Percentages are everywhere in daily life, from shopping discounts to test scores. They're a key way to express parts of a whole or changes in values. Understanding how to work with them is super useful for the SAT and beyond.

Converting between percentages, decimals, and fractions is a crucial skill. It helps you tackle a wide range of problems, from calculating tips to analyzing data. Mastering these conversions will make many SAT math questions much easier to solve.

Calculating Percentages of Quantities

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Understanding Percentages

• Percentage expresses a number as a fraction of 100, represented by the "%" symbol
• Calculate percentage of a quantity by multiplying the quantity by the percentage as a decimal
• Find original quantity by dividing the result by the percentage as a decimal
• In percentage problems, "whole" represents 100% and "part" represents a percentage of the whole
• Calculate percentage a part represents by dividing part by whole and multiplying by 100

Practical Applications

• Use percentages to calculate discounts (20% off a $50 item equals $10 discount)
• Determine tax amounts (8% sales tax on $100 purchase equals $8 tax)
• Calculate interest on loans or investments (5% interest on $1000 savings equals $50 interest)
• Analyze data in statistics (75% of survey respondents prefer product A)

Percent Increase and Decrease

Calculating Percent Changes

• Percent increase or decrease describes change in quantity as percentage of original amount
• Calculate percent increase: (difference between new and original values / original value) × 100
• Calculate percent decrease: (difference between original and new values / original value) × 100
• Find new value after percent increase: original value × (1 + percentage as decimal)
• Find new value after percent decrease: original value × (1 - percentage as decimal)

Combining Successive Percent Changes

• Convert percentages to decimals
• Add 1 to each decimal
• Multiply results together
• Subtract 1 from the product
• Convert back to percentage

Real-World Applications

• Analyze population growth (city population increased by 15% over 5 years)
• Track economic indicators (stock market decreased by 8% in one day)
• Evaluate sales performance (company sales increased by 25% compared to last quarter)
• Monitor health metrics (patient's cholesterol levels decreased by 20% after treatment)

Fractions, Decimals, and Percentages

Converting Between Representations

• Convert fraction to decimal by dividing numerator by denominator
• Convert decimal to percentage by multiplying by 100 and adding "%" symbol
• Convert percentage to decimal by dividing by 100 or moving decimal point two places left
• Convert decimal to fraction by writing decimal as numerator over 1, then multiplying both by 10 for each decimal place
• Convert fraction to percentage by first converting to decimal, then multiplying by 100 and adding "%"

Practical Uses and Examples

• Use fractions in cooking recipes (1/2 cup of sugar)
• Apply decimals in financial calculations (account balance of $1234.56)
• Utilize percentages in academic grading (scored 92% on the exam)
• Compare different representations (0.75 = 3/4 = 75%)
• Analyze probability (50% chance of rain equals 0.5 or 1/2 probability)