Download Scientific Notation, Metric Conversions, and Significant Figures

Scientific Notation To convert a number into scientific notation, follow these steps. Is the first thing a digit 1­9? (Is the number bigger than one or smaller than ­1?) 1) Write the important digits. Important digits are 1­9 and any zeros between them. 2) Put the decimal to the right of the first digit. (d) 3) Count the number of places (n) you had to move the decimal. This is the exponent. 4) Write the number in scientific notation by writing the decimal times 10 to the number of places( d ´ 10 n ). Example: 5,400,000 1) 54 2) 5.4 3) Six places 4) 5. 4 ´ 10 6 Is the first thing a decimal point or a zero? (Is the number between ­1 and 1?) 1) Write the important digits. Important digits are 1­9 and any zeros between them. 2) Put the decimal to the right of the first digit. (d) 3) Count the number of places (n) you had to move the decimal. This is the negative exponent. 4) Write the number in scientific notation by writing the decimal times 10 to the negative number of places( d ´10 - n ). Example: .000 000 120 3 1) 1203 2) 1.203 3) Seven places 4) 1. 203 ´ 10 -7 To convert a number in scientific notation to regular notation: 1. Write the number without the power of ten ( ´ 10 n ). 2. If the exponent is positive, move the decimal that many places to the right. 3. If the exponent is negative, move the decimal that many places to the left. Example: 8. 7 ´ 10 5 8.7 Five places to the right 870,000. Example: 2. 7 ´ 10 -4 2.7 Four places to the left .000 27
The Metric System Basic Metric Units of Measure Quantity Unit mass time distance gram second meter SI Unit (kilogram) (second) (meter) Metric Prefixes Prefix yotta zeta exa peta tera giga mega kilo unit milli micro nano pico femto atto zepto yocto Symbol Y Z E P T G M k m μ n p f a z y Power of 10 10 24 10 21 10 18 10 15 10 12 10 9 10 6 10 3 10 0 10 - 3 10 - 6 10 - 9 10 - 12 10 - 15 10 - 18 10 - 21 10 - 24 Decimal equivalent 1,000,000,000,000,000,000,000,000 1,000,000,000,000,000,000,000 1,000,000,000,000,000,000 1,000,000,000,000,000 1,000,000,000,000 1,000,000,000 1,000,000 1,000 1 0.001 0.000 001 0.000 000 001 0.000 000 000 001 0.000 000 000 000 001 0.000 000 000 000 000 001 0.000 000 000 000 000 000 001 0.000 000 000 000 000 000 000 001
Count by 3s : 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 Metric Conversions First Method: 1. Count how many lines you need to move up or down and multiply by three (or count by threes as you move each line.) 2. To go from a bigger prefix to a smaller prefix (down), move the decimal that many places to the right. 3. To go from a smaller prefix to a bigger prefix (up), move the decimal that many places to the left. NOTE: meters to centi­ is two right, centi­ to meters is two left. Example: Convert 5 km to mm. 1. Start at kilo and count: meter – 1, milli – 2. 2X3=6 Or start at kilo and count: meter – 3, milli – 6. 2. Kilo to milli goes down, so I move the decimal to the left. 5, 000 , 000 Second Method: 1. Multiply by the power of ten of the prefix that you have. 2. Divide by the power of ten of the prefix that you want. Example: Convert 5 km to mm. 1. 5 ´ 10 3 = 5 ´ 10 3 2. 5 ´ 10 3 ¸ 10 - 3 = 5 ´ 10 6 5,000,000
Significant Figures Rules 1. All nonzero digits are significant. 2. Zeros to the right of a nonzero digit and to the right of the decimal are significant. 3. Zeros between significant digits are significant. 4. All other zeros are not significant. When a number ends in zeros that are not to the right of a decimal point, the zeros are not necessarily significant. To show that they are, use scientific notation. Calculations 1. Exact numbers do not affect significant digits. 2. Addition and Subtraction: The place of significant digits is determined by the place of the greatest uncertainty. 123.56 +14.2 137.76 Round off to the tenths place 137.8 3. Multiplication and Division: The number of significant digits is determined by the number with the smallest number of significant digits. 111.11 (5 significant digits) X 1.10 (3 significant digits) 122.221 Round off to 3 sig. figs. 122 (3 significant digits)