How to Convert Decimals Expansions
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Learning text on the topic How to Convert Decimals Expansions
How to Convert Decimal Expansions – Introduction
In mathematics, the ability to convert decimal expansions into fractions, percentages and even different number systems like binary or hexadecimal, is essential. These skills are not only useful in practical situations, such as calculating sales discounts or analysing data, but also form the basis for more complex concepts encountered in high school and beyond.
Understanding Decimal Conversions – Explanation
Converting decimal expansions involves changing a decimal number into other forms, such as fractions, percentages, or different bases (binary, hexadecimal, octal), depending on the requirement.
The process may differ slightly depending on the target form, but generally includes multiplying, dividing, or applying specific rules to achieve the desired conversion.
| Conversion Type | Step | Example | Result |
|---|---|---|---|
| Decimal to Fraction | Write the decimal over 1 and simplify. | $0.75 \to \frac{0.75}{1}$ | $\frac{3}{4}$ |
| Multiply to eliminate the decimal point and simplify. | Multiply $0.75$ by $100$ to get $\frac{75}{100}$. | $\frac{3}{4}$ (after simplifying) | |
| Decimal to Percent | Multiply the decimal by 100 and add the percent symbol. | $0.75 \times 100$ | $75\%$ |
Converting Decimals to Fractions
Convert $0.5$ to a fraction.
- Write the decimal over 1: $ \frac{0.5}{1} $
- Multiply to remove decimal: Multiply by $10$ to get $ \frac{5}{10} $
- Simplify: Divide both by their greatest common divisor ($5$), resulting in $ \frac{1}{2} $
Converting Repeating Decimals to Fractions
Express $0.333...$ as a fraction.
- Let $ x = 0.333... $
- Multiply by $10$ to get $ 10x = 3.333... $
- Subtract $ x $ from $ 10x $ to find $ 9x = 3 $
- Divide both sides to find $ x = \frac{1}{3} $
Converting Decimals to Percentages
Express 0.5 as a percentage.
- Multiply by 100: $ 0.5 \times 100 = 50 $%
- Attach the percent symbol: 50%
How to Convert Decimal Expansions – Summary
Key Learnings from this Text:
- To convert decimals to fractions, multiply by $10n$ where n is the number of decimal places and simplify the fraction.
- Repeating decimals can be converted to fractions by setting up algebraic equations.
- Multiplying a decimal by 100 converts it to a percentage. *
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How to Convert Decimal Expansions – Frequently Asked Questions
