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Sig digs Significant Digits

Sig digs Significant Digits. What is a significant digit?. There are 2 kinds of numbers: Exact : the amount of money in your account. Known with certainty . Approximate : weight, height—anything MEASURED. No measurement is perfect. When to use Significant digits.

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Sig digs Significant Digits

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  1. Sig digs Significant Digits

  2. What is a significant digit? • There are 2 kinds of numbers: • Exact: the amount of money in your account. Known with certainty. • Approximate: weight, height—anything MEASURED. No measurement is perfect.

  3. When to use Significant digits • If you measured the width of a paper with your ruler you might record 21.7cm. • To a mathematician 21.70, or 21.700 is the same.

  4. But, to a scientist 21.7cm and 21.70cm is NOT the same • 21.700cm to a scientist means the measurement is accurate to within one thousandth of a cm.

  5. But, to a scientist 21.7cm and 21.70cm is NOT the same • If you used an ordinary ruler, the smallest marking is the mm, so your measurement has to be recorded as 21.7cm.

  6. How do I know how many Sig digs? • Rule: All digits are significant starting with the first non-zero digit on the left.

  7. How do I know how many Sig digs? • Exception to rule: In whole numbers that end in zero, the zeros at the end are not significant.

  8. How many Sig digs? • 7 • 40 • 0.5 • 0.00003 • 7 x 105 • 7,000,000 • 1 • 1 • 1 • 1 • 1 • 1

  9. How do I know how many Sig digs? • 2nd Exception to rule: If zeros are sandwiched between non-zero digits, the zeros become significant.

  10. How do I know how many Sig digs? • 3rd Exception to rule: If zeros are at the end of a number that has a decimal, the zeros are significant.

  11. How do I know how many Sig digs? • 3rd Exception to rule: These zeros are showing how accurate the measurement or calculation are.

  12. How many Sig digs here? • 1.2 • 2100 • 56.76 • 4.00 • 0.0792 • 7,083,000,000 • 2 • 2 • 4 • 3 • 3 • 4

  13. How many Sig digs here? • 3401 • 2100 • 2100.0 • 5.00 • 0.00412 • 8,000,050,000 • 4 • 2 • 5 • 3 • 3 • 6

  14. What about calculations with Sig digs? • Rule: When adding or subtracting measured numbers, the answer can have no more places after the decimal than the LEAST of the measured numbers.

  15. Add/Subtract examples • 2.45cm + 1.2cm = 3.65cm, • Round off to = 3.7cm • 7.432cm + 2cm = 9.432 round to  9cm

  16. Multiplication and Division • Rule: When multiplying or dividing, the result can have no more significant digits than the least reliable measurement.

  17. A couple of examples • 56.78 cm x 2.45cm = 139.111 cm2 • Round to  139cm2 • 75.8cm x 9.6cm = ?

  18. How many significant digits does each of these numbers have? 1) 5.40 ____ 6) 1.2 x 103 ____ 2) 210 ____ 7) 0.00120 ____ 3) 801.5 ____ 8) 0.0102 ____ 4) 1,000 ____ 9) 9.010 x 10-6 ____ 5) 101.0100 ____ 10) 2,370.0 ____

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