Main content

### Course: Arithmetic (all content) > Unit 1

Lesson 9: Ways to write whole numbers (expanded form and written form)- Expanded form of numbers
- Write numbers in number and expanded form
- Number and word form of a number
- Write numbers in number and word form
- Word form and expanded form
- Write numbers in word and expanded form
- Write numbers in different forms
- Writing a number in expanded form
- Write whole numbers in expanded form
- Writing a number in standard form
- Write numbers in written form
- Whole numbers in expanded form review
- Whole numbers in written form review

© 2024 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# Writing a number in standard form

This video demonstrates converting large numbers from expanded and written form to standard form. Using the example "six hundred forty-five million five hundred eighty-four thousand four hundred sixty-two," it explains the process and arrives at 645,584,462, emphasizing place value understanding. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

- is standard form writing it in numbers?(186 votes)
- Yes. Standard Form is told in the most common way we write it in: numbers.(164 votes)

- What's an easier way to remember place values for larger numbers?(75 votes)
- Basically, for whole numbers, you start at the right most digit, the "ones" place. Each time you move left to a new digit, you are basically multiplying by ten. Let's look at 500: we start at the right most digit, a zero, so there are zero "ones". Then we move left, remembering to multiply our "place value" by ten. One times ten is ten, so we are in the "tens" place! In my example, 500 has a "tens place value" of zero. Finally, we move once more to the left. Ten times ten is one hundred, so we are in the "hundreds" place. 500 has five hundreds in its "hundreds place". Just remember that place values are like groups of that amount. Having five in the "ones place" really just represents 5, but having five in the "thousands place" represents five thousand!(72 votes)

- If I multiply 500 and 1,000,000 it will give me 500,000,000?(7 votes)
- Yes, you can confirm with your calculator:)(4 votes)

- What is
**standard**`form`

?(4 votes)- Standard form is like instead of expanded form ( 100+20+3) it is just regular numbers (123)(3 votes)

- why do you quit thevideo like that?(4 votes)
- My homework says " Write the standard form of the equation of the line through the given points" I dont think is what I am looking for. Where should I go?(2 votes)
- The equation of a line is usually created initially using either slope intercept form or point-slope form. If you need your equation in standard form, then you convert it to that form. Here are the sections of videos that apply:

1) Writing equations in Slope Intercept form: https://www.khanacademy.org/math/algebra-home/alg-linear-eq-func#alg-writing-slope-intercept-equations

2) Writing equations in Point-Slope form: https://www.khanacademy.org/math/algebra-home/alg-linear-eq-func#alg-point-slope

3) Standard form: https://www.khanacademy.org/math/algebra-home/alg-linear-eq-func#alg-standard-form

Hope these help.(4 votes)

- How do you work out this?

The mass of a hydrogen atom is about 1.67x10 to the power -24g while that of a uranium atom is about 3.95x10 to the power of -22g.

About how many times heavier is uranium than hydrogen.

Answer to 3 sf.(3 votes)- The long way to do it would be to convert both masses (given in standard form) to ordinary numbers. Then you would divide the uranium atom's mass by the hydrogen atom's mass, to see how many times heavier the uranium atom is than the hydrogen atom.

However, you could also leave the numbers in standard form and do: 3.95 x 10^-22 divided by 1.67 x 10^-24 (using a calculator or use your index laws to do it without calculator).

= 236.5269461

And since you need the answer to 3 significant figures: = 237 times heavier.

I hope this helps.(1 vote)

- what is the compact or standard form of 23 tens and 8 ones?(2 votes)
- 23 tens = 23 * 10

8 ones = 8 * 1

So, do: (23*10) + (8*1) and you will have your answer.

Comment back if you get stuck.(2 votes)

- I am confused when it says "five hundered eight-four thousand" how does that translate to 584,000 and not 508 + 4,000(1 vote)
- 6,000,000,000 +900,000,000 +30,000.000+7,000,000(1 vote)

## Video transcript

Write six hundred forty-five
million five hundred eighty-four thousand
four hundred sixty-two in standard form. So let's tackle this
piece by piece. So the first part we
have six hundred and forty-five million. So let's think about that. So we have six hundred
and forty-five. But it's not just six
hundred forty-five. We have six hundred forty-five
millions. So we could view that as
645 times 1,000,000. One million is one followed
by six zeroes. So this piece right here is
this right over here. That is six hundred and
forty-five million. And what is that when
we write it out? If we were to multiply this
out, this is equal to-- it would be 645 times this 1 with
six zeroes behind it. So this would be equal to 600--
I'll write it like this. This is equal to 645, and then
we have our six zeroes. One, two, three, one,
two, three. That's just this part
of the number. And I'm going to do it kind
of slow and do all of the different parts of the problem,
but once you get some practice, you'll find that these
are a bit second nature, and you won't have to go through
all of these steps. You'll just be able to
write the number. Now, let's move on
to the next part. We have five hundred
and eighty-four. Let me write that down. Well, I'll write it like this. 584 thousand. So let me write the thousand. So 584 thousand. So it's 584 times 1,000. And what's that going
to look like? So that's this whole
part right here. So 584 times 1,000
is equal to what? Well, it's going to be 584 with
three zeroes behind it, or you could view it as 584
times the 1, and then you're going to have three zeroes
in the final answer. So it's going to be 584,000. We have our three zeroes
at the end. 584, three zeroes. So that's that part. And then finally, we have four
hundred sixty-two, and that's just 462, straight up. You could view it as 462 ones. So then you just
have 462, which obviously equals just 462. Now our number is all
of these combined. It is 645,000,000 and
584,000 and 462. So one way to think about it
is that you could add these three numbers. So if we were to add them,
we get 645,584,462. Now, I said it'll become a
little bit of second nature to you in a little bit, and the way
to think about that, the easiest way to think about that,
is millions will have six zeroes behind them,
thousands will have three zeroes behind them, and just
regular numbers have no zeroes behind them. So what you can do when you
kind of want to learn it second nature, you'll just look
at the six hundred and forty-five million, so you'll
write 645, and you'll kind of keep in the back of your mind
that you're going to have to have six more digits to
the right of this. And then you say five hundred
and eighty-four thousand, so then you have your five hundred
and eighty-four thousand, so then you write that
down, 584,000, keeping in mind that you're going to
need three digits to the right of that. And so if they didn't tell us
462, we would just put three zeroes here, and that would also
fulfill the six zeroes we need behind 645,000,000. But then they tell us 462, so we
just write that right here. 462.