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# Comparing decimals: 9.97 and 9.798

To compare two decimals, we should start by looking at the largest place value. If the numbers are the same, continue to smaller place values until we find a difference. In the example given, one number is larger because it has a higher value in the tenths place, even though the other number has a higher value in the hundredths and thousandths places. Created by Sal Khan.

## Want to join the conversation?

- How do you do this?(28 votes)
- When comparing decimals, it's always important to line up the digits correctly so you can properly interpret which one is bigger. Then, as you know, you can always add a zero after the decimal point and it won't change the value of the number. So you can add a zero to one of the decimals until they both have the same number of digits. Then you can compare.

Hope this helps,

- Iron Programming(48 votes)

- hi guys, so i just cant manage to pay attention. i just get really bored and cant focus. Do you know a way i can become more focused?(16 votes)
- You could try listening to music it helps sometimes(20 votes)

- At1:00why does Sal use "cue"(13 votes)
- In this context, it basically means "makes me think" or "gives me the impression".(6 votes)

- can yall give us hints that still give us credit bc mine keep sayin that I cant get credit and this suff is confusing(11 votes)
- this is easy im in grade 5 but this is easy(5 votes)
- it is not that hard(3 votes)

- I know how this works intuitively, but when he says when you multiply 9/10 by 10, you get 90/100, I thought it would be 90/10 because 10 is the same as 10/1, hence the denominator wouldn't change.(5 votes)
- i like this but its a little bit boring but it helps.(5 votes)
- Try listening to music(1 vote)

- Why is this lesson so long? It’s so boring, especially since I knew this stuff since fourth grade, but my dad’s making me redo it.(4 votes)
- It often helps to practice a skill more than once, to make sure you understand it well enough to remember it later.

Also, if you missed some questions when you did this skill before, your dad might want you to improve at this skill.

Have a blessed, wonderful day!(2 votes)

- what can you do with think points?(3 votes)
- I honestly don’t know(3 votes)

- This is kinda confusing(3 votes)
- ..... 9=9 9 > 7 so 9.97 > 9.798(3 votes)

## Video transcript

Let's compare 9.97 to 9.798. So to figure out which
one of these is greater, I like to start with
the largest place values and then keep moving to
smaller and smaller ones until we actually
see a difference. So they both have nine 1's. So at least in the
ones place, they seem comparable to each other. Now let's go to
the tenths place. So this number on the left
has a 9 in the tenths place, while the number on the right
has a 7 in the tenths place. So right now, we could
view this-- let's just write the whole numbers out. So this one is 9 plus 9/10. We haven't gone to the
hundredths place yet. So far, out of the two digits,
the two places we've looked at, this one on the
right is 9 plus 7/10. So this immediately cues to
me that the one on the left is the larger number. You're like, hey, how
do I know immediately that's the larger number? I have all this other
stuff to the right. I have this 98 to the right. I have this 7 to the right. And the way to think about it
is, no matter what you have, even if you really increase
this right-hand side here as much as possible,
you're still less than 9.8. In fact, if you keep
incrementing the thousandths here, you go from
9.798 to 9.799 to 9.8. So you would have to actually
increase to get to even 9.8. And this is at 9.9. So you can really just
look at the discrepancy in the largest place
value to recognize which number is greater. This has 9/10. This has 7/10. It doesn't matter what's
going on in the hundredths and the thousandths place. And to make that clear, let's
actually add up these numbers and compare them as fractions. So let's keep on
going with this. So you have 7/100 here. And here you have 9/100. And then finally,
here you have 0/1000. And here-- let me do that
in a different color. I already used blue. And here, you have 8/1000. So plus 8/1000. So let's put everything
in terms of thousandths so that we can add
these all up and have two fractions over
thousandths, or things in terms of thousandths. So 9 is the same
thing as 9000/1000. 9/10-- well, let's see. If you multiplied it by 10,
you would get 90 over 100. Multiply by 10 again,
you get 900/1000. 7/100 multiplied
by 10 is 70/1000. And let's do that over here. Once again, 9 is 9000/1000,
and then plus 700/1000 plus 90/1000-- just multiply
the numerator and denominator by 10-- plus 8/1000. And so what is this
number on the left? This number on the left is--
how many thousandths is it? It's 9,970. So it's 9970/1000, while
this number on the right here is 9798/1000. So here, once again, you're
comparing two numbers. They have the same
number of thousandths. This has 900. This only has 700. So even though
this is almost 800, 800 is still less than 900. So no matter how you think
about it, the number on the left is greater than the
number on the right.