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Add to table of contents: • Sci. Not. examples Pg. 10 • Scientific Notation Pg. 11

Measurement & Scientific Notation

What is Data? • Data is any type of information. • Data • Qualitative = description in words • The solution is blue. • Quantitative = measurement with numbers • The solution has a volume of 42.7 mL.

What Is a Measurement? • Quantitative observation. • Comparison to an agreed upon standard. • Every measurement has a number and a unit. • The unit tells you to what standard you are comparing your object.

Scientists have measured the average global temperature rise over the past century to be0.6 °C • °C tells you that the temperature is being compared to the Celsius temperature scale. • 0.6 tells you that: • The average temperature rise is 0.6 times the standard unit of 1 degree Celsius. • The confidence in the measurement is such that we are certain the measurement is between 0.5 and 0.7 °C.

Scientific Notation A way of writing large and small numbers.

An atom’s average diameter is 0.000 000 000 3 m. Big and Small Numbers • We commonly measure objects that are many times larger or smaller than our standard of comparison. • Writing large numbers of zeros is tricky and confusing. • Not to mention there’s the 8-digit limit of your calculator! The sun’s diameter is 1,392,000,000 m.

An atom’s average diameter is 3 x 10-10 m. Scientific Notation • Each decimal place in our number system represents a different power of 10. • Scientific notation writes the numbers so they are easily comparable by looking at the power of 10. The sun’s diameter is 1.392 x 109 m.

Exponents • When the exponent on 10 is positive, it means the number is that many powers of 10 larger. • Sun’s diameter = 1.392 x 109 m = 1,392,000,000 m. • When the exponent on 10 is negative, it means the number is that many powers of 10 smaller. Average atom’s diameter=3 x 10-10m=0.0000000003 m.

Exponent 1.23 x 10-8 Decimal part Exponent part Scientific Notation • To compare numbers written in scientific notation: • First compare exponents on 10. • If exponents are equal, then compare decimal numbers 1.23 x 105 > 4.56 x 102 4.56 x 10-2 > 7.89 x 10-5 7.89 x 1010 > 1.23 x 1010

Writing Numbers in Scientific Notation 1. Locate the decimal point. 2. Move the decimal point so that there is only 1 nonzero digit to the left of it. 3. Multiply the new number by 10n . • Where n is the number of places you moved the decimal point. 4. If you moved the decimal point to the left, then n is +; if you moved it to the right, then n is − . • If the original number is 1 or larger, then n is + . • If the original number is less than 1, then n is − .

Writing a Number in Scientific Notation, Continued 12340 1. Locate the decimal point. 12340. • Move the decimal point so that there is only 1 nonzero digit to the left of it. 1.234 3. Multiply the new number by 10n . • Where n is the number of places you moved the decimal point. 1.234 x 104 4. If you moved the decimal point to the left, then n is +; if you moved it to the right, then n is − . 1.234 x 104

Writing a Number in Scientific Notation, Continued 0.00012340 1. Locate the decimal point. 0.00012340 2. Move the decimal point to obtain a number between 1 and 10. 1.2340 3. Multiply the new number by 10n . • Where n is the number of places you moved the decimal point. 1.2340 x 104 4. If you moved the decimal point to the left, then n is +; if you moved it to the right, then n is − . 1.2340 x 10-4

Writing a Number in Standard Form 1.234 x 10-6 • Since exponent is -6, make the number smaller by moving the decimal point to the left 6 places. • When you run out of digits to move around, add zeros. • Add a zero in front of the decimal point for decimal numbers. 000 001.234 0.000 001 234

123.4 = 1.234 x 102 145000 = 1.45 x 105 25.25 = 2.525 x 101 1.45 = 1.45 x 100 8.0012 = 8.0012 x 100 0.00234 = 2.34 x 10-3 0.0123 = 1.23 x 10-2 0.000 008706 = 8.706 x 10-6 Practice—Write the Following in Scientific Notation, Continued

Multiplying and Dividing in Scientific Notation • Multiplying • Multiply the two decimal parts of each number and ADD the exponents • (3.32x105) * (2.56x107) = 8.50x1012 • Dividing • Divide the two decimal parts of each number and SUBTRACT the exponents • (8.56x1017) / (3.61x104) = 2.37x1013 • You may need to convert the final answer into proper scientific notation by moving the decimal and changing the exponent • (5.87x103) * (6.53x105) = 38.33x108 = 3.833x109

Stop here!

1.23 Input 1.23 +/- -1.23 Press EXP -1.23 00 Press -1.23 03 Input 3 +/- -1.23 -03 Press Inputting Scientific Notation into a Calculator -1.23 x 10-3 • Input the decimal part of the number. • If negative press +/- key. • (–) on some. • Press EXP. • EE on some. • Input exponent on 10. • Press +/- key to change exponent to negative.

Sci. Notation Example • The U.S. population in 2007 was estimated to be 301,786,000 people. Express this number in scientific notation. • 301,786,000 people = 3.01786 x 108 people

123.4 145000 25.25 1.45 8.0012 0.00234 0.0123 0.000 008706 Practice—Write the Following in Scientific Notation

2.1 x 103 9.66 x 10-4 6.04 x 10-2 4.02 x 100 3.3 x 101 1.2 x 100 Practice—Write the Following in Standard Form

2.1 x 103= 2100 9.66 x 10-4= 0.000966 6.04 x 10-2= 0.0604 4.02 x 100= 4.02 3.3 x 101= 33 1.2 x 100= 1.2 Practice—Write the Following in Standard Form, Continued

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