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Wood Strip

Significant Digits (Figures).

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Wood Strip

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  1. Significant Digits (Figures) Because the precision of all measuring devices is limited, the number of digits that are valid for any measurement is also limited. The valid digits are called the significant digits. Suppose you measure the length of a strip of wood with a meter stick. The smallest division on the meter stick is a millimeter 5.6 cm 5.64 cm Wood Strip • You should read the scale to the nearest millimeter then 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. Wood Strip 5 5 6 6 5.60 cm Suppose that the end of the wood strip is exactly on the 56 mm mark. In this case, you should record the measurement as 56.0mm. 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 transmits information 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.

  2. Significant Digits (Figures) Rules of Significant digits: 1 2 3 4 5 6 7 8 9 1. Non zero’s are always significant. 2.0 5.230 1116.210 2. All final zeros after a decimal point are significant. How many significant figures? 2 4 7 504 1020.5 3.0001 3. All zeros between 2 significant numbers are signifigant. How many significant figures? 3 5 5 30 0.000321 320,000 4. Zeros used for spacing or place holders are notsignificant. How many significant figures? 1 3 2 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) 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.

  3. Practice Problems Sig Figs: Write down the number of Sig Figs for each of the following measurements. 3 • 617 in = • 81.000 day = • 0.00002 ft = • 5.62 x 106 yd = • 0.001301 ns = • 93,500,200 miles = 5 1 3 4 6

  4. Practice Problems Sig Figs: Round these numbers to 3 sig figs: 1) 31.521678 m = 2) 2015.67812090 m = • 0.003145298 m= • 100.00412 m = • 6.7803211 x 10-6 m = 31.5m 2020m 0.00315 m 100.m 6.78 x 10-6m

  5. Practice Problems Sig Figs: Round to the correct number of sig figs: 1) 8.91 m * 7.3214 m = 2) 7.8 m / 0.123 s = • 8712 kg / 0.007 s = 4) 25.612 s + 4.1 s = 65.2m2 63 m/s 1 x 106kg/s 29.7 s

  6. Warm-Up for August 30th • 5.62 x 106 yd = • 2.00130 kg = • 93,500,200. miles = 3 • 6170 m = • 81.340 day = • 0.03032 s = 3 Write the number of Sig Figs for the following measurements. 6 5 8 4 Round these numbers to 4 sig figs: 7) 33.621678 m = • 410,145.6 m = • 0.03673679 m = • 9,000.00412 m = • 6.7803211 x 10-6 m = • 0.999967 m = 33.62 m 410,100 m 0.03674 m 9,000. m 6.78 x 10-6m 1.000 m

  7. Scientific Notation • Scientist often work with very large and very small quantities. • The mass of Earth is about • 6,000,000,000,000,000,000,000,000 kg Dang, I’m kinda a light weight • The mass of a proton is about • 0.00000000000000000000000000167 kg • Written in this form, the quantities 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. This method of expressing numbers is called exponential notation. • 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. M x 10n where M is between 1 and 9.999999 . . . and n is a positive or negative number.

  8. Scientific Notation 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). •  1.3 • 1,300 •  1.05 • 0.0000105 •  7.9208 • 7,920,800 • Count the number of places the decimal point was moved and use that number as the exponent of ten. • 1.3 x 103 (decimal moved 3 to left) • 1,300 • 1.05 x 10-5 (decimal moved 5 to right) • 0.0000105 • 7,920,800 •  7.9208 x 106(decimal moved 6 to left) Try these examples: 1. 0.00000752 = 2. 9,234,000,000 = 7.52 x 10-6 9.234 x 109

  9. Scientific Notation • Scientific Notation into numerical form • Remember if it is a positive number it is going to make the number bigger. • So 5.25 x 106 will move the decimal so that you get a bigger number. • Move decimal 6 times to right. 5,250,000 • If it is a negative number it is going to make the number smaller. • So 4.5 x 10-4 will move the decimal so that you get a smaller number. • Move decimal 4 times to the left. 0.00045 • Try these examples: • 3. 6.3 x 105= 4.721 x 10-2= 630,000 0.04721

  10. Scientific Notation Scientific Notation Math • To multiply two scientific notation numbers, you multiply the coefficients and add the exponents that are to the power of ten. • Example • 3 x 104 * 2 x 105 • 3 * 2 = 6 • First, multiply the coefficients • 4 + 5 = 9 • Second, add the exponents • Hence • 3 x 104 * 2 x 105 = (3 * 2 = 6) [multiply] x 10(4 + 5 = 9) [add]= 6 x 109 • To divide two scientific notation numbers, you divide the coefficients and subtract the exponents that are to the power of ten. • Example • 6 / 2 = 3 • First, divide the coefficients • 6 x 105 / 2 x 104 • 5 - 4 = 1 • Second, subtract the exponents • Hence • 6 x 105 / 2 x 104 = (6 / 2 = 3) [divide] x 10(5-4 = 1) [sutract] = 3 x 101 or 30

  11. Scientific Notation Video • http://www.teachertube.com/viewVideo.php?video_id=119236 • http://htwins.net/scale2/

  12. Scientific Notation Calculator – to use a calculator to check your answers. 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 example #9 – You will put 4E5 * 2E6 = ... You hopefully got 8E11 which means 8 x 1011. Try these examples: 11.9.76 x 1011 / 1.754 x 10-5 = _________________ 12. 3.76 x 1017 / 8.943 x 10-9 = _______________ On all boards problems give answer in both numerical and scientific notation format: Boards 1: 4.0 x 10-3 / 1.0 x 10-7 = Boards 2: 1.6 x 10-5 – 4.0 x 10-6 = Boards 3: (Use calculator) 7.1567 x 1017 / 3.87 x 1019 = Boards 4: Johnny wants to go to the moon(which is 2.39 x 105 miles away) , if he travels at a constant speed of 6.78 x 103 mph, how long will it take him to get there.

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