 # Accuracy, Precision, Signficant Digits and Scientific Notation.

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Accuracy, Precision, Signficant Digits and Scientific Notation

Accuracy and Precision Accuracy – refers to how close a given quantity is to an accepted or expected value (page 19) Precision – refers to how exact a measurement is. It also refers to how close measurements are to each other (see page 16 and 19)

Example

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Rules for Significant Digits 1.Digits from 1-9 are always significant. 2.Zeros between two other significant digits are always significant 3.One or more additional zeros to the right of both the decimal place and another significant digit are significant. 4. Zeros used solely for spacing the decimal point (placeholders) are not significant.

Examples of Significant Digits EXAMPLES# OF SIG. DIG.COMMENT 453 kg3 All non-zero digits are always significant. 5057 L4 Zeros between 2 sig. dig. are significant. 5.003 Additional zeros to the right of decimal and a sig. dig. are significant. 0.0071 Placeholders are not sig.

Multiplying and Dividing RULE: 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

Example: When multiplying 22.37 cm x 3.10 cm x 85.75 cm = 5946.50525 cm 3 We look to the original problem and check the number of significant digits in each of the original measurements: 22.37 shows 4 significant digits. 3.10 shows 3 significant digits. 85.75 shows 4 significant digits. Our answer can only show 3 significant digits because that is the least number of significant digits in the original problem. 5946.50525 shows 9 significant digits, we must round to the tens place in order to show only 3 significant digits. Our final answer becomes 5.95 x 10 3 cm 3.

Scientific Notation Use this method to express large numbers and doing calculations by using powers of 10 To do this, count the number of places you have to move the decimal point to yield a value between 1 and 10. This counted number is the exponent. The exponent is positive if the original number is greater than 10 and negative if the original number is less than 10 Examples: a.150 000 000 000 is 1.5 x 10 11 m b.0.000 000 000 050 is 5.0 x 10 -11 m

Adding and Subtracting RULE: When adding or subtracting your answer can only show as many decimal places as the measurement having the fewest number of decimal places.

Example: When we add 3.76 g + 14.83 g + 2.1 g = 20.69 g We look to the original problem to see the number of decimal places shown in each of the original measurements. 2.1 shows the least number of decimal places. We must round our answer, 20.69, to one decimal place (the tenth place). Our final answer is 20.7 g

Practice – sig figs 1) 400 2) 200.03) 0.00014) 218 5) 3.2 x 10 2 6) 0.005307) 22 5688) 4755.50 Answers: 1) 1 2) 4 3) 1 4) 3 5) 2 6) 3 7) 5 8) 6

Practice – Adding and substracting 1) 4.60 + 3 = 2) 0.008 + 0.05 =3) 22.4420 + 56.981 = 4) 200 - 87.3 = 5) 67.5 - 0.009 = 6) 71.86 - 13.1 = Answers 1) 8 2) 0.06 3) 79.423 4) 113 5) 67.5 6) 58.8

Practice – Multiplying and dividing 1) 50.0 x 2.00 = 2) 2.3 x 3.45 x 7.42 = 3) 1.0007 x 0.009 = 4) 51 / 7 = 5) 208 / 9.0 = 6) 0.003 / 5 = Answers 1) 1.00 x 10 2 2) 59 3) 0.009 4) 7 5) 23 6) 0.0006

Rounding Rules 1.If your answer ends in a number greater than 5, increase the preceding digit by 1. Example: 2.346 can be rounded to 2.35 2. If your answer end with a number that is less than 5, leave the preceding number unchanged Example: 5.73 can be rounded as 5.7

Rounding rules continued 3. If you answer ends with 5, increase the preceding number by 1 if it is odd. Leave the preceding number unchanged if it is even. For example, 18.35 can be round to 18.4, but 18.25 is rounded to 18.2