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Lesson 2: 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
• 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.
• What if the blue dot is before 1/10 and after zero what’s the answer
• 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.
• How do you make 1,999/2,000 a decimal?
• Umm… I'm not so sure. But I think it’s, 0.1999
• What is .76 as a fraction
• It is 76/100
• Why each hashmark represent a hundred?
• 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.
• 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?
• well for example 0.2 the 2 at the end is 10ths soo...
0.20 is 100ths and so on and on
• my question why do decimals end up with zero somtimes
• How can I make 16/24 as a decimal
• 0.66666666666... and goes on forever
• Can someone help I didn't get it at 1 min 35 sec
• 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].
• 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 one's-place (and is denoted as five)
In 50, 5 is in the ten's-place (and is denoted as fifty)
In 500, 5 is in the hundred's-place (and is denoted as five-hundred)
In 5000, 5 is in the thousand's-place (and is denoted as 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