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# Convert decimal from expanded form to standard form

Video transcript

I want to write this
expression here as a decimal. And the first question
that might pop in your head is do I multiply 4 times 1,000,
then add 3, then multiply 1,000, then add 67, then
multiply by 1 over 1,000? Or do I do the
multiplication first? To answer that
question, we just have to remind ourselves about
order of operations. Order of operations, if you
have a bunch of multiplication and addition in a
row like this, you will do the
multiplication first. Let me put some parentheses
here to remind us of that. So let's figure out what
each of these expressions in the parentheses
actually represent. What's 4 times 1 million? Well, that's 4 million. What's 3 times 1,000? Well that's 3,000. What is 67 times 1 thousandth? And there's a bunch of ways
of thinking about this. Actually, let me write
them all over here. Well, I'll do the most
obvious one right over here. 67 times 1 thousandth
is 67 thousandths. And we can represent this
literally as 67/1000. Or we could represent this as
60 over 1,000 plus 7 over 1,000. And what's 60 over 1,000? Well, 60 over 1,000
is 6 hundredths. So let me put that
in a different color. 6 hundredths, 7 thousandths. So you could view this
is 67 thousandths. Or you could view this is 6
hundredths and 7 thousandths. Either way, let's add all
of these things together. So we have 4 million. So the 4 in the millions place
literally represents 4 million. Then we have no
hundred thousands. We have no ten thousands. But then we have 3,000. So the 3 is in the
thousands place. Let me put a comma here, so
we can keep track of things. And then we have no hundreds. We have no tens. We have no ones. We don't even have any tenths. But we do have some hundredths. We have 6 hundredths. And then we have
some thousandths. We have 7 thousandths. So we put that 7 in
the thousandths place. So we could read this 4 million,
3 thousand, 6 hundredths and 7 thousandths. Or we could read it as
4 million, 3 thousand, and 67 thousandths.