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Significant Digits

Significant Digits. Ch 1 Notes. Significant Digits. Why pay attention to significant digits? (Essential Question) Used to round measured values when involved in calculations Used to guarantee that the calculated values are not shown to be more precise than the measurements.

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Significant Digits

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  1. Significant Digits Ch 1 Notes

  2. Significant Digits • Why pay attention to significant digits? (Essential Question) • Used to round measured values when involved in calculations • Used to guarantee that the calculated values are not shown to be more precise than the measurements

  3. Significant Digits • 1. Nonzero #’s are always significant 349 3 sig figs 1639 4 sig figs

  4. Significant Digits • 2. Leading Zeros are never significant 0.0055 2 sig figs 0.0000000393 3 sig figs .000004821 4 sig figs

  5. Significant Digits • 3. Captive Zeros are always significant 5908 4 sig figs 2100004 7 sig figs 60900932 8 sig figs

  6. Significant Digits • 4. 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 800 1 sig fig

  7. Significant Digits • 5. When in scientific notation, all numbers on left side of number are significant • 2.94 x 10-3 3 sig figs 3.06910 x 106 6 sig figs 6.02 x 1023 3 sig figs

  8. Operations with Sig Figs • Multiplication/Division rule (LT #9) 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

  9. Operations with Sig Figs • Addition/Subtraction Rule (LT #10) 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

  10. Sig Fig Examples #1: 23.0 4.25 + 25,620 #2: 2.3 x 10-4 316

  11. Examples Solutions #1: 23.0 4.25 + 25,620 25,647.25 rounds to25,650 #2: 2.3 x 10-42sf 316 3sf = 7.27 x 10-7 rounds to 7.3 x 10-7

  12. 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

  13. 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

  14. 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

  15. 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

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