Significant Digits Ch 1 Notes

Significant Digits Used to round measured values when involved in calculations When in scientific notation, all numbers on left side of number are significant

Significant Digits Nonzero #’s are always significant 3493 sig figs sig figs

Significant Digits Leading Zeros are never significant sig figs sig figs Captive Zeros are always significant sig figs sig figs

Significant Digits Trailing Zeros are significant IF there is a decimal point in the # 8001 sig fig sig figs sig figs sig figs

Operations with Sig Figs Multiplication/Division rule: Retain the same number of sig figs in the answer as the factor containing the least number of sig figs. 4.5 x 2 = 9.0 rounds to x 21 = 42000rounds to x 3 x 212 = 6996 rounds to 7000

Operations with Sig Figs Addition/Subtraction Rule leave the answer rounded to the same precision (same decimal place) as the least precise number involved in the operation = 4.3 rounds to = 131 rounds to – 2.90 = 1.75 rounds to 2

Sig Fig Examples #1: ,620 #2:2.3 x

Examples Solutions #1: ,620 25, , rounds to 25,650 #2:2.3 x sf 316 3sf =7.27 x rounds to 7.3 x 10 -7

Sig Fig Situation #1: Let’s Not But Say We Did Don’t worry about rounding combo problems until all the work in the calculator is done, but heed the rules as if you did to find out # of digits needed in the end: ( ) / 357 = (6.4454)/357 = Rounding: addition to tenths digit, which would leave 2 sig figs. 2 sig figs divided by 3 sig figs leaves 2 in answer: 0.018

Sig Fig Situation #2: Less than Zero 2000 (1 sig fig) vs (4 sig figs) What if you want 2000 to have 4 sig figs like 2001? x 10 3 for 4 sig figs 2.00 x 10 3 for 3 sig figs 2.0 x 10 3 for 2 sig figs 2 x 10 3 for 1 sig fig

Sig Figs Situation #3: Exact #’s Whenever a quantity has no uncertainty, it does not affect the # of sig figs in answer if x/÷/+/- Ex: four sides of a square…if one side has a length of 2.0 m, then 4 (exact #) x 2.0 m = 8.0 m (retain two sig figs cause exact # doesn’t matter to sig fig rounding

Sig Figs Situation #4: Units! Units are to be treated in the same algebraic sense as variables Units do not affect sig figs but must be common to add/subtract values 23 g g = rounds to 55 g 23 g x g = rounds to 740 g 2 23 kg + 27 ml cannot be simplified