# Thread: Can explain Trial and improvement starting from the basics

1. ## Can someone explain Trial and improvement starting from the basics

I used to know how to do this but I havent donethis for over a year and forget most of it.

I have looked at websites (like :Trial & Improvement n Maths Online)
and book ( book just confused me cos the example) but I dont know fully cos Im stressed and confused n a I get feeling that its gonna be on the calculator paper tommorrow

On Trial & Improvement site Trial & Improvement
The part I didnt understand the end part of the first example ..........

On the "Maths Online" Maths Onlineeverything made sense to me until I read :
"7.3 + 2.7 = 10, 7.3 x 2.7 = 19.71 too small, but pretty close.. not close enough ? !" I dont know why it isnt good enough.

2. Originally Posted by girliegal
I used to know how to do this but I havent donethis for over a year and forget most of it.

I have looked at websites (like :Trial & Improvement n Maths Online)
and book ( book just confused me cos the example) but I dont know fully cos Im stressed and confused n a I get feeling that its gonna be on the non calculator paper tommorrow

On Trial & Improvement site Trial & Improvement
The part I didnt understand the end part of the first example ..........

On the "Maths Online" Maths Onlineeverything made sense to me until I read :
"7.3 + 2.7 = 10, 7.3 x 2.7 = 19.71 too small, but pretty close.. not close enough ? !" I dont know why it isnt good enough.

a question on trial and improvement was answered here

see if it makes sense

3. Originally Posted by Jhevon
a question on trial and improvement was answered here

see if it makes sense
I have looked at before I posted the topic and I looked it again I dont get it.

4. "Look at the question to see how many decimal places are needed for x and keep going until you have an answer that is more accurate and then round off. For this example, the answer needs to be to 2dp, so we need one more decimal place to know whether to round up or down."

Is this what you were having trouble with? What you need to know in order to decide when to stop, is how accurate you want the answer to be.

In this case, you need the answer to be accurate to two decimal places. You keep going until you can be completely sure about the first two decimal places.. Before you did the last try, you knew that 1.72 was too big and 1.71 too small, so you know the answer is between those, but you don't know if you should round up or down. When you've tried 1.714 and that's too big, you have narrowed it down to between 1.71 and 1.714. These are both 1.71 when you use two decimal places, so you know the answer has to be 1.71.

In the Maths Online example, there was nothing in the problem about how accurate it needed to be, so it's actually a bit unclear. I think the explanation in the end is bad, though. You should probably keep going at least until you have one answer over and one under.

7 + 3 = 10, 7 x 3 = 21 too big
8 + 2 = 10, 8 x 2 = 16 too small
7.5 + 2.5 = 10, 7.5 x 2.5 = 18.75 too small
7.3 + 2.7 = 10, 7.3 x 2.7 = 19.71 too small, but pretty close.. not close enough ? !
7.2 + 2.8=10, 7.2 * 2.8= 20.16 (that's closer, so the previous one wasn't correct)
If you try 7.24*2.76 you go under again, so I think I would give the answer to two decimal places as 7.2 and 2.8.

5. Originally Posted by girliegal
I have looked at before I posted the topic and I looked it again I dont get it.
I'm sorry, I don't mean to sound insulting but what don't you get?

Here's another example for you and I want you to tell me exactly what it is that you don't understand.

Say we wish to solve for x:
$x^2 + x - 1 = 0$
for x between 0 and 1. We want the answer to 1 decimal place. (For convenience...Usually you would like 4 or 5 decimal places, but this will demonstrate the technique.)

Start by calculating the endpoints:
$0^2 + 0 - 1 = -1$
$1^2 + 1 - 1 = 1$

Start by guessing at the center of the interval: ie. x = 0.5
$0.5^2 + 0.5 - 1 = -0.25$

Our solution has to be between 0.5 and 1 (since x = 0.5 produces a negative number and x = 1 produces a positive.) Now choose the middle of this interval. I usually choose "round" numbers, so instead of 0.75 I'm going to do 0.7:
$0.7^2 + 0.7 - 1 = 0.19$

Our solution now has to be between 0.5 and 0.7. So choose x = 0.6:
$0.6^2 + 0.6 - 1 = -0.04$

So our solution is between 0.6 and 0.7. Now try x = 0.65:
$0.65^2 + 0.65 - 1 = 0.0725$

Now we are between 0.6 and 0.65. Try x = 0.63:
$0.63^2 + 0.63 - 1 = 0.0269$

(Actually we can stop here since we know the solution is between x = 0.60 and x = 0.63, thus to 1 decimal place x = 0.6. But to make sure you have enough to get an idea of the method I will continue.)
Now we are between 0.6 and 0.63. Try x = 0.62:
$0.62^2 + 0.62 - 1 = 0.0044$

Now we are between 0.6 and 0.62. Try x = 0.61:
$0.61^2 + 0.61 - 1 = -0.0179$

Now we are between 0.61 and 0.62. Try x = 0.615:
$0.615^2 + 0.615 - 1 = -0.006775$

Now we are between 0.615 and 0.62. etc.

If we continue this we get x = 0.618034.

-Dan

6. Originally Posted by MissTK
"Look at the question to see how many decimal places are needed for x and keep going until you have an answer that is more accurate and then round off. For this example, the answer needs to be to 2dp, so we need one more decimal place to know whether to round up or down."

Is this what you were having trouble with? What you need to know in order to decide when to stop, is how accurate you want the answer to be.

In this case, you need the answer to be accurate to two decimal places. You keep going until you can be completely sure about the first two decimal places.. Before you did the last try, you knew that 1.72 was too big and 1.71 too small, so you know the answer is between those, but you don't know if you should round up or down. When you've tried 1.714 and that's too big, you have narrowed it down to between 1.71 and 1.714. These are both 1.71 when you use two decimal places, so you know the answer has to be 1.71.

In the Maths Online example, there was nothing in the problem about how accurate it needed to be, so it's actually a bit unclear. I think the explanation in the end is bad, though. You should probably keep going at least until you have one answer over and one under.

7 + 3 = 10, 7 x 3 = 21 too big
8 + 2 = 10, 8 x 2 = 16 too small
7.5 + 2.5 = 10, 7.5 x 2.5 = 18.75 too small
7.3 + 2.7 = 10, 7.3 x 2.7 = 19.71 too small, but pretty close.. not close enough ? !
7.2 + 2.8=10, 7.2 * 2.8= 20.16 (that's closer, so the previous one wasn't correct)
If you try 7.24*2.76 you go under again, so I think I would give the answer to two decimal places as 7.2 and 2.8.
Thanks for posting it did help.Sorry I didnt reply earlier.I done the exam it was easier to me then the first one.

Dan I dont understand what u posted cos I wasn taught at basic level but thanks for trying to help me. what u posted will come useful to me for future( like in september possibly). u dont explain anything its ok.i just so glad i never have to do gcse maths paper again cos I think I did really well.