# question i can't figure out

• Oct 18th 2010, 09:45 AM
ArchitecturalEngineer
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 ?
• Oct 18th 2010, 10:04 AM
NOX Andrew
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?
• Oct 18th 2010, 10:12 AM
ArchitecturalEngineer
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...
• Oct 18th 2010, 10:18 AM
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.
• Oct 18th 2010, 10:42 AM
ArchitecturalEngineer
Quote:

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 ?
• Oct 18th 2010, 10:43 AM
wonderboy1953
I think it's just convention.
• Oct 18th 2010, 11:03 AM
Soroban

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.

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