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Questions and Answers
Convierte $\frac{3}{4}$ a decimal utilizando la estrategia de división.
Convierte $\frac{3}{4}$ a decimal utilizando la estrategia de división.
True
Es imposible convertir decimales a números fraccionarios.
Es imposible convertir decimales a números fraccionarios.
False
Para convertir el decimal $1.25$ a fracción, se puede expresar como $\frac{125}{100}$ y simplificar.
Para convertir el decimal $1.25$ a fracción, se puede expresar como $\frac{125}{100}$ y simplificar.
True
Un número decimal periódico, como $0.333...$, no puede ser expresado como fracción.
Un número decimal periódico, como $0.333...$, no puede ser expresado como fracción.
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La conversión de números fraccionarios a decimales no requiere ninguna estrategia especial.
La conversión de números fraccionarios a decimales no requiere ninguna estrategia especial.
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Study Notes
Converting Fractions to Decimals and Vice Versa
- Various strategies exist for converting fractions to decimals and decimals to fractions.
- The choice of method depends on the type of fraction or decimal.
Strategies for Converting Fractions to Decimals
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Division: Dividing the numerator by the denominator is a general method.
- If the division results in a finite decimal, the fraction represents a terminating decimal.
- If the division results in a repeating decimal, the fraction represents a repeating decimal.
-
Recognizing Equivalent Fractions: Some fractions can be easily converted to decimals by recognizing equivalent fractions with denominators that are powers of 10 (e.g., 10, 100, 1000).
- Example: 1/2 can be converted to 5/10 which is equal to 0.5
- Using a calculator: Many calculators can directly convert fractions to decimals.
Strategies for Converting Decimals to Fractions
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Terminating decimals: Convert the decimal to a fraction by writing the decimal as a numerator over a denominator that is a power of 10.
- The power of 10 is determined by the number of digits after the decimal point.
- Simplify the fraction to its lowest terms.
- Example: 0.75 = 75/100 = 3/4
-
Repeating decimals: Convert repeating decimals to fractions using a slightly more complex method.
- Express the repeating part as a fraction with the repeating digits representing the numerator and a power of 10 (number of repeating digits) representing the denominator.
- Subtract the non-repeating part from the decimal times the power of 10.
- Simplify the fraction to its lowest terms.
- Example: 0.333...
- Let x = 0.333...
- Multiply both sides by 10: 10x = 3.333...
- Subtract the first equation from the second: 10x - x = 3.333... - 0.333...
- This simplifies to 9x = 3, and then x = 1/3.
-
Mixed numbers: Convert the whole number part separately and combine with the fraction part.
- Example: 2.5
- The whole number is 2.
- The decimal part is 0.5.
- The fractional equivalent of 0.5 is 1/2
- Combine the two to yield 2 1/2.
- Improper fractions: Convert to mixed numbers for better readability.
Important Considerations
- Exact representations: Some decimals have exact fractional equivalents, others are approximations.
- Repeating decimals: Representing repeating decimals accurately often requires converting to fractions.
- Simplifying: Always simplify fractions to their lowest terms after conversion.
- Calculator Use: Calculators provide an initial form of the converted number but it is still important to understand and simplify if needed.
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Description
Este cuestionario explora varias estrategias para convertir fracciones a decimales y viceversa. Aprenderás a identificar tipos de fracciones y a usar métodos como la división y el reconocimiento de fracciones equivalentes. Domina las técnicas utilizando calculadoras para facilitar tus conversiones.
