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## Significant Digits

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**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 349 3 sig figs 1639 4 sig figs**Significant Digits**• Leading Zeros are never significant 0.0055 2 sig figs 0.0000000393 3 sig figs • Captive Zeros are always significant 5908 4 sig figs 2100004 7 sig figs**Significant Digits**• Trailing Zeros are significant IF there is a decimal point in the # 800 1 sig fig 2900 2 sig figs 800.0 4 sig figs 2900. 4 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 9 2000 x 21 = 42000 rounds to 40000 11 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. 2 + 2.3 = 4.3 rounds to 4 120 + 11 = 131 rounds to 130 1.65 + 3 – 2.90 = 1.75 rounds to 2**Sig Fig Examples**#1: 23.0 4.25 + 25,620 #2: 2.3 x 10-4 316**Examples Solutions**#1: 23.0 4.75 + 25,620 25,647.75 rounds to25,650 #2: 2.3 x 10-42sf 316 3sf = 7.27 x 10-7 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: • (3.5 + 2.9454) / 357 = (6.4454)/357 = 0.018054341 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. 2001 (4 sig figs) • What if you want 2000 to have 4 sig figs like 2001? 2.000 x 103 for 4 sig figs 2.00 x 103 for 3 sig figs 2.0 x 103 for 2 sig figs 2 x 103 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 + 32.00 g = 55.00 rounds to 55g 23 g x 32.00 g = 736.0000 rounds to 740g2 23 kg + 27 ml cannot be simplified