Bell Ringer 1. Name the following hazard signs: A. B. C. D. 2. What is the difference between PRECISION and ACCURACY? ACCURACY?

Significant Figures & Scientific Notation Significant Figures & Scientific Notation

How does the precision of measurements affect the precision of scientific calculations? What’s the difference between accuracy and precision? Limits of Measurement

Accuracy Accuracy is the closeness of a measurement to the actual or correct value of what is being measured. Precision Precision is a gauge of how exact a measurement is or how closely individual measurements agree with each other.

Limits of Measurement Example: Suppose a digital clock is running 15 minutes slow. Although the clock would remain precise to the nearest second, the time displayed would not be accurate. Example: Both Accurate & Precise -

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

If the least precise measurement in a calculation has 3 significant figures, then the calculated answer can have at most 3 significant figures. Mass = grams Mass = grams Volume = 4.42 cubic centimeters. Volume = 4.42 cubic centimeters. Rounding to 3 significant figures, the density is 7.86 grams per cubic centimeter.

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!

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)  = 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  = 2 sig figs  = ONLY 2 sig figs! Rules for Significant Digits

Why is scientific notation useful? Using Scientific Notation 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.

Scientific notation expresses a value in two parts:  First part: a number between 1 and 10  Second part: “10” raised to some power  Examples: 10 5 = 10 x 10 x 10 x 10 x 10 = 100, = 10 x 10 x 10 x 10 x 10 = 100, = 1 / 10 x 1 / 10 x 1 / 10 = 0.1 x 0.1 x 0.1 = = 1 / 10 x 1 / 10 x 1 / 10 = 0.1 x 0.1 x 0.1 = The 2 parts are then multiplied  Example: 5,430,000 = 5.43 x 10 6 Using Scientific Notation

 General Form is: A.BCD… x 10 Q  Numbers GREATER that 1 have POSTIVE Q’s (exponents)  Example: 1.23 x 10 4 = 12,300  Numbers LESS than 1 have NEGATIVE Q’s (exponents)  Example:7.6 x = 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 10 3  583,000= 5.83 x 10 5  15,060= x 10 4  = 5.6 x  = x Using Scientific Notation

Standard to Scientific Notation 1. 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  Write the multiplication sign and “10” after the new number  Example: 6.57 x 10

3. The number of spaces you moved the decimal from its original place to create the new number becomes the EXPONENT  Example: 6.57 x 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 Standard to Scientific Notation

Scientific Notation to Standard 1. Start with the EXPONENT  x Number of spaces & direction 1. Positive Exp – ending number greater than 1 2. Negative Exp – ending number less than 1 2. Move decimal the designated number of spaces   50903_. 3. Fill in empty spaces with ZERO’s  509,030.

Go to Worksheet Problems

Worksheet Problems 1) 46,583,000 = 2) x 10 3 = 3) = 4) x 10 8 = 5) x = 6) 90,294 = 7) = 8) 390 = x , x ,300, x x x 10 2

Worksheet Problems 9) x 10 0 = 10) x 10 1 = 11) 90,827 = 12) 100 = 13) x = 14) 8,940 = 15) x 10 6 = 16) x = x x x ,583,

Worksheet Problems 17) 67,290 = 18) = 19) = 20) 8.9 = 21) 409 = 22) x 10 4 = 23) x = 24) 50,903 = x x x x x , x 10 4