Math Antics - Converting Base-10 Fractions - Free Educational videos for Students in K-12 | Lumos Learning

Math Antics - Converting Base-10 Fractions - Free Educational videos for Students in k-12


Math Antics - Converting Base-10 Fractions - By mathantics



Transcript
00:03 Uh huh . Now that we know the basics of
00:07 how decimal numbers work , Let's see how we can
00:09 write some special fractions using decimal numbers . I'm going
00:13 to call these fractions based 10 fractions because they're bottom
00:16 numbers are all powers of 10 . Like 10 100
00:19 or 1000 . Let's start with this fraction 1/10 .
00:23 You should recognize that it's one of our building blocks
00:26 . And this should be easy to write down as
00:27 a decimal number because we have a number of place
00:30 just for counting 10th . So all we have to
00:33 do is put one in the 10th place like this
00:36 0.1 . Now when you write decimal numbers it's important
00:40 that you always include the ones place . But since
00:42 we don't have anyone's we just put a zero in
00:45 that spot . The zero makes the decimal point easier
00:47 to see . All right , so that's 1/10 .
00:50 But what if we have to over 10 instead ?
00:52 Well all we have to do is change the digit
00:54 in the 10th place to a two . So to
00:57 over 10 equals 0.2 . In fact we can keep
01:01 counting 10th like this . 3/10 456789 and finally 20th
01:07 . But look what happened when we got to 20th
01:10 now we don't have a digit for 10 . So
01:11 we had to use the next number place over the
01:13 ones place . But that makes sense because if you
01:16 have the fraction 10/10 that makes a whole and the
01:19 value is just one . Of course we don't really
01:21 need the zero in the 10th place to write one
01:24 but as long as the decimal points there at least
01:26 we won't confuse it with tin . Alright 10th are
01:29 pretty easy . But what about hundreds ? Let's start
01:31 with the hundreds . Building block one over 100 .
01:34 To write that as a decimal , we simply put
01:36 a one in the hundreds place . We also need
01:39 to put a zero in the 10th place to act
01:41 as a placeholder and show that we have no tents
01:43 and we still need to put a zero in the
01:45 ones place as usual . Next let's try to hundreds
01:49 for that . We simply put it to in the
01:50 hundreds place . Let's keep on counting with hundreds ,
01:53 just like we did for 10th 304 56789 and 10
01:59 hundreds . Ah but look what happened when we got
02:02 to 10 hundreds , just like before we have to
02:04 use the next number place to the left , the
02:06 10th place . This happens because any time you have
02:09 10 of a building block , they combined to form
02:12 one of the next biggest building block . For example
02:16 , 1000s is a 10th . 10/10 is a one
02:20 , 10 ones is a 10 and 10 tens is
02:23 100 . Now , the next fraction after 10 over
02:26 100 is 11 over 100 . Now , if you
02:28 think about it , you'll see that 11 hundreds is
02:30 really just a combination of 10 hundreds and 100 .
02:34 Knowing that will help us write it as a decimal
02:36 because a group of 10/100 is equal to 1/10 .
02:39 We put a one in the 10th place and we
02:41 still have that 1/100 leftover . So we put a
02:44 one in the hundreds place , they're 11 over 100
02:48 is just 0.11 as a decimal . Fortunately you don't
02:52 have to break up the fraction into 10th and 100th
02:54 each time anytime you have a two digit number over
02:57 100 all you have to do is put those digits
02:59 into the 10th and 100th . Place of your decimal
03:01 number . Let's look at a few more examples to
03:04 help you see the pattern . 24 over 100 would
03:07 be 0.24 32 over 100 would be 0.3 to 78
03:12 . Over 100 would be 0.78 and 99 over 100
03:16 would be 0.99 Now what do you think will happen
03:19 if we convert the fraction 100 over 100 into a
03:22 decimal ? Right 100 has three digits so we need
03:25 to use another number . Place Now . The next
03:27 one over is the ones place . And that makes
03:29 sense because 100 over 100 is a whole and its
03:32 value is just one . Now that we know how
03:35 to convert hundreds into decimals . Let's try converting thousands
03:38 . That's fractions that have 1000 as the bottom number
03:41 . Let's start with one over 1000 . Now this
03:44 should be easy . All we have to do is
03:45 put a one in the thousands place . Notice that
03:48 this time we need zeros in both the 10th and
03:50 100th place to act as placeholders . Next , Let's
03:53 strike in burning 10 over 1000 . Remember that 10,000
03:57 is the same as 100 . So put a one
03:59 in the hundreds place and we'll put a zero in
04:02 the thousands place . We don't really need the zero
04:04 at the end , but it helps us see that
04:06 this was 10 thousands . All right . What if
04:09 we have 100 over 1000 ? That's a three digit
04:11 number on top . So , we're going to need
04:13 to use three number places , the thousands place the
04:15 hundreds place on the 10th place . So , as
04:19 you can see , 100 over 1000 is just the
04:21 same as 1/10 . Let's see a few more examples
04:24 , 58 over 1000 is 0.58 73 Over 1000 is
04:29 0.73 365 . Over 1000 is 0.365 and 999 over
04:37 1000 is 0.999 . And finally , what do you
04:41 think we could get if we converted 1000 over 1000
04:44 ? Right ? Again , 1000 over 1000 is just
04:46 a whole . So its value would be one .
04:48 Okay , so we've learned how to convert based in
04:51 fractions into decimals . But we can go the other
04:53 way to we can start with the decimal and convert
04:56 it into a fraction . Let's say we want to
04:58 convert a decimal number into a fraction . All we
05:01 have to do is take the decimal digits and make
05:03 them the top number of a based infraction . The
05:06 bottom number will be determined by the smallest number place
05:08 used in our decimal for example , to convert 0.8
05:12 into a fraction , we put an eight on the
05:14 top and a 10 on the bottom because the smallest
05:16 number place in our decimal was the 10th place .
05:19 And to convert 0.29 into a fraction we put a
05:22 29 on top and we put 100 on the bottom
05:25 because the smallest number place in our decimal was 1/100
05:28 place . And finally to convert 0.568 into a fraction
05:32 we put 568 on top and 1000 on the bottom
05:36 because the smallest number place on our decimal was the
05:38 thousands of place . Okay , so far all of
05:41 the fractions that we've converted to decimal numbers and vice
05:44 versa have bottom numbers like 10 , 100 or 1000
05:48 . Those fractions are easy to convert because our number
05:50 system is based on powers of 10 . We have
05:53 number of places specifically for counting those . But what
05:56 if we want to take fractions with different bottom numbers
05:58 like one half 3/4 or eight 25th and write those
06:02 as decimal numbers . We don't have special number of
06:04 places for halves , fourths or 25th . So what
06:07 are we going to do ? Well you're gonna have
06:09 to watch the next section to find out . But
06:11 first let's take a minute and review all this .
06:14 If a fraction has a bottom number that is a
06:16 power of 10 , then it's easy to convert it
06:19 into a decimal number because there are a number of
06:20 places just recounting based infractions To convert tents . All
06:25 you have to do is put the top number in
06:27 the 10s . pl to convert hundreds . You have
06:30 to use both attempts and the hundreds of place together
06:33 . To convert thousands , you have to use three
06:36 number of places and so on . You can also
06:40 convert from a decimal number two , a fraction .
06:42 Just by making the decimal digits , the top number
06:44 of the fraction , and by using a bottom number
06:46 that's based on the smallest number . Place from our
06:48 decimal . You sure to do the exercises So you
06:51 get really good at converting based infractions . Learn more
06:56 at math antics dot com .
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