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### Course: Arithmetic > Unit 11

Lesson 1: Decimal fractions# Writing a number as a fraction and decimal

Sal shows the connection between decimals and fractions using a grid diagram and number lines.

## Want to join the conversation?

- any tips when my 10 yo daughter keeps writing 1/2 as 0.12 instead of 0.5? She is usually a quick learner but is struggling with simple fractions(54 votes)
- Well,@Adele Canny, you could teach your daughter to remember by conceiving that 1/2 means 0.5 as 2 slashes 1 and cuts it in half and thus leaving 0.5 in each side and when these two join up, they make a 1. 1/4 4 slices 1 into 4 parts and they are 0.25 and when the combine the make 1

If your daughter is a quick learner then I suggest that she should what sal khans videos again and again until she catches on.(37 votes)

- What if the blue dot is before 1/10 and after zero what’s the answer(17 votes)
- you would have to make it into 100ths. If it were before 1/100 and zero you would add a zero to make it 1000ths and so on.(9 votes)

- How do you make 1,999/2,000 a decimal?(16 votes)
- Umm… I'm not so sure. But I think it’s, 0.1999(5 votes)

- What is .76 as a fraction(11 votes)
- Why each hashmark represent a hundred?(9 votes)
- Each hash mark represents a hundredth (1/100) on this line, just because that's the way it is. You can figure this out because there's 10 evenly spaced hash marks from 0 to 1/10, so to get the increment of each hash mark, you divide 1/10 by 10, getting a length of 1/100 for each hash mark.

It's only 1/100 for this number line. You can make number lines with whatever scale you want to, to best help you solve the problem.(14 votes)

- Express the location of the point on the number line was confusing. Why counting by hundredths? What video can I see to review this concept further?(14 votes)
- well for example 0.2 the 2 at the end is 10ths soo...

0.20 is 100ths and so on and on(2 votes)

- my question why do decimals end up with zero somtimes(14 votes)
- How can I make 16/24 as a decimal(8 votes)
- 0.66666666666... and goes on forever(9 votes)

- Can someone help I didn't get it at 1 min 35 sec(4 votes)
- I have been struggling a lot with word from for decimals. Ex. 0.5 I don't know how to do it. Would it be zero.five like that? I don't know maybe one of you could help me. Thx.[Thanks].(2 votes)
- A bit of a long response, but hope this helps!

Similar to how integers (1, 10, 100, etc.) have different terms to represent different place values (i.e., orders of magnitude), decimals do too.

For example:

In 5, 5 is in the(and is denoted as**one's**-place*five*)

In 50, 5 is in the(and is denoted as**ten's**-place*fifty*)

In 500, 5 is in the(and is denoted as**hundred's**-place*five-hundred*)

In 5000, 5 is in the(and is denoted as**thousand**'s-place*five-thousand*)

So, for integers, depending on where the 5 is, it has a different term to represent the place value (or order of magnitude) of the value. I.e., e.g., one, ten, hundred, and thousand.

For decimals, they also have different terms to represent the place value or order of magnitude.

For 0.5, it is*five-*.**tenths**

For 0.05, it is*five-*.**hundredths**

For 0.005, it is*five-*.**thousands**

And so on. (Increasingly getting smaller the further you go to the right of the decimal.)

You may wonder why in 0.5, 5 is in the*tenths-place*and not the '*oneths-place*'. -- Think about it: 0.1 (or 10%) of a pie, is not a whole pie. It is only one part of a pie when it is cut into 10 parts. -*One-tenth*-- One-part of ten-parts. (Please note, for 0.5 it is,*five-tenths*and not*one-half*-- Similar to how it is not*one-half-thousand*for*five-hundred*(500))

(FYI: '*oneths*' is not an actual term.)

---

So, for the number, e.g., 2103.5:

2000 = two thousand

100 = one hundred

3 = three

0.5 = five tenths

The word form is: two thousand one hundred three and five tenths.

