Convert the decimal 0.984 to a fraction.
A. [tex]$\frac{984}{100}$[/tex]
B. [tex]$\frac{984}{1000}$[/tex]
C. [tex]$\frac{984}{999}$[/tex]
D. [tex]$\frac{984}{99}$[/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 need 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 simplify the fraction 1000 984 by finding the greatest common divisor (GCD) of 984 and 1000. We can use prime factorization to find the GCD.
Finding the Greatest Common Divisor (GCD) The prime factorization of 984 is 2 3 × 3 × 41 , and the prime factorization of 1000 is 2 3 × 5 3 . The GCD of 984 and 1000 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 Answer So, the simplified fraction is 125 123 . Now we compare this with the given options. The correct answer is 1000 984 , which simplifies to 125 123 .
Examples
Converting decimals to fractions is a fundamental skill in various real-life scenarios. For instance, when calculating proportions or ratios in cooking, finance, or engineering, you often need to convert decimal measurements into fractional representations for accurate calculations. For example, if you need to scale a recipe by 0.984, converting it to the fraction 125 123 allows for precise scaling of ingredients, ensuring the recipe turns out as intended.
To convert 0.984 to a fraction, we write it as 1000 984 and then simplify this fraction to 125 123 . The correct answer from the given choices is option B: 1000 984 .
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