Convert the decimal 0.984 to a fraction.
A. [tex]$\frac{984}{100}$[/tex]
B. [tex]$\frac{984}{99}$[/tex]
C. [tex]$\frac{984}{999}$[/tex]
D. [tex]$\frac{984}{1000}$[/tex]
Answer (2)
Convert the decimal 0.984 to a fraction by writing it as 1000 984 .
Find the greatest common divisor (GCD) of 984 and 1000, which is 8.
Divide both the numerator and the denominator by the GCD: 1000 ÷ 8 984 ÷ 8 = 125 123 .
The simplified fraction is 125 123 .
Explanation
Converting Decimal to Fraction We are asked to convert the decimal 0.984 into a fraction. To do this, we can write 0.984 as a fraction with a denominator that is a power of 10. Since there are three digits after the decimal point, we can write 0.984 as 1000 984 .
Simplifying the Fraction Now we need to simplify the fraction 1000 984 . To simplify, we find the greatest common divisor (GCD) of the numerator and the denominator and divide both by the GCD.
Finding the Greatest Common Divisor (GCD) To find the GCD of 984 and 1000, we can use the Euclidean algorithm or prime factorization. Let's use prime factorization. The prime factorization of 984 is 2 3 × 3 × 41 , and the prime factorization of 1000 is 2 3 × 5 3 . The GCD is the product of the common prime factors raised to the lowest power, which is 2 3 = 8 .
Dividing by the GCD Now, we divide both the numerator and the denominator by the GCD, which is 8: 1000 ÷ 8 984 ÷ 8 = 125 123
Final Simplified Fraction The simplified fraction is 125 123 .
Examples
Converting decimals to fractions is a fundamental skill with many practical applications. For example, when dealing with measurements in cooking or construction, you might need to convert a decimal measurement like 0.75 inches into a fraction, which would be 4 3 inches. This conversion allows for more precise and standardized communication of measurements, ensuring accuracy in recipes or building plans. Understanding how to convert decimals to fractions helps in everyday tasks requiring precision and clear communication of quantities.
The decimal 0.984 can be converted to the fraction 1000 984 , which simplifies to 125 123 . Among the options given, the correct representation before simplification is option D: 1000 984 .
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