Which fraction is equivalent to $1.240$?
A) $18 / 333$
B) $180 / 3333$
C) $180 / 333$
D) $180 / 33$
Answer (2)
The decimal 1.240 converts to the fraction 25 31 . After simplifying 1000 1240 , we find that none of the provided options match this value. So, there might be a typo in the given options since none are equivalent to 1.240 .
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Convert the decimal 1.240 to a fraction: 1.240 = 1000 1240 .
Simplify the fraction 1000 1240 by dividing both numerator and denominator by their greatest common divisor (GCD), which is 40: 1000 ÷ 40 1240 ÷ 40 = 25 31 .
Compare the simplified fraction 25 31 with the given options.
Since none of the options are equivalent to 25 31 , there must be a typo in the options. The correct answer cannot be determined without knowing the correct options.
Explanation
Problem Analysis We need to find which fraction is equivalent to the decimal 1.240 . To do this, we will convert the decimal to a fraction and simplify it. Then we will compare the simplified fraction to the given options.
Decimal to Fraction First, convert the decimal 1.240 to a fraction. We can write 1.240 as 1000 1240 .
Finding the GCD Next, we simplify the fraction 1000 1240 by finding the greatest common divisor (GCD) of the numerator and the denominator. The prime factorization of 1240 is 2 3 × 5 × 31 , and the prime factorization of 1000 is 2 3 × 5 3 . The GCD of 1240 and 1000 is 2 3 × 5 = 40 .
Simplifying the Fraction Now, divide both the numerator and the denominator by their GCD, which is 40: 1000 ÷ 40 1240 ÷ 40 = 25 31
Comparing with Options Now we need to check which of the given options is equal to 25 31 . We can convert 25 31 to a decimal to compare it with the options. 25 31 = 1.24 . Now we compare this with the given options: A) 333 18 ≈ 0.054 B) 3333 180 ≈ 0.054 C) 333 180 ≈ 0.541 D) 33 180 ≈ 5.455 None of these fractions equals 1.24 . However, we made an error in the options. Let's re-evaluate the options. We are looking for a fraction that equals 1.24 = 25 31 .
Final Answer Let's check if any of the options are equivalent to 25 31 .
A) 333 18 is not equal to 25 31 .
B) 3333 180 is not equal to 25 31 .
C) 333 180 is not equal to 25 31 .
D) 33 180 is not equal to 25 31 .
However, if option D was 25 31 after simplification, then 1.24 = 25 31 . None of the options are equal to 25 31 . There might be a typo in the question.
Assuming a Typo Since 1.240 = 1000 1240 = 100 124 = 25 31 , we are looking for a fraction equivalent to 25 31 . Multiplying the numerator and denominator by 4, we get 25 × 4 31 × 4 = 100 124 . If we multiply the numerator and denominator by other integers, we won't get any of the options. Therefore, there must be a typo in the options. However, if we assume that option D is 125 155 , then simplifying this fraction gives us 25 31 . So, let's assume that the correct answer should be D) 33 180 is a typo and it should be 125 155 .
Conclusion Since none of the given options are equivalent to 1.240 = 25 31 , there must be a typo in the options. However, without knowing the correct options, we can't choose the correct answer.
Examples
Understanding how to convert decimals to fractions is useful in many real-life situations. For example, when you are cooking and need to measure ingredients, you might encounter measurements like 1.25 cups. Knowing that 1.25 is equivalent to 4 5 or 1 4 1 cups can help you accurately measure the ingredients. Similarly, in finance, interest rates or percentage increases are often expressed as decimals, and converting them to fractions can help in understanding the underlying proportions and making informed decisions. For instance, an interest rate of 0.05 can be understood as 20 1 , meaning for every 20 dollars, you earn 1 dollar in interest.
