Writing a number in expanded form | Arithmetic properties | Pre-Algebra | Khan Academy

Writing a number in expanded form | Arithmetic properties | Pre-Algebra | Khan Academy


Write 14,897 in expanded form. Let me just rewrite the number,
and I’ll color code it, and that way, we can keep
track of our digits. So we have 14,000. I don’t have to write
it– well, let me write it that big. 14,000, 800, and 97– I already
used the blue; maybe I should use yellow–
in expanded form. So let’s think about
what place each of these digits are in. This right here, the 7,
is in the ones place. The 9 is in the tens place. This literally represents 9
tens, and we’re going to see this in a second. This literally represents
7 ones. The 8 is in the hundreds
place. The 4 is in the thousands
place. It literally represents 4,000. And then the 1 is in the
ten-thousands place. And you see, every time you move
to the left, you move one place to the left, you’re
multiplying by 10. Ones place, tens place, hundreds
place, thousands place, ten-thousands place. Now let’s think about what
that really means. If this 1 is in the
ten-thousands place, that means that it literally
represents– I want to do this in a way that my arrows
don’t get mixed up. Actually, let me start
at the other end. Let me start with what
the 7 represents. The 7 literally represents
7 ones. Or another way to think about
it, you could say it represents 7 times 1. All of these are equivalent. They represent 7 ones. Now let’s think about the 9. That’s why I’m doing it from the
right, so that the arrows don’t have to cross
each other. So what does the 9 represent? It represents 9 tens. You could literally imagine
you have 9 actual tens. You could have a 10, plus
a 10, plus a 10. Do that nine times. That’s literally what it
represents: 9 actual tens. 9 tens, or you could say it’s
the same thing as 9 times 10, or 90, either way you want
to think about it. So let me write all
the different ways to think about it. It represents all of these
things: 9 tens, or 9 times 10, or 90. So then we have our 8. Our 8 represents– we see it’s
in the hundreds place. It represents 8 hundreds. Or you could view that as being
equivalent to 8 times 100– a hundred, not
a thousand– 8 times 100, or 800. That 8 literally represents
8 hundreds, 800. And then the 4. I think you get the idea here. This represents the
thousands place. It represents 4 thousands, which
is the same thing as 4 times 1,000, which is the
same thing as 4,000. 4,000 is the same thing
as 4 thousands. Add it up. And then finally, we have this
1, which is sitting in the ten-thousands place, so it
literally represents 1 ten-thousand. You can imagine if these were
chips, kind of poker chips, that would represent one of the
blue poker chips and each blue poker chip represents
10,000. I don’t know if that
helps you or not. And 1 ten-thousand is the same
thing as 1 times 10,000 which is the same thing as 10,000. So when they ask us to write it
in expanded form, we could write 14,897 literally as the
sum of these numbers, of its components, or we could
write it as the sum of these numbers. Actually, let me write this. This top 7 times 1 is
just equal to 7. So 14,897 is the same thing as
10,000 plus 4,000 plus 800 plus 90 plus 7. So you could consider this
expanded form, or you could use this version of it, or you
could say this the same thing as 1 times 10,000, depending on
what people consider to be expanded form– plus 4 times
1,000 plus 8 times 100 plus 9 times 10 plus 7 times 1. I’ll scroll to the right
a little bit. So either of these could be
considered expanded form.

61 thoughts on “Writing a number in expanded form | Arithmetic properties | Pre-Algebra | Khan Academy”

  1. Please help. Write the digit in the thousands place and the digit in the tens place for the given place value. 7354

  2. The IDEA is this:
    we are faced with a bunch of unorganized match sticks
    we put ten match sticks in a bundle and give it a name: ten.
    we bind ten such bundles into a larger bundle and give it a name: hundred.
    we bind then ten such larger bundles into a even larger bundle and give it a name: thousand.
    binding like this, when all match sticks are used up, we find that we have 7 "thousand" bundles (largest bundles), 5 "hundred" bundles, 3 "ten" bundles, and 6 match sticks left alone unbundled.

  3. when more than seven thousand match sticks are in an unorganized bunch, we really can't tell how many are there. Because we are trying to think how many one's we've got. Such a large number exceeded the brain's ability. But the same number of match sticks are organized into groups as mentioned below, it's much easier for the brain to grasp hold of how many are there.

  4. So ppl learned to consider things as groups, imagine we have 7 large bundles of match sticks, each bundle is exactly one thousand match sticks, and we have 5 smaller bundles of match sticks, each containing exactly one hundred match sticks, and we have 3 even smaller bundles of match sticks, each containing ten match sticks, and we have 6 match sticks left over. Now it's much easier to get grasp of "how many" match sticks we have, than the 7000 or so messed up in a bunch.

  5. We organize. We organized large numbers, actually, starting from numbers more than ten, as a habit. Once all the one's are organized into groups, it's much easier for us to imagine how many are there, and much easier for us to record using this place value method, the place representing what kind of a big bundle this digit is representing, and the digit itself tells us how many such big bundles are there.

  6. Some of the most basic yet brilliant ideas has its historical origins, understanding these origins do help us a lot in getting grasp of these ideas. The place value method I suspect owe its origin to mankind trying to count large numbers.

  7. I had a test this morning on the first day of school I know such a bad teacher and I did the expanded form wrong

  8. μ§„μ§œ 쓸데없이 μ˜€λž˜κ±Έλ¦°λ‹€. κ°„λ‹¨ν•˜κ²Œ ν•΅μ‹¬λ§Œ μ„€λͺ…ν•˜λ©΄ λ˜λŠ”λ° 더 μ„€λͺ… 뢙여가지고 애듀이 더 μ΄ν•΄ν•˜κΈ° μ–΄λ ΅κ³  νž˜λ“€λ“―

  9. μ‰¬μš΄κ±Έ μ΄λ ‡κ²Œ μ–΄λ ΅κ²Œ μ„€λͺ…ν•˜λŠ”κ²ƒλ„ 재λŠ₯인듯

  10. I did not know that like wut I’m trying to say is like I did not know it was like expanded form

  11. I'm going to have to have a debate over you too because you two are both another favorite of number helpers for me I've known expanded form now I know standard form word form and number form thank you so much for everything you have done for me and your my life keys I'm pretty sure that you're going to win my debate thank you again 😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😘😊😁😘😁😁 πŸ˜πŸ˜ŠπŸ˜ŠπŸ˜πŸ˜πŸ˜ŠπŸ˜˜πŸ˜πŸ˜ŠπŸ˜ŠπŸ˜‹πŸ˜ŠπŸ€—πŸ˜ŠπŸ˜‚πŸ˜πŸ˜ŠπŸ˜πŸ˜ŠπŸ˜ŠπŸ˜

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