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Significant digits

Significant digits. Objectives: State the purpose of significant digits State and apply the rules for counting and doing calculations with significant digits. One way engineers use significant digits…. What's so significant about significant digits?. Significant digits.

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Significant digits

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  1. Significant digits Objectives: State the purpose of significant digits State and apply the rules for counting and doing calculations with significant digits

  2. One way engineers use significant digits….

  3. What's so significant about significant digits?

  4. Significant digits • Measurements that indicate the precision of the tool used • Important—we want to let other scientists and engineers know how “good” our measurements are!

  5. 3.42 cm • This means: • My tool had markings to the tenths place (I can COUNT them) • I estimated the hundredths place (the object was between 3.4 and 3.5 but closer to 3.4) •  3 significant digits

  6. 3900 cm • This means: • My tool had markings to the thousands place (I could COUNT them) • I estimated the hundreds place (the object was between 3000 and 4000 but much closer to 4000 ) •  2 significant digits

  7. 3900. cm • This means: • My tool had markings to the tens place (I could COUNT them) • I estimated the ones place (the object appeared to be right at 3900) •  4 significant digits

  8. Clues: How to know when a number is significant • It is a non-zero (1, 2, 3, 4, 5, 6, 7, 8, 9) • It is a zero at the END of a decimal AFTER a decimal point (4.500) • It is a zero between non-zeros (5,005) • It is a zero at the end of a whole number AND there is a decimal (50.)

  9. Rules for counting significant digits: • 2300 • 2300Non-zeros are significant • 2300 zeros are at the end of a number without a decimal = insignificant • 2300 = 2 s.f. • This means the tool allowed us to COUNT the thousands place, and estimate the hundreds place (we counted to 2000 and we estimated the value was between 2000 and 3000, but closer to 2000.)

  10. Counting significant digits: • 230. • 230. Non-zeros = significant • 230. zero here is at the end of a number WITH a decimal = significant • 230. = 3 s.f • This means the tool allowed us to COUNT to the ones place 230 and we estimated that the value was exactly at 230.

  11. Counting significant digits: • 2.300 x 10-3 • BIG IDEA: count the digits of the coefficient only • 2.300 x 10-3 Non-zeros = significant • 2.300 x10-3  zeros here are at the end of a number and AFTER a decimal = significant • 2.300 x 10-3= 4 s.f. • This means the tool allowed us to measure .00230, and we estimated it was exactly at .002300

  12. Counting significant digits - Practice • 0.00400 • 0.00400  Non-zeros = significant! • 0.00400 zeros here are at the beginning of a number = insignificant • 0.00400 zeros here are at the end of a number and AFTER a decimal = significant • 0.00400 = 3 s.f. • This means the tool allowed us to measure 0.0040, and we estimated it was exactly at 0.00400.

  13. Practice • Problems 1-10 on your notes

  14. Compare numbers – which is more precise and how do you know. Game – cc. add this to pracprobs • Give practical example – ie 2 diff thermoms to meas the same temp

  15. Practice - Answers State the number of significant digits. 1) 1234   4 2) 0.023  2 3) 890  2 4) 91010  4 5) 9010.0  5 6) 1090.0010  8 7) 0.00120  3 8) 3.4 x 104 2 9) 9.0 x 10-3 2 10) 9.010 x 10-2 4

  16. Calculations: • Addition and subtraction: USE lowest number of decimal places as the # of decimal places for your answer. Just do add probs in class maybe 1 subt. Prep to not have add and subt, and have it just in case • Another day multiplying and dividing USE least number of total sig figs as the # of sig figs for your answer.

  17. Example:

  18. Example:

  19. Practice • Problems 11-20 in your notes

  20. Practice - Answers • 5.33 + 6.020 = 11.350 11.35 • 5.0 x 8 = 40.0  40 • 81÷ 9.0 = 9.0  9.0 • 3.456 – 2.455= 1.001 1.001 • 5.5 – 2.500 =3.000  3.0 • 7.0 x 200 =1400.0  1000 • 300. ÷ 10.0 = 3.0  3 • (3.0 x 104)x (2.0 x 101)=6.0 x 105  6.0 x 105 • (9.000 x 10-2)÷ (3.00 x 101) =3.000 x 10-3  3.00 x 10-3 • (3.0 x 104) - (2.0 x 101) = 2.998 x 104 3.0 x 104

  21. Exit Ticket

  22. 2300

  23. Counting significant digits: • 450.0 • What do we know about the measurement made? • How many significant digits are in the answer? • Is this number more less precise than the previous answer?

  24. Counting significant digits: • 20 • What do we know about the measurement made? • How many significant digits are in the answer? • Is this number more less precise than the previous answer?

  25. Counting significant digits: • 0.000450 • What do we know about the measurement made? • How many significant digits are in the answer? • Is this number more less precise than the previous answer?

  26. Counting significant digits: • 3,006 • What do we know about the measurement made? • How many significant digits are in the answer? • Is this number more less precise than the previous answer?

  27. Counting significant digits: • 23.00 • 23.00  Non-zeros = significant! • 23.00  zeros here are at the end of a number and AFTER a decimal = significant • 23.00 = 4 s.f. • This means the tool allowed us to measure 23.0, and we estimated it was exactly at 23.0.

  28. Example:

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