Calcula la fracción generatriz de los siguientes decimales [tex]$1 ; 0 s ; 1, s ; 0,15$[/tex]
Answer (2)
The generating fraction of 1 is 1 1 .
The generating fraction of 0 is 1 0 .
Convert 1.5 to a fraction and simplify: 1.5 = 10 15 = 2 3 .
Convert 0.15 to a fraction and simplify: 0.15 = 100 15 = 20 3 .
The generating fractions are: 1 1 , 1 0 , 2 3 , 20 3 .
Explanation
Problem Analysis We are asked to find the generating fraction of the following decimals: 1, 0, 1.5, and 0.15. The generating fraction is a fraction that, when converted to a decimal, results in the given decimal.
Generating Fraction of 1 For the number 1, the generating fraction is 1 1 . Any integer can be written as a fraction with a denominator of 1.
Generating Fraction of 0 For the number 0, the generating fraction is 1 0 . Zero divided by any non-zero number is zero.
Generating Fraction of 1.5 For the number 1.5, we first convert it to a fraction. 1.5 = 10 15 . Now, we simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 5. 10 15 = 10 ÷ 5 15 ÷ 5 = 2 3 .
Generating Fraction of 0.15 For the number 0.15, we convert it to a fraction. 0.15 = 100 15 . Now, we simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 5. 100 15 = 100 ÷ 5 15 ÷ 5 = 20 3 .
Final Answer Therefore, the generating fractions for the given decimals are 1 1 , 1 0 , 2 3 , and 20 3 .
Examples
Generating fractions are useful in various real-life scenarios, such as converting decimal measurements to fractional units in cooking or carpentry. For example, if a recipe calls for 0.75 cups of flour, you can easily convert it to the fraction 4 3 of a cup. Similarly, in carpentry, if a piece of wood needs to be 0.625 inches thick, you can convert it to 8 5 of an inch, making it easier to measure with standard tools.
Las fracciones generatrices de los decimales dados son 1 1 para 1, 1 0 para 0, 2 3 para 1.5, y 20 3 para 0.15. Cada número decimal se convierte a una fracción simplificada según los pasos explicados. Así, hemos encontrado todas las fracciones generatrices solicitadas.
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