Scientific Notation PDF
Document Details
Tags
Summary
This document explains scientific notation, a method used in science to express very large or very small numbers. It includes examples and step-by-step instructions for converting numbers to and from scientific notation. The guide also covers operations like addition, subtraction, multiplication, and division with numbers in scientific notation.
Full Transcript
Name: Scientific Notation Notes: Additional Notes: cientific notation is frequently used in science to quickly and easily convey very large and very small S...
Name: Scientific Notation Notes: Additional Notes: cientific notation is frequently used in science to quickly and easily convey very large and very small S 5= 5 x 10(0) numbers. 50= 5 x 10(1) There are two important parts to the number in scientific notation, the coefficient which is a number 5000000= 5 x 10(6) greater than or equal to 1 and less than ten, and the exponent which is an integer. Positive exponents represent values larger than one and negative exponents are values that are less than one. Negative exponents means that you have a value less than 1 Positive exponents means that you can a value greater than 1 Coefficient must be greater or How to convert into scientific notation: equal to 1 but less that ten 1. L ook at the number and decide where to place the decimal point, so that there is only one number (not a zero) in front of the decimal point. 2. Count the places that the decimal point moved. 0.0000000052 3. If the original number was less than 1, make sure that the exponent is negative. 5.2 x 10(-9) or example: F Convert 28300 into scientific notation. 1. The new decimal point needs to move between the 2 and 8. 8.8 x 10(-4) 2. The original decimal point is after the last zero, so it needs to move 4 places. 0.00088 3. The original number is greater than 1, so the exponent is positive. 28300 in scientific notation is 2.83x104 (Don’t include the zeros at the end in your final number unless there is a visible decimal point, we will discuss this more when we get to significant figures! If the number in the example above were 28300., it would be written in scientific notation as 2.8300 x104) A Chemistry Guide How to convert into standard notation: . I f the exponent is negative, the number will be less than 1. 1 2. Move the decimal point by the places in the exponent. Add zeros as needed. or example: F Convert 8.81 x10-4 into standard notation. 1. This number will be less than one, because the exponent is negative. 2. We need to move the decimal point 4 places. We need to add zeros as we move the decimal point. 8.81x10-4 One place → 0.881 x10-3 Two places → 0.0881 x10-2 Three places → 0.00881 x10-1 Four places → 0.000881 to the left the decimal increases Addition and Subtraction: . C 1 onvert to the same exponent 2. Perform operation 3. Adjust so that the coefficient is still greater than or equal to 1 and less than 10. Multiplication: . M 1 ultiply the coefficients 2. Add the exponents 3. Adjust so that the coefficient is still greater than or equal to 1 and less than 10. Division: . D 1 ivide the coefficients 2. Subtract the exponents 3. Adjust so that the coefficient is still greater than or equal to 1 and less than 10. A Chemistry Guide Using your Calculator: se the engineering exponent function on your calculator to be sure that your scientific notation U calculations are correct. If you type 2.3x10^-6 on your calculator, your calculator considers it as two different numbers that are multiplied together, (2.3) and (10-6). Sometimes this is fine, but other timesthe order of operations will be incorrect. Enter this number on the calculator correctly you can either remember to always put scientific notation into parenthesis like this: (2.3*10^-6). Or you can use the engineering exponent. Both will work. Since I am lazy (or efficient?) I prefer to use the engineering exponent as it will always give the correct answer without needing to add parenthesis and it requires less typing on my calculator. ny scientific calculator will have an engineering exponent button. It is usually labeled as either “E”, A “EE” or “EXP”. On a TI graphing calculator it is the 2nd function of the [,] key which is above the number 7 key. When you see “E” on your screen it means “x10 ^” and it causes the calculator to link the coefficient and exponent as one number, so there are no order of operation problems. So 2.3E-6 on the calculator is the same as 2.3x10-6or 0.0000023. On a TI graphing calculator, to enter 2.3 x10-6, youwould type [. ] [2nd] [,] [(-)] I do: Answer: 1) Write the number 0.00362 in scientific notation. 1)3.62 x 10^-3 2) Write the number 842,000,000 in scientific notation. 2)8.42 x 10^8 3) Write the number 6.54 x 10-8in standard notation. 3)0.0000000654 4) Write the number 3.21 x 105 in standard notation. 4)321000 A Chemistry Guide We do: 1) Write the number 394,000 in scientific notation. 3.94 x 10^5 2) Write the number 1.118 x 1012in standard notation. 1118000000000 We do: 1) Write the number 0.000 000 89 in scientific notation. 8.9 x 10(-7) 2) Write the number 9.63 x 10-4in standard notation. 0.000963 You do: Always use a leading zero before a decimal point, for example 0.023 not.023. 1) Write the number 25.7 in scientific notation. 2.57 x 10(1) 2) Write the number 789,000,000,000 in scientific notation. 7.89 x 10(11) 3) Write the number 0.000 000 0271 in scientific notation. 2.71 x 10(-8) 4) Write the number 0.695 in scientific notation. 6.95 x 10(-1) A Chemistry Guide 5) Write the number 7.97 x 10-3in standard notation. 0.00797 6) Write the number 9.29 x 10-3in standard notation. 0.00929 7) Write the number 1.93 x 102in standard notation. 193 8) Write the number 9.36 x 108 in standard notation. 936000000 9) Calculate 1.50 x 10-3x 4.00 x 10-6 6 x 10(-9) 10) Calculate 4.44 x 10-9/ 2.00 x 10-3 2.22 x 10(-12) 11) Calculate 1.1 x 10-3+ 2.21 x 10-2. Write your answerin scientific notation. 13.21 x 10(-2) 12) Calculate 8.140 x 108- 6.68 x 107. Write your answerin scientific notation. 7.472 x 10(8) A Chemistry Guide
