Write 4 3/4% as a decimal (not as a percentage)
The Correct Answer and Explanation is :
The correct answer is:0.0475.
To convert the percentage 4¾% to a decimal, follow these steps:
- Convert the Mixed Number: Start with the mixed number 4¾%. To convert it into an improper fraction, multiply the whole number (4) by the denominator (4) and add the numerator (3). This gives:
[
4 \times 4 + 3 = 16 + 3 = 19
]
Thus, 4¾ can be expressed as (\frac{19}{4}). - Convert the Percentage to a Decimal: A percentage means “per hundred,” so to convert a percentage to a decimal, you divide by 100. Therefore:
[
4¾\% = \frac{19}{4} \div 100 = \frac{19}{4} \times \frac{1}{100} = \frac{19}{400}
] - Perform the Division: Now, calculate (\frac{19}{400}):
[
\frac{19}{400} = 0.0475
]
Thus, 4¾% as a decimal is 0.0475.
Explanation
Understanding how to convert percentages to decimals is crucial in various fields, including finance, science, and everyday calculations. A percentage represents a fraction of 100. Hence, to convert any percentage into a decimal, we divide it by 100.
In the case of a mixed number like 4¾%, we first simplify it into an improper fraction. This step is necessary to maintain the correct numerical representation while facilitating easier division. Converting to an improper fraction involves finding a common unit that combines both the whole number and the fraction into one single entity. This method prevents mistakes that can occur when handling mixed numbers.
Once in fraction form, dividing by 100 is straightforward, as it scales the value down to a decimal format. The resulting decimal (0.0475) retains the value of the original percentage while being more adaptable for mathematical operations, such as addition, subtraction, multiplication, or division.
This conversion skill is particularly useful when dealing with calculations in statistical analysis, financial projections, or any scenario where precise numeric representation is necessary.