Convert the decimal 0.92 to a fraction.
The Correct Answer and Explanation is:
Correct Answer:
The decimal 0.92 converted to a fraction is 2325\frac{23}{25}2523.
Explanation (Approximately 300 Words):
To convert 0.92 to a fraction, follow these steps:
Step 1: Understand the Place Value
The decimal 0.92 means 92 hundredths, or: 0.92=921000.92 = \frac{92}{100}0.92=10092
This is because the last digit (2) is in the hundredths place.
Step 2: Simplify the Fraction
We now simplify 92100\frac{92}{100}10092 by finding the greatest common divisor (GCD) of 92 and 100.
Let’s list the factors:
- Factors of 92: 1, 2, 4, 23, 46, 92
- Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
The greatest common factor is 4.
Now divide both the numerator and denominator by 4: 92÷4100÷4=2325\frac{92 ÷ 4}{100 ÷ 4} = \frac{23}{25}100÷492÷4=2523
So, 0.92=23250.92 = \frac{23}{25}0.92=2523
Why This Works:
Decimals can always be expressed as fractions with denominators that are powers of 10 (10, 100, 1000, etc.), based on the number of decimal places.
Since 0.92 has two decimal places, we initially use 100 as the denominator. Once you write it as 92100\frac{92}{100}10092, you just simplify by dividing both numbers by their GCD.
Real-Life Use:
Converting decimals to fractions is helpful in situations involving measurements, money, or cooking, where fractions are commonly used. For example, if a recipe says “use 0.92 cups of milk,” converting to a fraction like 2325\frac{23}{25}2523 can help when measuring with standard kitchen tools.
Final Answer:
0.92=2325\boxed{0.92 = \frac{23}{25}}0.92=2523
