Rounding in the Sciences; Sig Figs and Calculations

what is a similarity between the final answer from a calculation that uses sigfigs and its beginning measurements

the final answer must have the same level of Accuracy as well as precision as all the measurements in the calculation started with. Cannot make worse/better, must match.

- reason why we choose the least precise measurement in the calculation is to ensure that the final answer reflects the limitations of the least accurate measurement used.

Rules for Rounding in Science

1. If the number you are dropping is less than 5, the number in front of it will be left as is.

   ex. 17.32cm to 17.3cm

2. If the number you are dropping is greater than 5, the number in front of it will be increased by 1.

   ex. 42.68g to 42.7g

the next rules are for dropping 5

3. If the number you are dropping is a 5, and there are other non-zero numbers behind the 5, the number in front of 5 will be increased by 1

   42.359g to 42.36g

4. a. If the digit to be dropped is a 5, and there

   are ONLY ZERO(S) OR NOTHING

   behind the 5, the number in front of the 5 is increased by 1 if it is an odd number (1, 3, 5, 7, 9)

   ex. 4.3750c to 3 sigfigs - 4.38

   4.-bIf the digit to be dropped is a 5, and there are only zero(s) or nothing behind the 5, the number in front of the 5 is kept as is if it is an even number (0, 2, 4 , 6, 8)

   ex. 4.3650c to 3 sigfigs - 4.36c

Calculations with Multiplication and Division

the final answer must have the same number of significant figures as the measurement with the least number of significant figures used in the calculation.

ex. 4.3g/44.002mL = 0.09772283
(2 SF) = 0.098g/mL

Calculations using Subtraction/Addition

the final answer must have the same number of decimal places as the measurement with the least number of decimal places used in the calculation. For example, 12.11 + 0.3 = 12.41, but rounded to 12.4.