Expressing decimals in multiple forms

we're asked which two of the following expressions have the same value as eight point seven six pause this video and see if you can figure this out on your own alright now let's do it together and 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 eight point seven six so there's a couple of ways that 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 hundreds hundreds 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 8 times one and two 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 hundred 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 these 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 if we were to write this out and take out each of the decimal parts so the eight ones you would just write that as eight the seven tenths seven tenths 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 tents and they're not wearing a hundreds place and we're gonna 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 here they wrote six thousands here so we can rule that one out and then if we were to write it out in words we would say this is eight eight and I'll 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 the lowest place that you have or the most the most precise place that you have so you could view seven tenths as 70 hundredths or you could view you could view this whole thing as seventy six hundredths so it could be eight and seventy seventy six hundreds hundreds but what they wrote over here they did write eight but instead of seventy six hundredths they wrote eight and sixty seven hundredths a little tricky so we would rule that one out as well