# Thread: question i can't figure out

1. ## question i can't figure out

" why do you think we round up when a 5 is the next digit to the right of the place in witch we are rounding ? "

i'm guessing it has something to do with numbers starting out at zero ?

2. 0.5 is the same as one-half. If you are walking home from school and you are one-half of the distance to your home when it starts to rain, would you keep going home or turn around and head back to school?

3. i still don't understand the reason for rounding up when its at 5, infact i don't understand the reasoning for rounding at all since if you didn't round you would have a more accurate number i would think...

4. Do you think it would be reasonable to give everytime all the numbers in pi for example?

One other thing... when you take a reading, you always take it to the nearest reading you can measure. If the exact length of something was 1.0652 cm, you will only be able to measure a length of 1 cm with a common ruler.

Rounding off is a means to simplify numbers and remove unnecessary details. This eases work. Where some accuracy is required, then you don't round off.

5. Originally Posted by Unknown008
Do you think it would be reasonable to give everytime all the numbers in pi for example?

One other thing... when you take a reading, you always take it to the nearest reading you can measure. If the exact length of something was 1.0652 cm, you will only be able to measure a length of 1 cm with a common ruler.

Rounding off is a means to simplify numbers and remove unnecessary details. This eases work. Where some accuracy is required, then you don't round off.
why do we round up at 5 why not down ?

6. I think it's just convention.

7. Here;s my justification.

When rounding a number, the critical digit can be any of ten digits:
. . . $\displaystyle \{ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}$

It seems "fair" that half of them round-down and the other half round-up.

. . . $\displaystyle \underbrace{0,\:1,\:2,\:3,\:4,}_{\text{round down}}\:\underbrace{5,\:6,\:7,\:8,\:9}_{\text{roun d up}}$