Write 0.96 as fraction in simplest form
The Correct Answer and Explanation is :
To convert 0.96 to a fraction in its simplest form, follow these steps:
Step-by-Step Solution
- Express 0.96 as a Fraction:
(0.96 = \frac{96}{100}) - Simplify the Fraction:
Find the greatest common divisor (GCD) of 96 and 100, which is 4. [
\frac{96 \div 4}{100 \div 4} = \frac{24}{25}
]
So, (0.96) as a fraction in simplest form is:
[
\frac{24}{25}
]
Explanation (300 words)
When converting a decimal like 0.96 to a fraction, the goal is to express it as a ratio of two integers. The first step is to write the decimal over a power of 10. Since 0.96 has two decimal places, place it over 100 (since (10^2 = 100)). This gives us ( \frac{96}{100} ).
Next, simplify the fraction by finding the greatest common divisor (GCD) of the numerator and the denominator. The GCD is the largest number that divides both numbers without a remainder. For 96 and 100, the GCD is 4. Dividing both the numerator and the denominator by 4 reduces the fraction: ( \frac{96 \div 4}{100 \div 4} = \frac{24}{25} ).
Reducing fractions to their simplest form is essential because it provides the most basic representation of the ratio. In this case, (\frac{24}{25}) is in simplest form because 24 and 25 have no common divisors other than 1.
Representing decimals as fractions is helpful in various fields, such as mathematics and science, where precise values are crucial. For instance, in measurements, fractions allow for exact representations, while decimals might round up or down, potentially leading to small inaccuracies. Converting and simplifying decimals into fractions is a foundational math skill that supports more complex problem-solving and critical thinking in everyday situations.