Converting between fractions, decimals, and percents. Converting measures within the same system, between systems and using conversion factors.
Understand the Problem
The question is asking for methods or explanations on how to convert between fractions, decimals, and percentages, as well as how to convert measures within the same unit system and between different systems using conversion factors.
Answer
Fractions to decimals: divide numerator by denominator. Decimals to fractions: express decimal as a fraction. Decimals to percentages: multiply by 100. Percentages to decimals: divide by 100. Use conversion factors for measures.
Answer for screen readers
Fractions can be converted to decimals by dividing the numerator by the denominator, decimals to fractions by making a fraction out of the decimal, decimals to percentages by multiplying by 100, percentages to decimals by dividing by 100. For measurements, use conversion factors based on known equivalences.
Steps to Solve
- Converting Fractions to Decimals
To convert a fraction to a decimal, divide the numerator by the denominator. For example, to convert the fraction $\frac{3}{4}$ to a decimal: $$ 3 \div 4 = 0.75 $$
- Converting Decimals to Fractions
To convert a decimal to a fraction, write the decimal as a fraction with 1 as the denominator (e.g., $0.5$ becomes $\frac{0.5}{1}$). Then multiply top and bottom by 10 for every number after the decimal point, simplify if possible. For $0.25$: $$ 0.25 = \frac{25}{100} = \frac{1}{4} $$
- Converting Decimals to Percentages
To convert a decimal to a percentage, multiply the decimal by 100. For example: $$ 0.75 \times 100 = 75% $$
- Converting Percentages to Decimals
To convert a percentage to a decimal, divide by 100. For example, to convert $75%$ to a decimal: $$ 75 \div 100 = 0.75 $$
- Using Conversion Factors for Measures
To convert between units, use a conversion factor. For example, converting 5 meters to centimeters involves knowing that 1 meter = 100 centimeters, thus: $$ 5 \text{ meters} \times \frac{100 \text{ centimeters}}{1 \text{ meter}} = 500 \text{ centimeters} $$
- Converting Between Different Measurement Systems
To convert between different systems (like miles to kilometers), use the appropriate conversion factor. For instance, to convert 1 mile to kilometers where $1 \text{ mile} \approx 1.60934 \text{ kilometers}$, calculate: $$ 1 \text{ mile} \times 1.60934 \text{ kilometers/mile} = 1.60934 \text{ kilometers} $$
Fractions can be converted to decimals by dividing the numerator by the denominator, decimals to fractions by making a fraction out of the decimal, decimals to percentages by multiplying by 100, percentages to decimals by dividing by 100. For measurements, use conversion factors based on known equivalences.
More Information
Understanding how to convert between fractions, decimals, and percentages, as well as different measurement units, is essential in everyday calculations, finance, cooking, and various fields of science and engineering.
Tips
- Not simplifying fractions: After converting a decimal to a fraction, some may forget to simplify the fraction.
- Confusing the order of operations: When converting percentages to decimals, some might mistakenly divide by 10 instead of 100.
- Incorrectly applying conversion factors: Ensure you are using the correct factors for conversions, especially between different measurement systems.
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