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Significant Figures

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

brenden-maynard
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Significant Figures

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  1. Significant Figures

  2. What is a significant figure? • There are 2 kinds of numbers: • Exact: the amount of money in your account. Known with certainty.

  3. What is a significant figure? • Approximate: weight, height—anything MEASURED. No measurement is perfect.

  4. When to use Significant figures • When a measurement is recorded only those digits that are dependable are written down.

  5. When to use Significant figures • 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.

  6. 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.

  7. 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.

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

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

  10. 7 40 0.5 0.00003 7 x 105 7,000,000 1 1 1 1 1 1 How many sig figs?

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

  12. How do I know how many Sig Figs? • 3rd Exception to rule: If zeros are at the end of a number that has a decimal, the zeros are significant. (showing how accurate the measurement is)

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

  14. Scientific Notation A short-hand way of writing large numbers without writing all of the zeros.

  15. The Distance From the Sun to the Earth 93,000,000

  16. Step 1 • Move decimal left • Leave only one number in front of decimal 93,000,000 = 9.3000000

  17. Step 2 • Write number without zeros 93,000,000 = 9.3

  18. 7 93,000,000 = 9.3 x 10 Step 3 • Count how many places you moved decimal • Make that your power of ten

  19. The power of ten is 7 because the decimal moved 7 places. 7 93,000,000 = 9.3 x 10

  20. 93,000,000 --- Standard Form • 9.3 x 107 --- Scientific Notation

  21. 9.85 x 107 -----> 6.41 x 1010 -----> 2.79 x 108 -----> 4.2 x 106 -----> Practice Problem Write in scientific notation. Decide the power of ten. • 98,500,000 = 9.85 x 10? • 64,100,000,000 = 6.41 x 10? • 279,000,000 = 2.79 x 10? • 4,200,000 = 4.2 x 10?

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