 # Significant Figures & Scientific Notation

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Significant Figures & Scientific Notation

Rules for Significant Digits
1. All non-zero numbers (1-9) are significant (meaning they count as sig figs) 613 = 3 sig figs = 6 sig figs 2. Zeros located between non-zero digits are ALWAYS significant (they count) 5004 = 4 sig figs 602 = 3 sig figs = 16 sig figs!

Rules for Significant Digits
3. Trailing zeros (those at the end) are significant only if the number contains a decimal point; otherwise they are insignificant (they don’t count) 5.640 = 4 sig figs = 6 sig figs = ONLY 2 sig figs 4. Placeholder Zeros at the beginning of a decimal number are not significant = 3 sig figs 0.052 = 2 sig figs = ONLY 2 sig figs!

Limits of Measurement Significant figures are all the digits that are known in a measurement, plus the last digit that is estimated. The precision of a calculated answer is limited by the least precise measurement used in the calculation.

Limits of Measurement Addition & Subtraction: The solution to the calculation is limited by the least precise measurement: = Limited to only one place past the decimal Correct answer = 162.7

Multiplication & Division:
Limits of Measurement Multiplication & Division: The solution to the calculation is limited by the measurement with the least number of sig figs: 40.9 x 7.2 = Limited to only 2 sig figs  Round the number Correct Answer = 290 240/6 = 40 Limited to only 1 sig fig  40 only has 1 sig fig (no decimal)

Using Scientific Notation
Why is scientific notation useful? Scientists often work with very large or very small numbers. Astronomers estimate there are 200,000,000,000 stars in our galaxy. The nucleus of an atom is about meters wide. These an be awkward numbers to fully write out and read.

Using Scientific Notation
Scientific notation expresses a value in two parts: First part: a number between 1 and 10 Second part: “10” raised to some power Examples: 105 = 10 x 10 x 10 x 10 x 10 = 100,000 10-3 = 1/10 x 1/10 x 1/10 = 0.1 x 0.1 x 0.1 = 0.001 The 2 parts are then multiplied Example: 5,430,000 = 5.43 x 106

Using Scientific Notation
General Form is: A.BCD… x 10Q Numbers GREATER that 1 have POSTIVE Q’s (exponents) Example: x 104 = 12,300 Numbers LESS than 1 have NEGATIVE Q’s (exponents) Example: 7.6 x 10-5 =

Using Scientific Notation
“Placeholder” zero’s are dropped Placeholders are used between the last non-zero digit and the decimal (even if decimal is not shown) Examples: 2,570 = 2.57 x 103 583,000 = 5.83 x 105 15,060 = x 104 = 5.6 x 10-3 = x 10-2

Standard to Scientific Notation
Move the decimal to create a number between 1-10 (there should never be more than one number to the left of the decimal!) Drop any zeros after the last non-zero number Example: 6,570  6.57 Write the multiplication sign and “10” after the new number Example: 6.57 x 10

Standard to Scientific Notation
The number of spaces you moved the decimal from its original place to create the new number becomes the EXPONENT Example: 6.57 x 103 If the original number was GREATER than 1 you are done (the exponent will remain positive). If the original number was LESS than 1 (a decimal number) then your exponent will be NEGAVTIVE Example:  x 10-3

Scientific Notation to Standard
Start with the EXPONENT  x 105 Number of spaces & direction Positive Exp – ending number greater than 1 Negative Exp – ending number less than 1 Move decimal the designated number of spaces   50903_. Fill in empty spaces with ZERO’s  509,030.

Go to Worksheet Problems

Worksheet Problems 46,583,000 = 2.0094 x 103 = 0.0000945 =
90,294 = = 390 = x 107 2, x ,300, x x x 102

Worksheet Problems 5.928 x 100 = 3.872 x 101 = 90,827 = 100 =
8,940 = x 106 = x 10-4 = x x x 103 3,583,

Worksheet Problems 67,290 = 0.000027 = 0.001435 = 8.9 = 409 =
x 104 = x 10-1 = 50,903 = 6.729 x x x x x , x 104