10000 is ten 1000s, and it is read ten thousand.
A five-digit number has, from right to left, a ones, tens, hundreds, thousands and ten thousands place, and in any place ten of a kind make 1 in the place to its left.
The same digit stands for a different amount depending on its place: in 52037 the 5 means 50000 and the 2 means 2000.
Pick a number to see the five place-value columns and the expanded form change, and pick two numbers to compare them with bars and a comparison sign.
Numbers in the Ten Thousands
To read numbers longer than four digits you need a fifth column, the ten thousands place. From right to left the places are ones, tens, hundreds, thousands and ten thousands, and ten of anything in one place make 1 in the place to its left. That is why the same digit 2 means 20000 in the ten thousands place but 2000 in the thousands place. You can read 23456 as twenty-three thousand four hundred fifty-six only because each column has a name; without the names, a row of digits does not tell you what each one is worth.
🏙️ Where We Meet Large Numbers
①A whole school usually has a few hundred students
②A city's population or a stadium crowd can be tens of thousands
③Ten 1000s make 10000, read ten thousand
④Three 10000s make 30000, read thirty thousand
Understanding Place Value
23456
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A five-digit number split into ten thousands, thousands, hundreds, tens and ones, with its expanded form
At the top of the first picture is the five-digit number chosen with the slider, and below it are five columns: ten thousands, thousands, hundreds, tens and ones. Each column shows its place name and its digit, with that many small squares underneath. The first line at the bottom writes the number as a sum like 2 × 10,000 + 3 × 1,000, and the second line writes the same number in expanded form, like 20000 + 3000. In the second picture, horizontal bars show the size of two numbers, scaled so that the bar for the larger number fills the full length. At the very bottom, the two numbers are written with >, < or = between them.
💡 Reading Place Value
①From right to left: ones, tens, hundreds, thousands, ten thousands
②23456 is read twenty-three thousand four hundred fifty-six
③A digit times the value of its place gives the amount it stands for
④In any place, ten of a kind move up to the place on the left
⑤Counting by 10000s, as in 10000, 20000, 30000, raises only the ten thousands digit by 1
Comparing Large Numbers
When two numbers have the same number of digits, it is easy to decide which is larger from the first digit alone. If the ten thousands digits match, you are not done yet: look at the thousands, and if those match too, look at the hundreds. 34500 and 34200 have the same ten thousands and thousands digits and first differ in the hundreds, 5 and 2, so 34500 is larger. Because the bars in the second picture are scaled to the larger number, the two bars can look almost the same, so compare the place where the digits first differ instead of the bar lengths.
34500
34200
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Two numbers compared with bars and a comparison sign
⚖️ Comparing Large Numbers
①If the numbers have different numbers of digits, the one with more digits is larger
②If they have the same number of digits, start with the highest place
③If the digits in that place match, move one place to the right
④In the first place where the digits differ, the number with the bigger digit is larger
Summary
Place Value
ones → tens → hundreds → thousands → ten thousands
Every ten of a kind move up one place to the left
Comparing Numbers
Compare from the highest place down
With the same number of digits, check ten thousands, thousands, hundreds, tens, then ones
Counting On
by 10s, 100s, 1000s, 10000s
Watch which digit goes up by 1 to see the pattern
🎯 Summary
①10000 is ten 1000s, read ten thousand
②A five-digit number has ones, tens, hundreds, thousands and ten thousands places
③The same digit stands for different amounts in different places
④Compare from the highest place; the first place that differs decides
⑤Splitting a large number by place value makes it easier to read and use
Examples and Unit Test
Example 1
In 52037, which digit is in the ten thousands place, and what amount does it stand for?
1
From right to left the places are ones, tens, hundreds, thousands and ten thousands, so the ten thousands digit is 5.
2
The 5 in the ten thousands place stands for 5 × 10000 = 50000.
▸ Digit 5, value 50000
In the same number, the 2 is in the thousands place, so it stands for 2000.
Example 2
Which is greater, 45600 or 45200?
1
They have the same number of digits, so compare from the highest place: the ten thousands digit 4 and the thousands digit 5 match.
2
In the hundreds place, 6 > 2, so 45600 is greater.
▸ 45600 (45600 > 45200)
The first place where the digits differ decides which number is greater.
Unit Test
What number is made of 4 ten thousands, 7 thousands and 2 hundreds?
①4720
②40720
③47200
④47020
▸ ③ 47200
1
4 ten thousands are 40000, 7 thousands are 7000 and 2 hundreds are 200.