Comparing decimals: place value difference | Decimals | Pre-Algebra | Khan Academy

It's not uncommon to be asked to compare two decimals and judge which one is larger. How do you do that? This video will gave you the confidence to answer that question.

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We're asked to compare
156.378 to 156.348.

So I assume that they're asking
us which of these is greater.

And so let's rewrite
these numbers.

156.378, and we want to
compare that to 156.348.

And it might already
be obvious to you

which of these is greater.

But I'll work through
it step-by-step, just

in case it's not.

So let's first go to
the hundreds place.

And you could view this
as, to some degree,

the most significant
place, because this

is where they have the largest--
the 1 in the hundreds place

represents a lot more than
a 1 in the tens place or a 1

in the six's place.

A 1 in the hundreds
place represents 100.

It's this many hundreds.

But we have the same number of
hundreds in both situations.

We have 1 hundred and
we have 1 hundred.

Let's go to the tens place.

We have 5 tens
here, which is 50.

And we have 50 right over here.

So, so far they're
equal, so far,

if you just look at the
hundreds and the tens place.

Let's go the ones place.

We have a 6 here in
the ones place, 6 ones,

which is really just 6.

And you also have 6 ones.

So, so far, they're equal again.

Let's go to the tenths
place-- 3 tenths, 3 tenths.

Let's go to the
hundredths place.

So we're going into
smaller and smaller places.

So then you have
the 7 hundredths.

And now we have 4
hundredths here.

So this has less hundredths
than this does over here.

And if we go to the thousandths
place, these are equal.

But it doesn't matter,
even if these were unequal.

It doesn't matter, even if this
one was larger than this one,

because in the more
significant place,

this number was larger
than this number.

So 7 is greater than 4.

We have 7 hundredths here.

We have 4 hundredths here.

So we get this number is greater
than this number down here.

Or 156.378 is
greater than 156.348.

And in particular, it's because
of the hundredths place.