Question

how do i visualise 0.03 / 0.1

3 hundredeths divided by 1 tenth

I understand that It is just just 3/100 x 10 as you get the reciprocal of 1/10 but I struggle to understand how 0.1 divides in .03 visually.

Answer 1

.1 doesn't go into 0.03 unless you get the recirical of 1/10 which is 10 and times it bhy 0.03.

Answer 2

Nice question. May be lets look at an example problem : Imagine you have a `bag full of chocolates` and you want to distribute them to `students in a classroom`.

Answer 3

If it was 0.3/0.1 it would be easy enough but if its 0.03/0.1 i get confused.

Answer 4

How is it easy if it were 0.3/0.1 ?

Answer 5

.1 goes into .3 = 3 times

Answer 6

Do you mean 0.1 x 3 = 0.3 ?

Answer 7

I don't think so.

.3/.1=3 as .3 x 10=3

Answer 8

but 0.1 doesnt go into 0.03

Answer 9

Not sure if I ake any sense sorry.

Answer 10

You're absolutely correct.
0.1 doesn't go into 0.03 directly. For one reason, 0.1 is greater than 0.03. How can you divide something so small (0.03) by something so big (0.1) ? Doesn't look plausible.

But we don't stop here. There will be situations where we want to perform this kind of division anyways. Let's look at the example problem I gave you earlier..

Answer 11

Also assume that your bag has thousands of of chocolates, but you want to give away only 3/100 th of them.

Answer 12

Does the below phrase make sense ?

"3/100 th of the chocolates in your bag"

Answer 13

but 0.03/.1 = .3 so arent we still dividing it somehow?

Answer 14

That makes sense.

Answer 15

Yes, we are able to divide; its just that the result 0.3 is not a good looking integer

Answer 16

Good. Let me ask a quick question. If you have 1000 chocolates in your bag, how many of them you're going to give away ?

Answer 17

30/1000 = 3/100

Answer 18

? i think

Answer 19

Nope. Please read my question again. I think if the question makes sense, you will be able to answer it correctly :)

Answer 20

What is 3/100th of 1000 ?

Answer 21

If you have 100 chocolates, you will be giving away 3 chocolates.

If you have 1000 chocolates, how many will you be giving away ?

Answer 22

wouldnt the equivalent in thousandths be 30 chocolates?

because you x10 to both numerator and demoninator?

Answer 23

Yes!

Answer 24

Here is the story so far :

You have a lot of chocolates in you bag and you want to give away 3/100 of them to the students.

Answer 25

would that make the equation 0.0030 / 0.1 ?

Answer 26

But wait, you don't really want to give the chocolates to all the students.
You just want to give the chocolates to only 1/10 th of the students.

Answer 27

Again, a quick question : If there are 50 students in the class, how many of them will be getting your chocolates ?

Answer 28

1/10 of them?

Answer 29

Yes, what's 1/10 th of 50 ?

Answer 30

5

Answer 31

Excellent! Thank you for surviving so far and responding brilliantly :) Let's keep going..

Answer 32

Here is the story so far :

You have a lot of chocolates in you bag and you want to give away 3/100 of them to the students. Also you want to give the chocolates to only 1/10th of the students.

Answer 33

Yep that makes sense.

Answer 34

so far

Answer 35

Since that situation makes sense, below expression also should make sense.

\[\dfrac{3/100\times \color{blue}{1000}}{1/10\times \color{blue}{50}}\]

Answer 36

\(\color{blue}{1000}\) chocolates are there in your bag.
\(\color{blue}{50}\) students are there in the class.

Answer 37

The expression in the top : \(3/100\times \color{blue}{1000}\) represents below :

3/100th of the chocolates in your bag.

Answer 38

similarly the expression in the bottom : \(1/10\times \color{blue}{50}\) represents below :

1/10th of the students in the class.

Answer 39

still with me ?

Answer 40

im not sure how you get the 50 students

Answer 41

I have to go for today. But I appreciate the help.

Answer 42

I've been thinking could I say it's

3 of the chocolates devided by 0.1

30 but 30 is x100 overvalued

so its 30/100 which simplifies to 0.1

Answer 43

i mean 0.3

Answer 44

?

Answer 45

Starting with 0.03 / 0.1 with the goal of making the arithmetic easier: eliminate the decimal fractions. You could accomplish this by multiplying both numerator and denom. by 100. @australia10, would you please do this and share your result here.

Answer 46

how do i visualise 0.03 / 0.1
the same way you would "visualise" 3/10
If you can make sense of 3/10 , then use that same idea to understand 0.03/.1
(it's the same fraction, but scaled down by 100)