Overview
This lecture reviewed key techniques for solving percentage problems, including converting between percentages and decimals, calculating portions, and rounding results appropriately.
Converting Percentages and Calculating "Of"
- To find a percentage of a number, convert the percent to a decimal and multiply by the total.
- The word "of" in math often means multiply.
- To convert a percent to a decimal, move the decimal two places left (e.g., 5% becomes 0.05).
- Example: 5% of 38,410 is 0.05 × 38,410 = 1,920.5.
Rounding and Interpreting Results
- When a problem asks for the number of people, round to the nearest whole number since partial people do not exist.
- If the decimal is 0.5 or higher, round up; otherwise, round down.
- Example: 1,920.5 rounds up to 1,921 people.
Calculating What Percent One Number is of Another
- To find what percent a part is of the whole, divide the part by the whole and multiply by 100.
- Always place the part on top (numerator) and the whole on the bottom (denominator) in the division.
- Example: 18,053 out of 38,410 is 18,053 ÷ 38,410 = 0.470007..., which is 47.0007% before rounding.
Rounding Percents
- To round to a specified number of decimal places, look at the digit following and round up if it is 5 or higher.
- Always follow instructions for rounding as stated in the problem or assignment.
Practice Problems and Class Discussion
- Students practiced calculating and rounding answers to whole numbers or to specific decimal places.
- Emphasis on reporting answers as whole numbers when counting people or objects.
Key Terms & Definitions
- Percent — a number out of 100; a way to express a ratio as a fraction of 100.
- Decimal — a number based on the number 10; used to express non-whole numbers.
- Rounding — adjusting a number to the nearest specified place value (whole number, tenth, etc.).
- Numerator — the top number in a fraction, representing the part.
- Denominator — the bottom number in a fraction, representing the whole.
Action Items / Next Steps
- Practice similar percentage problems, focusing on conversion, calculation, and correct rounding.
- Complete lab and online homework assignments involving percentages.