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### Course: Staging content lifeboat > Unit 14

Lesson 28: Comparing decimals# Comparing decimals 2

Sal compares decimals like 0.0093 and 0.01 with greater and less than symbols. Created by Sal Khan.

## Want to join the conversation?

- couldn't it just be 0.070 seventy(11 votes)
- It couldn't be 70 as in "seven times ten".

However, It**could**be seventy*thousandths.*0.070 = 70/1000 or 7/100.

Remember, if you multiply the numerator and denominator of a fraction by the same amount, it won't change the value.(6 votes)

- What is the lowest Decimal?(8 votes)
- it's 100 minus 99.999 with a bar on top of the .99(3 votes)

- How is Comparing decimals 2 different from Comparing decimals 3?(8 votes)
- Decimals like 0.0093 and 0.01 with greater and less than symbols.(1 vote)

- which is bigger 1.6 or 1.28? and why?(4 votes)
- 1.6 is bigger. You can think as 1.6 as 1.60, and we can easily see that 1.60 is bigger than 1.28.(3 votes)

- At1:37you said 0.093 but it is 0.0093.(5 votes)
- how do you round i forgot?(2 votes)
- To round any number to a certain place, you have to look at the place that is directly to the right of the place you're rounding to. If the value in that place is between 0-4, inclusive, you round down. This means that you take every place that's after the place you're rounding to and make it a zero. If the value of the place right next to the place you're rounding to is instead 5-9, you round up. This means that you do the same thing as when rounding down, but increase the value of the place you're rounding to by 1.

For example, let's say we have to round 4508232 to the nearest 1000. We look at the thousands place, then the digit that is one smaller than it, which is the 2 in the hundreds place. The 2 is from 0-4, so we round down. Everything after the thousands place becomes a zero, and you get 4508000.(4 votes)

- at0:45, wouldn't 0.070 be bigger because it is in the hundredths place?(1 vote)
- I think you are confusing hundreds with hundredths. 0.070 is 7/100, which means you have 7 parts out of 100 parts where 100 parts will create 1 whole number.

Sal is comparing that to 1/10. If you change 1/10 to hundredths you get 10/100. 10 out of 100 parts is larger than 7 out of 100 parts.(6 votes)

- how many ways can u do 0.070(2 votes)
- why is there different ways to say decimals?(2 votes)
- what is 0.68+ what = 0.7(2 votes)

## Video transcript

Let's compare 0.1 to 0.070. So this 1 right over here,
it is in the tenths place. So it literally
represents 1 times 1/10, which is obviously the
same thing as 1/10. Now, when we look at this
number right over here, it has nothing in
the tenths place. It has 7 in the
hundredths place. So this is the hundredths
place right over here. And then it also has nothing
in the thousandths place. So this number can be rewritten
as 7 times 1/100, or 7/100. And now we could compare
these two numbers. And there's two ways you
could think about it. You could try to turn
1/10 into hundredths. And the best way to do that, if
you want the denominator to be increased by a factor
of 10, you need to do the same thing
to the numerator. So all I did is I multiplied
the numerator and denominator by 10. Ten 100's is the exact
same thing as 1/10. And here it becomes
very clear, 10/100 is definitely larger than 700. Another way you could
think about this is, look, if you were to
increment by hundredths here, you would start at
7/100, 8/100, 9/100, and then you would
get to 10/100. So then you would
get to that number. So this number, multiple ways
you could think about it, is definitely larger. So let me write this down. This is definitely
larger, greater than. This is greater than that. The greater than symbol
opens to the larger value. So here we have 0.093
and here we have 0.01. So let's just think
about this a little bit. So this 9-- get
a new color here. This 9 is not in the
tenths, the hundredths. It's in the thousandths place. It's in the thousands place. And this 3 is in the-- I'm
running out of colors again. This 3 is in the ten
thousandths place. So the 3 is in the
ten thousandths place. So you could literally view
this as 9/1,000 plus 3/10,000. And if you just wanted to write
it in terms of ten thousandths, you can multiply the
9 and 1,000 by 0. And so it becomes 90/10,000. And if you want to add them
together, you could, of course, write this as 93/10,000. Ten thousandths. I always have trouble with
that "-ths" at the end. Now, let's think about this
number right over here, 0.01. Well, this 1 right over here
is in the hundredths place. It's in the hundredths place. So it literally
represents 1/100. So how can we compare
1/100 to 93/10,000? So the best way
to think about it is, well, what's 1/100 in
terms of ten thousandths? Well, let's just multiply
both the numerator and the denominator
here by 10 twice. Or you could say, let's
multiply them both by 100. If you multiply by 10 once,
you get to ten thousandths. It's the same thing as 1/100. Multiply by 10 again, you get
100/10,000 is the same thing as 1/100. And we know that, 100
times 100 is 10,000. So here it becomes very
clear, 100/10,000, or 1/100, is definitely a
larger than 93/10,000. So this quantity
right over here is less than this quantity there. Less than symbol, the small end
points to the smaller number, larger end to the larger number. In fact, that's true with the
less than and greater than. So let's see, this one right
over here, 0.6 versus 0.06. So here, I have a 6
in the tenths place. So it literally represents 6/10. And in the second, I have a
6 in the hundredths place. Well, 6/100 is definitely
smaller than 6/10. A hundredth is a
tenth of a tenth. So this one is pretty
straightforward. This is going to be
the larger value. 0.6 is greater than 0.06. Now, let's think
about 0.3 versus 0.06. So this 3 literally
represents 3/10 while this 6 right over
here represents 6/100. And if you wanted to
compare them directly, you could multiply 3/10 times--
well, both the numerator and the denominator by 10 so
you're not changing its value. 10/10 is essentially
1, or it is 1. So this becomes 30/300. 3/10 is the same
thing as 30/100. And 30/100 is a lot
larger than 6/100. So this is greater than.