thousands, 4 hundreds and 2 tens: 4,420.

Count every whole hundred

How many whole hundreds fit in 4,352? The 4 thousands hold 40 hundreds. Add the 3 hundreds to get 43 hundreds. There are 52 ones left over.

4,352 = 4,300 + 52 = 43 hundreds + 52 ones

The hundreds digit is 3, but the number holds 43 whole hundreds.

To count whole hundreds, cover the last two digits. To count whole tens, cover the last digit. In 4,352, that shows 435 whole tens, with 2 ones left over.

Use a helpful split

Pencils come in boxes of 100. To pack 3,400 pencils into full boxes, you need 34 boxes.

Splitting also helps you add mentally. For 2,700 + 1,500, break 1,500 into 300 + 1,200. Add 300 first to reach 3,000. Then add 1,200 to reach 4,200.

Adding 10 means adding one ten. Adding 100 means adding one hundred. Watch what happens when a place fills up or is empty.

Change one group

Start with 6,482. Add one thousand to get 7,482. Add one hundred to the starting number to get 6,582. Add one ten to get 6,492.

You can take those groups away too. From 6,482, one thousand less is 5,482; one hundred less is 6,382; one ten less is 6,472. Each of these steps changes just one digit because no trade is needed.

Add when a place has 9

Find 100 more than 3,950. The number has 9 hundreds. One more hundred makes 10 hundreds, which you trade for a thousand.

• The thousands go from 3 to 4.
• The hundreds become 0.
• The 5 tens stay, so the answer is 4,050.

Each written place holds one digit. Regroup the 10 hundreds instead of trying to squeeze “10” into the hundreds place.

For 7,095 + 10, ten tens make one hundred. The answer is 7,105.

Take away when a place is empty

Find 10 less than 4,005. There are no tens to remove. Trade one thousand for 10 hundreds. Then trade one of those hundreds for 10 tens.

You now have 3 thousands, 9 hundreds, 10 tens and 5 ones. Take away one ten. There are 9 tens left, giving 3,995.

Several digits can change during one step. Adding 10 to 9,990, adding 100 to 9,900, or adding 1,000 to 9,000 all reach 10,000.

Follow a counting pattern

Count in thousands from 2,406: 2,406; 3,406; 4,406; 5,406. The last three digits stay the same.

Count back in hundreds: 8,250; 8,150; 8,050; 7,950. To find the step, compare neighboring numbers. From 8,050 to 7,950 is 100 less. Two digits change, but the step is still 100.

Smaller steps can cross hundreds too. Count in 25s: 1,000; 1,025; 1,050; 1,075; 1,100. In 50s: 1,000; 1,050; 1,100; 1,150; 1,200. Add the whole step each time.

Which is greater: 7,998 or 8,001? Start with thousands. Eight thousands are already more than seven thousands, so 8,001 is greater.

Find the first difference

Line up the places and compare from the left. For 6,405 and 6,045:

1. Both have 6 thousands. Keep going.
2. Their hundreds are 4 and 0. This is the first difference.
3. Four hundreds are more than zero hundreds, so 6,405 is greater.

You can stop at that first difference. Smaller places cannot overturn it. Starting with ones would lead you wrong for 7,998 and 8,001.

Adding the digits does not compare the numbers either. The digits of 2,099 add to 20. The digits of 3,000 add to 3. Yet 3,000 is greater because it has more thousands.

Use a comparison sign

The open side faces the greater number. The point faces the smaller number. Read the statement from left to right to check your sign.

For whole numbers written without extra zeros in front, more digits means a greater number. So 10,000 > 9,999 and 1,000 > 999.

Put a list in order

Order 4,809; 4,089; 4,890; 4,098 from least to greatest. All have 4 thousands. Split them by hundreds: the numbers with 0 hundreds come before those with 8 hundreds.

Compare tens within each pair. In the first pair, 8 tens come before 9 tens: 4,089 < 4,098. In the second, 0 tens come before 9 tens: 4,809 < 4,890.

The order is 4,089; 4,098; 4,809; 4,890. Reverse it for greatest to least.

Compare different forms

Write expanded numbers in standard form first. For example, 4,000 + 30 is 4,030. It is less than 4,300 because 0 hundreds are less than 3 hundreds.

You can also find missing digits. In 5,?72 > 5,672, the hundreds digit must be greater than 6. It can be 7, 8 or 9. Using 6 would make the numbers equal, and the sign asks for greater.

A number line puts smaller numbers on the left and greater numbers on the right. Its equal spaces show equal changes in value.

Work out one step

Read two labels before you count along a line. Find the difference between them, then count the equal spaces between them.

A line runs from 3,000 to 4,000 in 10 equal steps. The whole distance is 1,000. Ten steps of 100 make 1,000, so each step is 100. The marks begin 3,000; 3,100; 3,200; 3,300.

Count spaces, not marks. The start mark is where you begin. The first space takes you to the next mark.

Find a point

On a line from 0 to 10,000 with 10 equal steps, each step is 1,000. Seven steps right from 0 reach 7,000.

