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Converting a fraction to a repeating decimal

CCSS.Math:

Video transcript

express the rational number 19 over 27 or 1927 as a terminating decimal or a decimal that eventually repeats include only the first six digits of the decimal in your answer let me give this a shot so we want to we want to express 19 over 27 which is the same thing as 19 divided by 27 as the decimal so let's divide 27 into 19 so 27 going into 19 and we know it's going to involve some decimals over here because 27 is larger than 19 and it doesn't divide perfectly so let's go into get into this so 27 doesn't go into 1 it doesn't go into 19 it does go into 190 and it looks like 27 is roughly 30 it's a little less than 30 and 30 times 6 would be 180 so let's go with it going 6 times let's see if that works out well 6 times 7 is 42 6 times 2 is 12 plus 4 is 16 and when we subtract 190 minus 162 is going to get us actually we could have add another 27 in there because when we subtract so we get a 10 from the tens place so that becomes 8 tens this became 28 so we could have put one more 27 in there so let's do that so let's put one more 27 in there so 727s 7 times 7 is 49 7 times 2 is 14 plus 4 is 18 and now our remainder is 1 we can bring down another 0 you can bring down another 0 27 goes into 10 0 times 0 times 27 is 10 subtract with remainder of 10 but now we get to bring down another 0 so let's bring down this 0 right over here so now 27 it goes into 100 3 times 3 times 27 is 60 plus 21 is 81 81 3 times 7 yep 21 81 and then when we subtract 100 minus 81 well we could take 100 from the hundreds place and make it 10 tens and then we could take one of those tens from the tens place and make turn it into ten ones and so nine minus nine 10s minus eight tens is equal to 110 and then 10 minus 1 is 9 so it's equal to 19 you probably you might have been able to do that in your head and then we have and I see something interesting here because we bring down our next 0 we see 190 again we saw 190 up here but let's just keep going so 27 goes into 190 we already we already played this game it goes into it seven times seven times 27 we already figured out was 189 we subtracted you have two remainder of one then we brought down another zero bring down another zero we said 27 goes into 10 zero times zero times 27 is zero subtract then you have still have the 10 but we got to bring down another zero we got to bring down another zero so you have 27 goes into 100 we've already done this three times so you see something happening here it's zero point seven zero three seven zero three and we're just going to keep repeating seven zero three this is going to be equal to zero point seven zero three seven zero three seven zero three seven zero three on and on and on forever so the the the notation for representing a repeating decimal like this is to say this is zero point seven zero three and you put a line over the part that's going to repeat so you put a line all over the seven the zero and the three so this means that the seven zero three will keep repeating on and on and on so let's actually input it into the exercise now so it's zero point seven zero three seven zero three and they tell us to include only the first six digits of the decimal in your answer and they don't tell us to round or approximate because obviously if they said round to that that's that smallest six the decimal place then you would round up because the next digit is a seven but they don't ask us to round they just say include only the first six digits of the decimal in your answer so that should do the trick and it did you