Notice the "and" before "five tenths." Think of this as the decimal point.`hundreds | tens | ones | . | tenths | hundredths | thousandths`

100 | 10 | 1 | . | 0.1 | 0.01 | 0.001

You can practice writing decimals in word form in the following exercise: https://www.khanacademy.org/math/cc-fourth-grade-math/imp-decimals/imp-intro-to-decimals/e/decimals-in-words

And you can watch a video on the topic here: https://www.khanacademy.org/math/cc-fourth-grade-math/imp-decimals/imp-intro-to-decimals/v/decimals-as-words

(The video will go over how to represent a number in word form in cases where there is e.g., both a tenths and hundredths place.)

If you have any questions, please don't hesitate to ask.(4 votes)

## Video transcript

- [Voiceover] We are told the square below represents one whole. So this big square here
represents a whole. Express the shaded area as
both a fraction and a decimal. So let's see, we've taken the whole and we've divided it into
one, two, three, four, five, six, seven, eight,
nine, ten, equal sections. Each of these columns or
each of these tall rectangles represent one tenth of the whole because they are ten equal sections
that it has been split into. So each of these is a tenth and let's see we have filled in one,
two, three, four, five, six, of those tenths. So if I wanted to
represent it as a fraction I would say this is 6/10 and
if I were to represent it as a decimal I would say, okay, well, I have zero ones and I have six tenths, so as a decimal it is 0.6. Let's do a couple more of these examples. So let's say, so okay, look at that. Now I have, let's see, the big
square represents one whole. Express the shaded area as both a fraction and a decimal. So what's going on over here? So I have ten rows and in
each row I have ten squares. So ten times ten. This has a hundred squares in it. So I've divided my whole into
a hundred equal sections. So each of these little
squares is one hundredth. So here I have shaded in one, two, three, four, five out of
the hundred hundredths, or I could say I have five
hundredths right over here. So as a fraction, I
could write this as 5/100 and as a decimal I could
say, oh, I have no ones. I have no tenths and I
have five hundredths. Let's do a couple more examples of this. So let's say that I wanted to... Let's see, it says, express
the location of the point on the number line as both
a fraction and a decimal. All right. So let's think about it. So this is 2/10, this is 3/10. And you see it is 0/10, 1/10, or this is 0, 1/10, 2/10, 3/10, and before each, or between each tenth they've split it into ten equal sections. One, two, three, four, five,
six, seven, eight, nine, ten. So each of these, each
of these little hashmarks represent one hundredth. So one way you could view this is we're at two tenths,
so we have two tenths, and then we're going to
have one, two, three, four, five, six, seven hundredths. So we could view this point as two tenths and seven hundredths. So actually let me write
it as a decimal first. So we have two tenths and
we have seven hundredths. Now another way to think about this is we have 27 hundredth. You can count them. Remember each of these is one hundredth. So zero, one, two, three, four, five, six, seven, eight, nine, ten,
11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23,
24, 25, 26, 27, 27 hundredths. And most people when they see this number they won't say two tenths
and seven hundredths. They'll just say 27 hundredths. Well how do you write 27
hundredths as a fraction? Well, it's 27/100. 27 over, over 100. Let's do, I don't know,
I'm kind of in the mood. Let's do one more of these. The big square represents one whole. Express the shaded area as both a fraction and a decimal. So we've already seen,
there's a hundred of these. The whole is split into a
hundred equal, smaller sections. So each of these small
squares is a hundredth and so how many hundredths
do we have shaded in? So this is going to be ten
hundredths, 20 hundredths, 21 hundredths. So as a fraction I'd write that as 21/100. Now, you could, there's a couple
of ways to think about it. If we're familiar with it
already we would say okay, look, two tenths is the
same thing as 20 hundredths, so it's going to be two
tenths and one hundredth, or 21 hundredth. Another way to think about it is this first row right over
here, that's a tenth, then this next one is a
tenth, so you have two tenths, and then you have a hundredth over here. So any way you want to think about it. This is 21 hundredths or two
tenths and one hundredth.