Convert the decimal 0.984 to a fraction.
A. [tex]$\frac{984}{1000}$[/tex]
B. [tex]$\frac{984}{999}$[/tex]
C. [tex]$\frac{984}{100}$[/tex]
D. [tex]$\frac{984}{99}$[/tex]
Answer (2)
Convert the decimal 0.984 to a fraction: 1000 984 .
Simplify the fraction by finding 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 decimal 0.984 can be represented as the fraction 1000 984 .
Explanation
Initial Fraction We are asked to convert the decimal 0.984 to a fraction. First, we can write the decimal as a fraction with a denominator of 1000:
Decimal to Fraction 0.984 = 1000 984
Simplifying the Fraction Now, we need to simplify the fraction by finding the greatest common divisor (GCD) of the numerator and the denominator.
Finding the GCD The greatest common divisor of 984 and 1000 is 8. Dividing both the numerator and the denominator by 8, we get:
Dividing by the GCD 1000 ÷ 8 984 ÷ 8 = 125 123
Simplified Fraction So, the simplified fraction is 125 123 .
Comparing with Options Comparing this with the given options, we see that none of the options match the simplified fraction. However, the question asks us to convert the decimal to a fraction, and 1000 984 is a valid representation of the decimal 0.984.
Examples
Converting decimals to fractions is a fundamental skill with many practical applications. For instance, when you're cooking and need to measure ingredients, you might encounter measurements like 0.75 cups. Knowing that 0.75 is equivalent to 4 3 allows you to accurately measure out the ingredients. Similarly, in construction or woodworking, converting decimals to fractions helps in precise measurements when cutting materials or designing structures. This ensures accuracy and stability in your projects.
The decimal 0.984 can be represented as a fraction 1000 984 . Although it can be further simplified to 125 123 , the original fraction is often more relevant in certain contexts. Therefore, the correct option is A: 1000 984 .
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