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Converting fractions to decimals

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    I'll now show you how
    to convert a fraction
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    into a decimal.
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    And if we have time, maybe
    we'll learn how to do a
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    decimal into a fraction.
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    So let's start with, what
    I would say, is a fairly
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    straightforward example.
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    Let's start with
    the fraction 1/2.
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    And I want to convert
    that into a decimal.
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    So the method I'm going to
    show you will always work.
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    What you do is you take the
    denominator and you divide
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    it into the numerator.
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    Let's see how that works.
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    So we take the denominator-- is
    2-- and we're going to divide
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    that into the numerator, 1.
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    And you're probably saying,
    well, how do I divide 2 into 1?
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    Well, if you remember from the
    dividing decimals module, we
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    can just add a decimal point
    here and add some trailing 0's.
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    We haven't actually changed the
    value of the number, but we're
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    just getting some
    precision here.
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    We put the decimal point here.
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    Does 2 go into 1?
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    No.
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    2 goes into 10, so we go 2
    goes into 10 five times.
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    5 times 2 is 10.
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    Remainder of 0.
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    We're done.
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    So 1/2 is equal to 0.5.
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    Let's do a slightly harder one.
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    Let's figure out 1/3.
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    Well, once again, we take the
    denominator, 3, and we divide
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    it into the numerator.
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    And I'm just going to add a
    bunch of trailing 0's here.
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    3 goes into-- well, 3
    doesn't go into 1.
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    3 goes into 10 three times.
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    3 times 3 is 9.
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    Let's subtract, get a
    1, bring down the 0.
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    3 goes into 10 three times.
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    Actually, this decimal
    point is right here.
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    3 times 3 is 9.
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    Do you see a pattern here?
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    We keep getting the same thing.
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    As you see it's
    actually 0.3333.
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    It goes on forever.
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    And a way to actually represent
    this, obviously you can't write
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    an infinite number of 3's.
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    Is you could just write 0.--
    well, you could write 0.33
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    repeating, which means that
    the 0.33 will go on forever.
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    Or you can actually even
    say 0.3 repeating.
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    Although I tend to
    see this more often.
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    Maybe I'm just mistaken.
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    But in general, this line on
    top of the decimal means
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    that this number pattern
    repeats indefinitely.
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    So 1/3 is equal to 0.33333
    and it goes on forever.
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    Another way of writing
    that is 0.33 repeating.
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    Let's do a couple of, maybe a
    little bit harder, but they
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    all follow the same pattern.
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    Let me pick some weird numbers.
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    Let me actually do an
    improper fraction.
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    Let me say 17/9.
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    So here, it's interesting.
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    The numerator is bigger
    than the denominator.
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    So actually we're going to
    get a number larger than 1.
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    But let's work it out.
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    So we take 9 and we
    divide it into 17.
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    And let's add some trailing 0's
    for the decimal point here.
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    So 9 goes into 17 one time.
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    1 times 9 is 9.
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    17 minus 9 is 8.
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    Bring down a 0.
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    9 goes into 80-- well, we know
    that 9 times 9 is 81, so it has
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    to go into it only eight times
    because it can't go
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    into it nine times.
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    8 times 9 is 72.
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    80 minus 72 is 8.
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    Bring down another 0.
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    I think we see a
    pattern forming again.
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    9 goes into 80 eight times.
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    8 times 9 is 72.
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    And clearly, I could keep
    doing this forever and
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    we'd keep getting 8's.
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    So we see 17 divided by 9 is
    equal to 1.88 where the 0.88
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    actually repeats forever.
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    Or, if we actually wanted to
    round this we could say that
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    that is also equal to 1.--
    depending where we wanted
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    to round it, what place.
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    We could say roughly 1.89.
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    Or we could round in
    a different place.
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    I rounded in the 100's place.
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    But this is actually
    the exact answer.
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    17/9 is equal to 1.88.
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    I actually might do a separate
    module, but how would we write
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    this as a mixed number?
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    Well actually, I'm going
    to do that in a separate.
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    I don't want to
    confuse you for now.
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    Let's do a couple
