CHEMISTRY UNCERTAINTY

Question

what is the uncertainty of these measurements

write as +/- the number and the unit

1) 1.O569g _____

2) 7.56mL _______

3) 1.815cm _______

Answer 1

1.0569 grams = 1.0569 +/- 0.00005 grams.

it was rounded up or down by 0.00005 grams

or possibly not rounded at all, but exactly 1.0569, although extremely unlikely,

so unlikely as to be zero probability of being exactly 1.0569

that 5th & more digits to the right of the decimal point could have been as high as 0.00004999...

or the 4th digit and more digits could have been as low as 0.00058000...

1.0569 means the actual number could be anywhere in the interval (1.05685, 1.05694999...)

or 1.0569 + or - 0.00005

1.05685 as low as possible, including that lower limit

1.05695 the upper limit but not including that upper limit

given the usual practice of rounding up to next highest digit if half a digit or more

and rounding down if less than half a digit

although some people round to nearest even integer.

which in this case would round the 1.05685 down to 1.0568, not up to 1.0569

in that case, the +/- does not include either end point

8.5 gets usually rounded up to 9 (but down to 8 if going for the nearest even integer)

9.5 gets rounded up to 10

9.4999... gets rounded down to 9

7.56 mL

= 7.56 +/- 0.005 mL

1.815 cm

= 1.815 +/- 0.0005 cm

All the above is based on rounding practice.

but if the problem is about statistical margins of error, it all depends on

confidence intervals, alpha level, and sample size,

but nothing in the problem gives enough information to calculate a confidence interval