Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**SteveB****Member**- Registered: 2013-03-07
- Posts: 594

Right I think we should look at an example that does not terminate exactly. What is 1 divided by 3 ?

Offline

**mandy jane****Member**- Registered: 2010-09-23
- Posts: 1,162

1 divided 3 = 3 am I right?

Offline

**SteveB****Member**- Registered: 2013-03-07
- Posts: 594

Your answer is not correct. See below.....

Right here goes:

------------

3 | 1. 0 0 0

1 divided by 3 is zero remainder 1. The 1 becomes a ten in the next column....

10 divided by 3 is .....

*Last edited by SteveB (2013-03-26 02:38:03)*

Offline

**SteveB****Member**- Registered: 2013-03-07
- Posts: 594

So we have:

0 . 3

----------------------

3 | 1 . [10] [10] 0

Offline

**mandy jane****Member**- Registered: 2010-09-23
- Posts: 1,162

10 divided 3= 9.1 am I right?

Offline

**SteveB****Member**- Registered: 2013-03-07
- Posts: 594

Yes 3 x 3 = 9 is the right times table so 10 divided by 3 gives us 3 with a remainder of one.

Do you see what is going to happen next ?

Offline

**mandy jane****Member**- Registered: 2010-09-23
- Posts: 1,162

The next step is the same as this one am I right?

Offline

**SteveB****Member**- Registered: 2013-03-07
- Posts: 594

Well that remainder of one is going to give us 10 again. Which gets divided by 3 again.

So we get this happening:

0 . 3 3 3 3 .....

-------------------------------

3 | 1 . [10] [10] [10] [10] ....

The decimal could in principle go on forever like this. We need a sensible way of writing this.

*Last edited by SteveB (2013-03-26 02:45:36)*

Offline

**mandy jane****Member**- Registered: 2010-09-23
- Posts: 1,162

So is the answer 0.330 then am I right?

Offline

**SteveB****Member**- Registered: 2013-03-07
- Posts: 594

We could say that it is 0. 333 to 3 decimal places (rounded).

Some mathematicians will put a dot over a 3 to indicate that it is a recurring decimal. so 0.3 (with a dot over the 3)

(I can't display that very well at the moment I will need to find out later how Latex could be used to show that.)

*Last edited by SteveB (2013-03-26 02:49:50)*

Offline

**SteveB****Member**- Registered: 2013-03-07
- Posts: 594

So the fraction (4 / 5) gave us 0.8 this could be converted into a percentage. How can we do this ?

Offline

**SteveB****Member**- Registered: 2013-03-07
- Posts: 594

( 4 / 5 ) = 0 . 8 = ( 0 . 8 x 100) as a percentage = 80 %

*Last edited by SteveB (2013-03-26 02:57:47)*

Offline

**mandy jane****Member**- Registered: 2010-09-23
- Posts: 1,162

Hi steveb mandy here. I am finding this hard to do? Is there a website that show you how to do this?

Offline

**SteveB****Member**- Registered: 2013-03-07
- Posts: 594

Do you know how to access the Math Is Fun teaching part of the website?

You can go to the main page of this site and choose the first thing in of the bar at the top.

This is called "Math is Fun" the forum we are on is called "Math is Fun Forum".

I will have a look at it now and come back. If you are able to read this then I am back ....

*Last edited by SteveB (2013-03-26 03:18:00)*

Offline

**SteveB****Member**- Registered: 2013-03-07
- Posts: 594

I cannot give you a link as a post because I have to be a more established member to do that. However there are some useful

thinks on the Math Is Fun website.

Look at things like "how to convert fractions into decimals" and "how to convert decimals into fractions". Tell me what you think.

I will have a break and come back. However I will check the computer in ten minutes or so.

*Last edited by SteveB (2013-03-26 03:08:49)*

Offline

**mandy jane****Member**- Registered: 2010-09-23
- Posts: 1,162

Hi steveb mandy here the Page you got me to. Look at is very good thanks for that? Now what do you want me to do?

Offline

**SteveB****Member**- Registered: 2013-03-07
- Posts: 594

I could take you through another example of fractions being converted into a decimal and then a percentage.

Try 1 divided by 6 ? (Do you know how to start this one?)

*Last edited by SteveB (2013-03-26 03:21:30)*

Offline

**mandy jane****Member**- Registered: 2010-09-23
- Posts: 1,162

Is it 6 divided 10 = 1 remainder 4 am I right?

Offline

**SteveB****Member**- Registered: 2013-03-07
- Posts: 594

OK

0 .

-----------------------

6 | 1 . 0 0 0 0 0

1 divided by 6 is 0 remainder 1. The one becomes a ten in terms of the next column. So [10] goes where the first zero is.

0 . 1 6

-----------------------

6 | 1 . [10] [40] 0

Yes well done. 10 divided by 6 is one remainder 4. So we pass the 4 to the next zero as a [40].

What is 40 divided by 6 ?

Hint: 6 x 6 = 36

In other words 40 divided by 6 gives us 6 remainder 4. This becomes a [40] to start the next division (and so it repeats).

So we end up with this:

0 . 1 6 6 6 6 6 (and so on forever...)

----------------------------------------

6 | 1 . [10] [40] [40] [40] [40] [40]

*Last edited by SteveB (2013-03-26 03:36:50)*

Offline

**mandy jane****Member**- Registered: 2010-09-23
- Posts: 1,162

Hi steveb mandy here is the answer 0.6666 then am I right?

Offline

**SteveB****Member**- Registered: 2013-03-07
- Posts: 594

That is not quite right I will edit the above post #844 to show you in a minute.

Offline

**mandy jane****Member**- Registered: 2010-09-23
- Posts: 1,162

40 divided 6=6 remade 4 am I right?

Offline

**SteveB****Member**- Registered: 2013-03-07
- Posts: 594

That is correct. Look at the post #844 I have updated it to show the result.

It turns out that 1 / 6 = 0.166666.....

If we round this to 3 decimal places what should we give the answer as strictly speaking ?

*Last edited by SteveB (2013-03-26 03:39:53)*

Offline

**mandy jane****Member**- Registered: 2010-09-23
- Posts: 1,162

So now what do you want me to do?

Offline

**SteveB****Member**- Registered: 2013-03-07
- Posts: 594

What is ( 1 / 6 ) rounded to 3 decimal places? (Be careful with that one)

What is this as a percentage ?

Offline