Topic 1: Mathematical Conventions

Question 1

scientific notation rules

Answer 1

from scientific notation to decimal notation (5.0x10^3 = 5000):
positive exponent: decimal moves to right (large numbers)
negative exp: decimal moves left (small numbers <1)
opposite for decimal to scientific (127 = 1.27x10^2)

Question 2

5 significant digits rules

Answer 2

1. digits 1-9 are significant
2. zeros between 2 non zero digits are significant
3. zeros right of non zero digit is significant if it’s also to right of decimal
4. zeros right of non zero digit without a decimal is significant
5. zeros left of non zero digits are not significant

Question 3

calculation w/ sig digs

Answer 3

answer has same sig digs as the fewest sig digs in the question (ex. 4.02+0.001: 3 is the number of sig digs for answer = 4.02)

Question 4

measurement uncertainy

Answer 4

• an error associated with the precision of equipment for measuring things
• # of decimal places a measurement is rounded to must be same as # of decimals in uncertainty
• ex. scale: if uncertainty is +/-0.01g, when recording mass it should be rounded to 2 decimal places (42.11g)

Question 5

analogue equipment uncertainty

Answer 5

• uncertainty is half of smallest scale division
• ex. ruler: if smallest scale is 0.1cm, uncertainty is +/-0.05cm; so answer is rounded to 2 decimal places