I think this is a rounding question. Not sure my thinking is correct

[MathsFormula]

I'm a little confused about rounding up and down type questions. Here is a question from a book and my calculation. I need someone to check my thinking please:


Q1 A toy car travels 180 cm, correct the nearest 10 cm. It takes 7 seconds, correct to the nearest second, to travel this distance.

Work out the greatest possible value of the average speed of the toy car.

A1

<-------------------- range is 10 cm ------------------>
175 cm <-------------- 180 cm ---------------------> 185 cm
175 cm <-------------- 180 cm ---------------------> 184 cm (I've changed this to 184 because this is the maximum number it can be for it to be rounded DOWN to 180)



<-------------------- range is 1 s ------------------>
6.5 s <-------------- 7 s ---------------------> 7.5 s
6.5 s <-------------- 7 s ---------------------> 7.4 s (I've changed this to 7.4 because this is the maximum number it can be for it to be rounded DOWN to 7)


Speed = d/t


Speed = 184/6.5 (the values 184 and 6.5 were chosen because these will give the greatest value for speed in the calculation)

Speed = 28.3 cm/s This is the correct answer according to the book.



It took me a long time to figure out a method to work these questions out. I got the correct answer to the question above so all is fine and dandy. BUT the next question looked just as easy but i got the answer WRONG so I'm concerned that I don't know what I am doing. Please look at my next Q & A:


Q2 Each side of a regular pentagon has a length of 101 mm, correct to the nearest millimeter.

(i) Write down the least possible length of each side.
(ii) Write down the greatest possible length of each side.


A2
<-------------------- range is 1 mm ------------------>
100.5 mm <-------------- 101 mm ---------------------> 101.5 mm
100.5 mm <-------------- 101 mm ---------------------> 101.4 cm (I've changed this to 101.4 because this is the maximum number it can be for it to be rounded DOWN to 101)

So (i) least possible length of each side is 100.5 mm (CORRECT according to book)

(ii) greatest possible length of each side is 101.4 mm (WRONG according to book). Book answer is 101.5 mm.

Please advise what I'm doing wrong. Thank you

 

[Ishuda]

I'm a little confused about rounding up and down type questions. ...

Please advise what I'm doing wrong. Thank you

Strange - It seems to me the book is changing the rules between question 1 and question 2.

To sort of start over let's do 10 cm to the nearest 1 cm
<---------------------------- range = 1 cm ---------------------------->
9.5000... ----------------------------------------------------------- 10.4999...
so that the values would essentially be a min of 9.5 and max of 10.5, i.e.
value = \(\displaystyle given\, rounded\, value\, \pm\, \frac{range}{2}\)

So for Q1 we want the maximum speed with
Speed = d/t,
d = \(\displaystyle 180\, \pm\, 5\, cm\),
and
t = \(\displaystyle 7\, \pm\, 0.5\, sec\).
So maximize d [use d=185 cm] and minimize t [use t=6.5 sec] to get
max speed = 185/6.5 cm/sec ~ 28.46154 cm/sec ~ 28.4615 cm/sec ~ 28.462 cm/sec ~ 28.46 cm/sec ...
and I disagree with the book.

For Q2 we want the minimum and maximum length of something 101 mm, correct to the nearest millimeter. So
L = \(\displaystyle 101\, \pm\, 0.5 mm\)
and
min L = 100.5 mm
and
max L =101.5 mm

 

[MathsFormula]

To sort of start over let's do 10 cm to the nearest 1 cm
<---------------------------- range = 1 cm ---------------------------->
9.5000... ----------------------------------------------------------- 10.4999...

I disagree with the book....... THAT'S A CONCERN

That 10.49999 .. surely that's being too precise if the book says to the nearest 1 cm ??

 

[Ishuda]

That 10.49999 .. surely that's being too precise if the book says to the nearest 1 cm ??

I don't believe so. Let's look at it another way using the 10 cm to the nearest 1 cm. Now the range is 1 cm and the lower limit is 9.5 cm (I think we both agree to that). So, since the range is 1 cm, a minimum 9.5 cm plus 1 cm gives a maximum of 10.5 cm, correct?

Oh, and that's actually the basis of the book answer for Q2 as I read it.

 

[MathsFormula]

Thanks Ishuda. I think the book's author has made an error (as you suggested). I'll do the questions again and show you what I think the results should be:

Q1 A toy car travels 180 cm, correct the nearest 10 cm. It takes 7 seconds, correct to the nearest second, to travel this distance.

Work out the greatest possible value of the average speed of the toy car.

A1

<-------------------- range is 10 cm ------------------>
175 cm <-------------- 180 cm ---------------------> 185 cm


<-------------------- range is 1 s ------------------>
6.5 s <-------------- 7 s ---------------------> 7.5 s


Speed = d/t


Speed = 185/6.5

Speed = 28.5 cm/s (Book answer of 28.3 cm/s is WRONG .... Ishudu please can you confirm this)




Q2 Each side of a regular pentagon has a length of 101 mm, correct to the nearest millimeter.

(i) Write down the least possible length of each side.
(ii) Write down the greatest possible length of each side.


A2

<-------------------- range is 1 mm ------------------>
100.5 mm <-------------- 101 mm ---------------------> 101.5 mm


So (i) least possible length of each side is 100.5 mm (CORRECT according to book)

(ii) greatest possible length of each side is 101.5 mm (CORRECT according to book). Book answer is 101.5 mm.

 

[Ishuda]

...
Q1 A toy car travels 180 cm, correct the nearest 10 cm. It takes 7 seconds, correct to the nearest second, to travel this distance.

Work out the greatest possible value of the average speed of the toy car.
...
Speed = 28.5 cm/s (Book answer of 28.3 cm/s is WRONG .... Ishudu please can you confirm this)
...

That is the answer I got to the nearest 0.1 cm/s, i.e
Speed = 28.5 \(\displaystyle \pm\) 0.1 cm/s

 

[MathsFormula]

^^ Thanks for your help