Convert 0.96 to a fraction. Give your answer in its simplest form.
The correct answer and explanation is:
Answer:
0.96 as a fraction in its simplest form is 24/25.
Step-by-Step Explanation (with 300 words):
To convert a decimal like 0.96 to a fraction, we need to follow a series of logical steps.
Step 1: Understand the Decimal
The decimal 0.96 means 96 hundredths. That is: 0.96=961000.96 = \frac{96}{100}
Step 2: Simplify the Fraction
Now we simplify the fraction 96100\frac{96}{100}. To do this, we find the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 96 and 100 is 4.
Now divide both the numerator and the denominator by 4: 96÷4100÷4=2425\frac{96 \div 4}{100 \div 4} = \frac{24}{25}
So, 0.96=24250.96 = \frac{24}{25} in its simplest form.
Step 3: Confirm the Answer
To check our answer, we convert the fraction back to a decimal: 2425=0.96\frac{24}{25} = 0.96
So the conversion is accurate.
Why Simplification Is Important
When converting decimals to fractions, we often first get a fraction that is not in its lowest terms. Simplifying helps express the number in the most efficient and universally accepted form. For example, while 96100\frac{96}{100} is technically correct, 2425\frac{24}{25} is simpler and cleaner.
Conclusion
Converting decimals like 0.96 to a fraction is a foundational skill in math. By expressing 0.96 as 96100\frac{96}{100} and simplifying to 2425\frac{24}{25}, we turn a decimal into an exact rational number. This is useful in algebra, geometry, and many real-world applications involving measurements and ratios.