Not every line uses hundreds or thousands. A line from 4,000 to 5,000 with 4 equal steps uses steps of 250. Its marks are 4,000; 4,250; 4,500; 4,750; 5,000.

If labels go 2,600; 2,650; 2,700, the steps are 50. The next mark is 2,750. Use the labels to choose the step size each time.

Find halfway

A halfway point is equally far from both ends. Between 6,000 and 7,000, the halfway point is 6,500: 500 from each end. Between 6,400 and 6,500, it is 6,450: 50 from each end.

Halfway between neighboring thousands ends in 500. But 2,000 and 4,000 are two thousand apart. Their halfway point is 3,000. Check the actual distance between your endpoints.

Estimate a position

Suppose a line shows only 2,000 and 3,000. Where would 2,400 go? The middle is 2,500. Since 2,400 is 100 less, place it a little left of the middle.

You can also estimate a number from its position. Halfway along a line from 0 to 10,000 is 5,000. Halfway from there to 10,000 is 7,500. An arrow near that point shows about 7,500.

Position shows order too. 5,980 lies just left of 6,000, while 6,020 lies just right. So 5,980 < 6,000 < 6,020.

Rounding replaces a number with a nearby number that is easier to use. You choose the nearest ten or hundred, depending on what you need.

Use a halfway point

To round 347 to the nearest ten, find the tens on either side: 340 and 350. Halfway is 345. Since 347 is past halfway, it is closer to 350. So 347 rounds to 350.

Exactly halfway rounds up. For example, 85 is equally far from 80 and 90. It rounds to 90.

Round to the nearest ten

Look at the ones digit. Ones from 0 to 4 keep you at the lower ten. Ones from 5 to 9 take you to the next ten. Change the ones digit to zero.

• 243 has 3 ones, so it rounds to 240.
• 247 has 7 ones, so it rounds to 250.

The ones digit tells you which side of halfway you are on. A number already at a ten stays there: 470 rounds to 470.

Round to the nearest hundred

Now look at the tens digit. Tens from 0 to 4 keep the hundreds digit the same. Tens from 5 to 9 take you to the next hundred. Change the tens and ones to zeros.

347 lies between 300 and 400. Halfway is 350. It is below halfway, so it rounds to 300. Its tens digit, 4, gives the same decision.

381 has 8 tens, so it rounds to 400. At the exact middle, 650 rounds to 700. A whole hundred stays the same: 600 rounds to 600.

“Round down” means choose the lower hundred. It does not mean take one away from the hundreds digit. Rounding 347 down gives 300, not 200.

Cross into a new thousand

996 lies between 990 and 1,000. Halfway is 995, so 996 rounds up to 1,000 to the nearest ten. Likewise, 961 is past 950, so it rounds to 1,000 to the nearest hundred.

Start from the original number

Round 349 straight to the nearest hundred. It is below 350, so the answer is 300. If you round to tens first, you get 350. Rounding that new number to hundreds gives 400. The first rounding changed the number you were judging.

The place you round to changes how much detail you keep. The same number can have different rounded answers.

Choose the place first

Round 4,736 three ways:

For the nearest thousand, look at hundreds. If that digit is 0–4, keep the thousands digit. If it is 5–9, go up one thousand. Change hundreds, tens and ones to zeros.

2,499 is below halfway between 2,000 and 3,000, so it rounds to 2,000. At halfway, 2,500 rounds to 3,000.

Look just one place right

For the nearest hundred, the tens digit decides. In 7,049, that digit is 4. The answer is 7,000. The 9 ones do not move the number past the halfway point, 7,050.

Zeros inside a number count too. For 6,005 to the nearest ten, the 5 ones send you up to 6,010. To the nearest hundred, the 0 tens keep you at 6,000.

Regroup when you round up

Round 3,962 to the nearest hundred. The 6 tens tell you to go up. One more hundred makes 10 hundreds, so trade them for a thousand. The answer is 4,000.

Close to 10,000, the same trade can reach a fifth digit. 9,962 rounds to 9,960 to the nearest ten, but to 10,000 to the nearest hundred or thousand. To the nearest ten, 9,995 rounds up to 10,000.

Keep zeros in the smaller places. Rounding 4,762 to the nearest hundred gives 4,800. Keeping the 62 would leave too much detail; dropping the zeros would shrink the number.

Find all the numbers with one rounded answer

What whole numbers round to 4,000 to the nearest thousand? Find halfway on each side: 3,500 and 4,500.

3,500 rounds up to 4,000, so include it. 4,500 rounds up to 5,000, so stop one before it. The whole-number range is 3,500 through 4,499.

Always round the original number. For 4,449 to the nearest hundred, look at its 4 tens. It rounds to 4,400. Rounding to tens first would change which side of halfway it falls on.

An estimate is a quick answer close to an exact answer. Rounding first makes a sum or difference easier to work out.