    more problems.
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    Let me do a real weird one.
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    Let me do 17/93.
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    What does that equal
    as a decimal?
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    Well, we do the same thing.
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    93 goes into-- I make a really
    long line up here because
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    I don't know how many
    decimal places we'll do.
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    And remember, it's always the
    denominator being divided
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    into the numerator.
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    This used to confuse me a lot
    of times because you're often
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    dividing a larger number
    into a smaller number.
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    So 93 goes into 17 zero times.
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    There's a decimal.
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    93 goes into 170?
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    Goes into it one time.
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    1 times 93 is 93.
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    170 minus 93 is 77.
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    Bring down the 0.
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    93 goes into 770?
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    Let's see.
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    It will go into it, I think,
    roughly eight times.
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    8 times 3 is 24.
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    8 times 9 is 72.
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    Plus 2 is 74.
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    And then we subtract.
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    10 and 6.
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    It's equal to 26.
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    Then we bring down another 0.
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    93 goes into 26--
    about two times.
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    2 times 3 is 6.
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    18.
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    This is 74.
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    0.
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    So we could keep going.
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    We could keep figuring
    out the decimal points.
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    You could do this indefinitely.
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    But if you wanted to at least
    get an approximation, you would
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    say 17 goes into 93 0.-- or
    17/93 is equal to 0.182 and
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    then the decimals
    will keep going.
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    And you can keep doing
    it if you want.
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    If you actually saw this on
    exam they'd probably tell
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    you to stop at some point.
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    You know, round it to the
    nearest hundredths or
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    thousandths place.
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    And just so you know, let's try
    to convert it the other way,
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    from decimals to fractions.
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    Actually, this is, I
    think, you'll find a
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    much easier thing to do.
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    If I were to ask you what
    0.035 is as a fraction?
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    Well, all you do is you say,
    well, 0.035, we could write it
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    this way-- we could write
    that's the same thing as 03--
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    well, I shouldn't write 035.
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    That's the same
    thing as 35/1,000.
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    And you're probably
    saying, Sal, how did
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    you know it's 35/1000?
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    Well because we went to 3--
    this is the 10's place.
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    Tenths not 10's.
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    This is hundreths.
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    This is the thousandths place.
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    So we went to 3 decimals
    of significance.
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    So this is 35 thousandths.
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    If the decimal was let's
    say, if it was 0.030.
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    There's a couple of ways
    we could say this.
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    Well, we could say, oh well
    we got to 3-- we went to
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    the thousandths Place.
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    So this is the same
    thing as 30/1,000.
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    or.
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    We could have also said, well,
    0.030 is the same thing as
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    0.03 because this 0 really
    doesn't add any value.
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    If we have 0.03 then we're only
    going to the hundredths place.
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    So this is the same
    thing as 3/100.
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    So let me ask you, are
    these two the same?
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    Well, yeah.
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    Sure they are.
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    If we divide both the numerator
    and the denominator of both of
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    these expressions by
    10 we get 3/100.
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    Let's go back to this case.
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    Are we done with this?
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    Is 35/1,000-- I
    mean, it's right.
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    That is a fraction.
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    35/1,000.
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    But if we wanted to simplify it
    even more looks like we could
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    divide both the numerator
    and the denominator by 5.
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    And then, just to get
    it into simplest form,
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    that equals 7/200.
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    And if we wanted to convert
    7/200 into a decimal using the
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    technique we just did, so we
    would do 200 goes into
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    7 and figure it out.
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    We should get 0.035.
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    I'll leave that up to
    you as an exercise.
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    Hopefully now you get at least
    an initial understanding of how
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    to convert a fraction into a
    decimal and maybe vice versa.
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    And if you don't, just do
    some of the practices.
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    And I will also try to record
    another module on this
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    or another presentation.
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    Have fun with the exercises.
Title:
Converting fractions to decimals
Description:

How to express a fraction as a decimal

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Video Language:
English
Duration:
09:22

English subtitles

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