A number as large as ten thousand gets easier once you know place value.
From the right the places are ones, tens, hundreds, thousands, and ten-thousands, and every 10 in a place climb one step left.
The same digit changes its worth by place, so a 5 in the ten-thousands place means 50000.
Pick a number like a neighborhood or a country population, and the place-value chart and the compare bars fill in.
Numbers Beyond 10,000
Once a number passes four digits, you need a fifth slot, the ten-thousands place, to say it out loud. From the right the slots are ones, tens, hundreds, thousands, and ten-thousands, and 10 in one slot become 1 in the slot to the left. The same digit 2 is 20000 in the ten-thousands slot and 2000 in the thousands slot, so you name all five slots before the number holds together. Drop the slot names and you are left with five digits and no way to say which one is the ten-thousands.
🏙️ Why we need large numbers
①School has hundreds of students
②Town has tens of thousands of people
③A crowd over 10,000 is read with the ten-thousands place. This page goes up to ten-thousands
④You need to read and write large numbers!
Understanding Place Value
23456
seegongsik.com
Place-value chart from ten-thousands to ones
At the top of the first picture the five-digit number from the slider is written out, and below it are five cells: ten-thousands, thousands, hundreds, tens, and ones. Each cell shows the place name and its digit large, with as many small squares under it as that digit. Further down, one line adds the places by name and another unpacks them as values like 20000, and both lines point to the same number. Change the number and only the digits, the square counts, and those two lines change; the cells stay put. In the second picture the bar lengths are not scaled to 99999. They are scaled to whichever of the two numbers you picked is larger. Underneath, the two numbers are not written side by side; only >, <, or = is there.
②23456 → "twenty-three thousand four hundred fifty-six"
③Digit × place value = the value of that place
④10 of one place becomes 1 of the next
⑤Skip-count by 10, 100, 1000, or 10000 to keep going
Comparing Number Sizes
When two numbers have the same count of digits, it is easy to look only at the leftmost digit and call the size settled. If the ten-thousands slots match, you are not done: you still look at the thousands, and if those match too you look at the hundreds. The compare bars fill up to the larger of the two numbers, so even two small numbers can look long. How much of the screen a bar fills is not the size. The size is the first slot where the digits split.
34500
34200
seegongsik.com
Two numbers compared with bars
⚖️ How to Compare Large Numbers
①More digits → bigger number
②Same digits → compare from the highest place
③If ten-thousands match, compare thousands; then hundreds...