Estimate a sum

For 2,894 + 4,117, round each number to the nearest thousand. You get 3,000 + 4,000 = 7,000. So the sum is about 7,000.

The sign ≈ means “is about.” Write 2,894 + 4,117 ≈ 7,000. The exact sum is 7,011. Use = for an exact result and ≈ for an estimate.

Subtraction works too. For 6,120 − 2,980, use 6,000 − 3,000 = 3,000. The estimated difference is 3,000; the exact difference is 3,140.

Choose how closely to round

Try 347 + 281. Rounding to hundreds gives 300 + 300 = 600. Rounding to tens gives 350 + 280 = 630. The exact answer is 628, so the tens estimate is closer here.

Bigger rounding places give simpler numbers. Smaller rounding places keep more detail and usually give a closer estimate. Choose the place that fits the check you need.

A bike costs $289 and a helmet costs $38. For a quick total, round to tens: $290 + $40 = $330. The exact cost is $327.

Spot an answer that needs checking

Mia writes “3,912 + 1,895 = 4,807.” Round the starting numbers: 4,000 + 2,000 = 6,000. Her answer is far below this estimate, so she should check her work. The exact sum is 5,807.

Being near an estimate still leaves room for a small error. Both 5,807 and 5,817 are close to 6,000. Only 5,807 is the exact sum. An estimate helps spot a large mistake; check the exact calculation for smaller mistakes.

Know when to keep the exact count

A report can say “about 4,000 people” when 3,862 people came to a fair. That gives a quick idea of the crowd’s size. To the nearest hundred, the report could say “about 3,900 people.”

But suppose 1,230 people each need one chair. They need 1,230 chairs. Rounding down to 1,200 leaves 30 people without a chair. Use the exact count when everyone needs an item.

Roman numerals use letters to stand for numbers. You may see them on a clock or beside a chapter title in a book.

Learn the first five letters

When the letters go from greatest value to least, add them. VII is 5 + 1 + 1 = 7. XXV is 10 + 10 + 5 = 25. LXXX is 50 + 10 + 10 + 10 = 80.

In standard Roman numerals, repeat I, X or C up to three times in a row. III is 3, and XXX is 30. Do not repeat V or L. Two Vs make ten, written X. Two Ls make one hundred, written C.

Use the subtracting pairs

Sometimes a smaller letter comes just before a larger one. Read these special pairs together:

• IV is 5 − 1 = 4.
• IX is 10 − 1 = 9.
• XL is 50 − 10 = 40.
• XC is 100 − 10 = 90.

These are the four subtracting pairs you need up to 100. You cannot make a pair from any two letters. For example, 49 is not written IL.

Build tens and ones separately

To write 49, split it into 40 + 9. Write XL for 40 and IX for 9. Join them: XLIX.

For 76, split 70 + 6. Seventy is LXX, and six is VI. Join them to make LXXVI.

Keep the tens part before the ones part, even when a part has a subtracting pair. For 99, use 90 + 9: XC + IX gives XCIX.

Read from left to right

For XCIV, spot XC and IV. Their values are 90 and 4, giving 94. Reading each letter as a separate amount would miss both pairs.

Roman numerals have no zero symbol and do not use place value. X is always worth ten. To show twenty, write XX; to show two hundred, write CC. Our digit 2 changes value with its place, but a Roman letter keeps its value.

Some clocks use IIII for four. In standard writing, use IV. You can also find Roman numerals in names, such as Henry VIII, read “Henry the Eighth.”

Two more letters let you write bigger Roman numerals. D is worth 500, and M is worth 1,000.

Build the hundreds

The hundreds follow the same pattern as tens and ones:

CD means 500 − 100 = 400. CM means 1,000 − 100 = 900. Keep each pair together when you read. D is not repeated. M can repeat up to three times: MMM is 3,000.

Write a year in parts

Write 2026 in Roman numerals. Split the year into 2,000 + 20 + 6.

1. Two thousand is MM.
2. There are no hundreds, so write no hundreds letters.
3. Twenty is XX.
4. Six is VI.

Join the parts: MMXXVI. There is no Roman zero to fill the empty hundreds place.

Read a year back

Try MCMXC. Start on the left. M is 1,000, CM is 900, and XC is 90. Add 1,000 + 900 + 90 to get 1990.

If you read MCM as three separate letters, you would add 1,000 + 100 + 1,000. That misses CM, the pair for 900. MCM means 1,900.

For another building date, MDCCLXXVI splits into M + DCC + LXX + VI. These are 1,000 + 700 + 70 + 6, so the year is 1776.

Check the value, not the length

A longer string of letters can be a smaller number. VIII has four letters and means 8. X has one letter and means 10. Read their values before comparing them.

You can use all the parts together. The number 3,999 is 3,000 + 900 + 90 + 9: MMM + CM + XC + IX. Join them to get MMMCMXCIX. This is the greatest number in standard Roman numerals using these seven letters with the three-repeat rule.

You may see years written this way on buildings, monuments or at the end of films. Split them into their thousands, hundreds, tens and ones parts as you read.