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A graph represents the relationship between two variables.

1.4 Key Math Skills for Chemistry. A graph represents the relationship between two variables.

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A graph represents the relationship between two variables.

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  1. 1.4 Key Math Skills for Chemistry A graph represents the relationship between two variables. Learning Goal Review math concepts used in chemistry: place values, positive and negative numbers, percentages, solving equations, interpreting graphs, and writing numbers in scientificnotation.

  2. A. Identifying Place Values A premature baby has a mass of 2518 grams. A silver coin has a mass of 6.407 grams. Key Math Skill Identifying Place Values For any number, we can identify the place value for each of the digits in that number. The place values for two numbers are listed below:

  3. B. Using Positive and Negative Numbers in Calculations Key Math Skill Using Positive and Negative Numbers in Calculations A positive number is any number that is greater than zero and has a positive sign (+). Often the positive sign is understood and not written in front of the number. A negative number is any number that is less than zero and is written with a negative sign (−).

  4. Multiplication and Division: Positive and Negative Numbers 1. When two positive numbers or two negative numbers are multiplied or divided, the answer is positive (+). 2. When a positive number and a negative number are multiplied or divided, the answer is negative (−).

  5. Addition: Positive and Negative Numbers 1. When two positive numbers are added, the answer is positive. 2. When two negative numbers are added, the answer is negative. 3. When a positive number and a negative number are added, the smaller number is subtracted from the larger number and the result has the same sign as the larger number.

  6. Subtraction: Positive and Negative Numbers When two numbers are subtracted, change the sign of the number to be subtracted and then follow the rules for addition.

  7. Calculator Operations On your calculator, there are four keys used for basic mathematical operations. The change sign key is used to change the sign of a number.

  8. Calculator Operations—Example

  9. C. Calculating Percentages Key Math Skill Calculating Percentages To determine a percentage, divide the parts by the total (whole)and multiply by 100%. If the percentage of red balls is 5, it means there are 5 red balls in every 100 balls.

  10. D. Solving Equations Key Math Skill Solving Equations Equations can be rearranged to solve for an unknown variable. 1. Place all like items on one side. 2. Isolate the variable you need to solve for. 3. Check your answer.

  11. Study Check Solve the following equation for P1.

  12. Solution Solve the following equation for P1. To solve for P1,divide both sides by V1.

  13. E. Interpreting Graphs Key Math Skill Interpreting Graphs A graph represents the relationship between two variables. contains two perpendicular axes. has a horizontal axis, or x axis. has a vertical axis, or y axis.

  14. Interpreting Graphs In the following graph, the volume of a gas in a balloon is plotted against its temperature. y axis represents the volume (L) of the gas in the balloon. x axis represents the temperature (°C) of the gas. title indicates that the volume of the balloon was measured at different temperatures. points represent the volume of gas that was measured at a specific temperature.

  15. Interpreting Graphs The line on the graph • indicates a direct relationship: that the volume of a gas in a balloon increases with increasing temperature. • can be used to determine the gas volume at various temperatures.

  16. F. Scientific Notation Key Math Skill Writing Numbers in Scientific Notation People have an average of 1 × 105 hairs on the scalp. Each hair is about 8 ×10−6 m wide.

  17. Scientific Notation Numbers written in scientific notation have two parts: CoefficientPower of 10 To write 2400 in the correct scientific notation, the coefficient is 2.4. the power of 10 is 3. write the product of the coefficient multiplied by a power of 10. 2.4 × 103

  18. Scientific Notation 2 400 = 2.4 × 1 000 = 2.4 × 103  3 places Coefficient × Power of 10 0.00086 = = 8.6 × 10−4 4 places  Coefficient × Power of 10

  19. Some Positive Powers of 10

  20. Some Negative Powers of 10

  21. Measurements in Scientific Notation Diameter of chickenpox virus = 0.000 000 3 m = 3 × 10−7 m

  22. Some Measurements Written in Scientific Notation

  23. Scientific Notation and Calculators Numbers in scientific notation can be entered into a calculator using the EXP or EE key. The calculator display shows a number between1 and 10 followed by a space and the power of 10.

  24. Guide to Writing a Number in Scientific Notation

  25. Study Check Write each of the following in correct scientific notation: A. 64 000 B. 0.021

  26. Solution Write each of the following in correct scientific notation: A. 64 000 STEP 1 Move the decimal point to obtain a coefficient that is at least 1 but less than 10. 6.4 STEP 2 Express the number of places moved as a power of 10. 104 STEP 3 Write the product of the coefficient multiplied by the power of 10. 6.4 ×104

  27. Solution Write each of the following in correct scientific notation: B. 0.021 STEP 1 Move the decimal point to obtain a coefficient that is at least 1 but less than 10. 2.1 STEP 2 Express the number of places moved as a power of 10. 10−2 STEP 3 Write the product of the coefficient multiplied by the power of 10. 2.1 ×10−2

  28. Concept Map

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