Write 0.925 as a percent and as a simplified fraction

Write 0.925 as a percent and as a simplified fraction.
A. 92.5% and
40
37
​
B. 92.5% and
40
37
​
C. 925% and
40
37
​
D. 9.25% and
1000
925
​

The Correct Answer and Explanation is :

To express the decimal 0.925 as a percent and a simplified fraction, we can follow these steps:

Converting 0.925 to a Percent

1. Understand the Concept: A percent is a way of expressing a number as a fraction of 100. To convert a decimal to a percent, we multiply the decimal by 100.
2. Calculation:
   [
   0.925 \times 100 = 92.5\%
   ]
   Thus, 0.925 as a percent is 92.5%.

Converting 0.925 to a Simplified Fraction

1. Expressing as a Fraction: The decimal 0.925 can be expressed as a fraction. Since it has three decimal places, we can write it as:
   [
   \frac{925}{1000}
   ]
2. Simplifying the Fraction: To simplify (\frac{925}{1000}), we need to find the greatest common divisor (GCD) of 925 and 1000.

• Finding the GCD: The prime factorization of 925 is (5^2 \times 37), and the prime factorization of 1000 is (2^3 \times 5^3). The common factor here is (5).
• Dividing by the GCD:
  [
  \frac{925 \div 25}{1000 \div 25} = \frac{37}{40}
  ]

Therefore, 0.925 as a simplified fraction is (\frac{37}{40}).

Final Answer

The correct answer is A. 92.5% and (\frac{37}{40}).

Explanation

The process of converting a decimal to a percent involves simple multiplication. This straightforward method provides a clear understanding of how a decimal relates to the whole. In this case, 0.925 indicates that we have 925 out of 1000 parts, which corresponds directly to 92.5 out of 100 parts, reflecting the relationship between these values.

For the fraction conversion, recognizing how to manipulate the fraction and simplify it accurately is crucial. Understanding prime factorization helps in determining the GCD effectively, ensuring that the fraction is in its simplest form.

This exercise illustrates the connection between decimals, percentages, and fractions, emphasizing their interchangeable nature in expressing values, which is essential in various applications, from everyday calculations to more complex mathematical scenarios.