1. The precision of all measuring devices is limited! Because of this limitation, there are a limited number of digits that can be valid for any measurement. These valid digits are called the significant digits or significant figures. You should read the scale on the meter stick to the nearest millimeter. Then you can estimate any remaining length as a fraction of a millimeter. The wood strip above is somewhat longer than 5.6 cm or 56 mm. Looking closely at the scale, you can see the end of the strip is about 4/10th of the way between 56mm and 57mm. Therefore, the length is best stated as 56.4mm. The last digit is an estimate. It might be 4 but is likely not to be any greater than 5 or less than 3. You measurement, 56.4mm, contains 3 significant digits. There are 2 digits you are for sure of 5 and 6 and one estimated digit 4. 56 Wood Strip 5.6 cm 5.64 cm Suppose you measure the length of a strip of wood with a meter stick. The smallest division you can see on the meter stick is a millimeter.

2. Suppose that the end of the wood strip is exactly on the 56 mm mark. In this case, you should record the measurement as 56.0 mm. The zero indicates that the strip is not 0.1 mm more or less than 56 mm. The zero is a significant digit because it informs us about the precision of the measurement. It is the uncertain or estimated digit, but it is significant. The last digit of a measurement is always estimated or uncertain. 56 5.60 cm Wood Strip

3. 1. Non zero’s are always significant. 2. All final zeros after a decimal point are significant. 3. All zeros between 2 significant numbers are signifigant. 6. Always put zeros in front of decimal points. For example do not write,.12 as an answer, but instead 0.12. To write.12 can often be confused thus a wrong answer. 5. Significant digits only apply to measurement and all measurements must have a number and units to follow the number. (like 0.2 cm – the unit is centimeters) 4. Zeros used for spacing or place holders are not significant. 2 How many significant figures? 47 355 132

4. Practice Problems Sig Figs: Write down the number of Sig Figs for each of the following measurements. 1)617 in = 4) 5.62 x 10 6 yd = 2) 81.000 day =5) 0.001301 ns = 3) 0.00002 ft = 6) 93,500,200 miles = 3 Round these numbers to 3 sig figs: 7) 31.521678 m = 8) 2015.67812090 m = 9) 0.003145298 m= 10) 100.00412 m = 11) 6.7803211 x 10 -6 m = 31.5m 2020m 0.00315 m 100.m 6.78 x 10 -6 m 5 1 3 4 6

5. Practice Problems Sig Figs: Round to the correct number of sig figs: 65.2m 2 63 m/s 1 x 10 6 kg/s 29.7 s 1) 8.91 m * 7.3214 m = 2) 7.8 m / 0.123 s = 3)8712 kg / 0.007 s = 4) 25.612 s + 4.1 s =

6. Scientist often work with very large and very small quantities. These numbers are too big when written like this!! They take up much space and are difficult to use in calculations. To work with such numbers more easily, we write them in shortened form by expressing decimal places as powers of ten. The mass of Earth is about 6,000,000,000,000,000,000,000,000 kg The mass of a proton is about 0.00000000000000000000000000167 kg Dang, I’m kinda a light weight Scientific Notation is based on exponential notation. In scientific notation, the numerical part of a measurement is expressed as a number between 1 and 10 multiplied by a whole number power of 10. For Example: M x 10 n where M is between 1 and 9.999999... and n is a positive or negative number. This method of expressing numbers is called exponential notation.

7. Writing Scientific Notation: Move the decimal point until only one non-zero digit remains on the left. Do not include zeros before or after last number (remember significant figures). Count the number of places the decimal point was moved and use that number as the exponent of ten. 1,300 0.0000105 7,920,800 1,300 Try these examples: 1. 0.00000752 = 2. 9,234,000,000 = 0.0000105 7,920,800  1.3  1.05  7.9208  1.3 x 10 3 (decimal moved 3 to left)  1.05 x 10 -5 (decimal moved 5 to right)  7.9208 x 10 6 (decimal moved 6 to left) 7.52 x 10 -6 9.234 x 10 9

8. Scientific Notation into numerical form Remember if it is a positive number it is going to make the number bigger. So 5.25 x 10 6 -  5,250,000 If it is a negative number it is going to make the number smaller. So 4.5 x 10 -4 -  0.00045 Try these examples: 3) 6.3 x 10 5 =4) 7.21 x 10 -2 = 630,000 0.0721

9. To multiply two scientific notation numbers, you multiply the coefficients and add the exponents that are to the power of ten. To divide two scientific notation numbers, you divide the coefficients and subtract the exponents that are to the power of ten. Scientific Notation Math Example Hence 3 x 10 4 * 2 x 10 5 = (3 * 2 = 6) [multiply] x 10 (4 + 5 = 9) [add] = 6 x 10 9 3 x 10 4 * 2 x 10 5 First, multiply the coefficients 3 * 2 = 6 Second, add the exponents 4 + 5 = 9 6 x 10 5 / 2 x 10 4 Example Hence 6 x 10 5 / 2 x 10 4 = (6 / 2 = 3) [divide] x 10 (5-4 = 1) [sutract] = 3 x 10 1 or 30 First, divide the coefficients 6 / 2 = 3 Second, subtract the exponents 5 - 4 = 1

10. 1. Make sure you are in scientific notation (SCI). Either find SCI or push mode and then SCI. 2.Put in the numbers using E. The “E” stands for x 10 so you do not need both. The E on your calculator may be “EXP”, “EE” or “E” Do not choose lower case e which stands for exponential. For 8.0 x 10 8 / 2.0 x 10 10 Push 8E8 / 2E10 =... Did you get 4E-2??: Try these: 9.76 x 10 11 / 1.754 x 10 -5 = ________ 3.76 x 10 17 / 8.943 x 10 -9 = ________ 5.56E16 4.20E25

11. Extra Warm-Up problems Write the number of Sig Figs for the following measurements. 1)6170 m = 2)81.340 day = 3)0.03032 s = 3 5 4 4)5.62 x 10 6 yd = 5)2.00130 kg = 6)93,500,200. miles = Round these numbers to 4 sig figs: 7) 33.621678 m = 8)410,145.6 m = 9)0.03673679 m = 10) 9,000.00412 m = 11) 6.7803211 x 10 -6 m = 12) 0.999967 m = 33.62 m 410,100 m 0.03674 m 9,000. m 6.78 x 10 -6 m 1.000 m 3 8 6