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Lesson 5: Decimals in different forms

# Expressing decimals in multiple forms

Learn all about understanding how to express decimals in various forms. Learn to break down decimals into place values, show how to write them in expanded form, separate each decimal part, and explain how to say them in words.

## Want to join the conversation?

• Can we write long decimal in scientific notation? like 0.0000000045 •  Yes, you can very easily:
1. Turn 0.0000000045 into a number between 1 and 10. Call this number x.
`This number would be 4.5. So, x is 4.5`
2. Move the decimal place back and count how many times you had to move it. Call this number y.
``      0.͜0͜0͜0͜0͜0͜0͜0͜0͜4.5      We had to move it over to the left 9 times. So, y is -9 (left is negative, right is positive)``

3. Now the number in scientific notation is x * 10^y
`Plugging the numbers in, the answer is 4.5 * 10^(-9)`

• This is the summary of the video.
We're asked which two of the following expressions have the same value as 8.76? Pause this video and see if you can figure this out on your own. All right now let's do it together. Before I even look at these choices, I'm just going to really understand what this number represents and let me just rewrite it. So we have 8.76 so there's a couple of ways we could think about it, we can look at our place values, this right over here this is the ones place, this right over here this is the tenths place, and this right over here is the hundredths, hundredths place. And so we could view this as eight ones and seven tenths and six hundredths or eight ones plus seven tenths plus six hundredths. Well that's exactly what they wrote right over here. Eight ones, seven tenths, and six hundredths, so I would choose that one for sure. Now this second choice looks like an expanded form, but before I even look at it let's see how we would think about it over here. If we wanted to essentially write the same idea but in expanded form, eight ones is the same thing as eight times one and actually let me color code it so you see where things are coming from. So eight ones that's the same thing as eight times one and to that we would add seven tenths, so that's plus seven times 1/10 so seven tenths plus and I'll do this in this orange color, six hundredths so that's plus six times a hundredth, six hundredths. So this would be this number in expanded form is that what they put right over here, yes it is indeed what they put right over here, so I will circle that in. Now if you're doing this on your own we know that we just picked two answers, but let's see whether these other forms or let's see if we can write this in these other forms and see how these might not be the exact answer. So if we were to write this out and take out each of the decimal parts, so the eight ones you'd just write that as eight, the seven tenths, seven tenths well that would be plus 0.7 this is seven tenths right over here, this and this and this part right over here are all equivalent and then last but not least you have your six hundredths, so plus so that's our ones, that's our tenths, and then we're in our hundredths place and we're going to have six of them. So this would be equal to our original value but that's not what they wrote over here, they did write eight ones, they did write seven tenths, but they did not write six hundredths, they wrote six thousandths here. So we could rule that one out. And then if we were to write it out in words we would say this is eight eight and do and in a neutral color, now you might say and seven tenths and six hundredths, or you could often what's normally is you express it in the lowest place that you have or the most precise place that you have so you could do seven tenths as 70 hundredths or you could view, you could view this whole thing as 76 hundredths so it could be eight and 70, 70 six hundredths, hundredths. But what they wrote over here they did write eight but instead of 76 hundredths, they wrote eight and 67 hundredths a little tricky so we would rule that one out as well. • how can you use decimals in real life? • Is there a limit on the amount of numbers used in a decimal?? • Instead of saying 8 ones and 76 hundredths can i say eight point seven six? • (On iPhone 13 mini btw) Is it possible for me to get a whole number by multiplying 2 x 0.23? No. Multiplying these two numbers will never give you wholes. Instead it’s just basic math. 23 x 2 = 46 meaning your answer to 2 x 0.23 is 0.46 Decimals work the same like whole numbers, but never come out as a whole number. (if there is a way to make this easier please comment and make it better understanding!) • Can you rate yourself on a one to ten? • I still don't understand ;~;   