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SCIENTIFIC NOTATION

SCIENTIFIC NOTATION. 5.67 x 10 5 Coefficient Base Exponent

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SCIENTIFIC NOTATION

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  1. SCIENTIFIC NOTATION 5.67 x 105 • Coefficient • Base • Exponent • 1. The coefficient must be greater than or equal to 1 and less than 10.2. The base must be 10.3. The exponent must show the number of decimal places that the decimal needs to be moved to change the number to standard notation.  A negative exponent means that the decimal is moved to the left when changing to standard notation.

  2. EXAMPLES 102 • = 10 X 10  100 10-4 • =.0001 6.03 x 107 • Remember • 107 = 10 x 10 x 10 x 10 x 10 x 10 x 10 = 10 000 000 • 6.03 x 107 = 6.03 x 10 000 000 = 60,300,000

  3. NEGATIVE • Change 5.3 x 10-4 to standard notation • The exponent tells us to move the decimal four places to the left • = 0.00053 • Change 0.000000902 into SN • 9.02 x 10-7

  4. DIVIDE SN • Ex. 1 Divide 3.5 x 108 by 6.6 x 104 • rewrite the problem as:                 3.5 x 108                                                 _________________                                                          6.6 x 104 • Divide the coefficients and subtract the exponents to get:      0.530303 x 104 • Change to correct scientific notation and round to correct significant digits to get: 5.3 x 103 • Note - We subtract one from the exponent because we moved the decimal one place to the right

  5. MULTIPLY SN • Multiply  (3.45 x 107) x (6.25 x 105) • first rewrite the problem as:     (3.45 x 6.25) x (107 x 105) • Then multiply the coefficients and add the exponents:    21.5625 x 1012 • Then change to correct scientific notation and round to correct significant digits:  2.16 x 1013 • NOTE - we add one to the exponent because we moved the decimal one place to the left

  6. ADD OR SUBTRACT • Add 3.76 x 104 and 5.5 x 102 • move the decimal to change 5.5 x 102 to 0.055 x 104 • add the coefficients and leave the base and exponent the same:  3.76 + 0.055 = 3.815 x 104 • following the rules for rounding, our final answer is 3.815 x 104

  7. Significant Figures • Digits from 1-9 are always significant. • Zeros between two other significant digits are always significant • One or more additional zeros to the right of both the decimal place and another significant digit are significant. • Zeros used solely for spacing the decimal point (placeholders) are not significant.

  8. Examples of Significant Digits • 453 kg • 3 • All non-zero digits are always significant. • 5057 L • 4 • Zeros between 2 sig. dig. are significant. • 5.00 • 3 • Additional zeros to the right of decimal and a sig. dig. are significant. • 0.007 • 1 • Placeholders are not sig.

  9. Significant Figures • When multiplying or dividing, your answer may only show as many significant digits as the multiplied or divided measurement showing the least number of significant digits. • When adding or subtracting your answer can only show as many decimal places as the measurement having the fewest number of decimal places.

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