Decimals in expanded form
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Convert decimal from expanded form to standard form
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.