In these problems we want to identify the 
decimal plotted on the number line.
So notice we have a value here plotted between
zero and one. Now I think it's probably going to be easier if we actually write this is a fraction
first,
and then write the fraction as a decimal. So from zero to one, this is divided into one, two,
three, four pieces. Which means each of these would be one-fourth,
so this would be one-fourth,
two-fourths,
three-fourths,
four-fourths, or one.
So the number plotted is three-fourths.
Now you may recognize the decimal four and three-fourths,
but let's just say that we don't. If we can
write an equivalent fraction with the
denominator of ten, or a hundred, or a thousand,
its going to make it much easier to write the decimal for three-fourths.
And since four times twenty-five is equal to one hundred,
if we multiply the denominator by twenty-five, and the numerator by twenty-five, we'll have an
equivalent fraction.
So this is equivalent to seventy-five hundredths.
So if we know our place values, we can
rewrite this as a decimal as
zero point seven, five. This would be seventy-five hundredths.
Let's try another one. Notice here we
have a number somewhere between six and
seven.
And noticed that between six and seven we have one,
two, three, four, five equal parts.
So this would be six and one-fifth,
six
and two-fifths,
six and three-fifths, six and four-fifths,
and then we're finally at seven.
And maybe I should include the sixes here just be more accurate.
But now our goal is to rewrite six and three-fifths
as a decimal.
And for three-fifths
we can write an equivalent fraction with the denominator of ten
rather than a hundred like we did for
the first example. We can multiply
this by two,
and multiply this by two, so this is
equivalent to six
and six-tenths. Well if we know our place values,
six and six-tenths would be six point
six. So the value plotted on the number line, six and three-fifths,
written as a decimal is six point six.
Let's go ahead and take a look at one more example. Now on this last example it's a little
bit different because
we have a decimal value plotted on the number line,
and this decimal value is divided into equal parts.
And there are one, two, three, four equal parts between zero and zero point two.
So we could probably figure out that this value in the middle would have to be zero point one.
And the value that would be halfway between zero and zero point one
would be zero point zero, five. And if that's hard to determine remember we could add an extra
zero here,
and then it's easier to see that half of point ten would be point zero, five.
And so we may also want to add a zero here, two
point two. So now we can just start counting by
five-hundredths, or zero point five to determine the missing value.
Here we have five-hundredths, ten-hundredths,
this would be fifteen-hundredths written as zero point one, five.
And then we have twenty-hundredths.
So because the given values is already in decimal form,
this approach was a little bit different.
