The number 0.063897
is between what two numbers
in the hundredths place value?
So to start off, we need to recognize that
looking at the given number,
this six here is in the
hundredths place value.
So we want to find what
two numbers is it between
using just the hundredths place value.
So we want to figure out
what number is just less than
the given number using just
the hundredths place value,
so this number's going to be greater than
some number in the form of zero point,
and then two decimal places.
We also want to know what
number is just less than,
using the same number of decimal places.
So we'd have a number here
in the form of zero point,
and then two decimal places.
One way to do this is to think
of rounding this number down,
and then rounding this number up
to the hundredths place value.
So rounding this number down
to the hundredths place value,
we would keep this a six
and eliminate the remaining
digits to the right.
So, we would have 0.06
or six hundredths here,
and even though this
number doesn't round up,
if it did, it would
change the six to a seven.
So this number would
have to be less than 0.07
using the hundredths place value.
So these would be the two numbers
that the given number is between
using the hundredths place value,
which means if you were
to plot these two numbers
on the number line;
for example, if we put 0.06
here or six hundredths,
and 0.07 here or seven hundredths,
notice how this number here has a three
in the thousandths place value,
so it's going to be a little bit
closer to the left or to 0.06.
Let's go and say that
it would be right here.
And one way to compare
decimals is to make sure
they have the same number of digits
to the right of the decimal point.
Notice how this has six digits
to the right of the decimal point?
So let's go and add four zeros here.
So this has six digits to the right,
and four zeros here for the same reason.
Now, let's take a moment
and compare corresponding place values.
Notice how they all contain
a zero in the tenths.
Next, there's a six in
the hundredths here,
as well as for this number here.
Notice the number on the right has a seven
in the hundredths place value.
So we know 0.07 is larger
than the given number.
If we go one more place value,
notice how here we have a
three in the thousandths,
but this number here has
a zero in the thousandths,
so it has to be less
than the given number.
So now we've verified
that the given number
is between these two numbers
to the hundredths place value.
We do want to make sure
that we only give our answer
using the hundredths place value,
which means the given number
is greater than 0.06 or six hundredths,
and less than 0.07,
or seven hundredths.
I hope this explanation helps.
We'll take a look at another
example in the next video.
