3/400 as a percent step by step explanation
The Correct Answer and Explanation is:
To convert ( \frac{3}{400} ) into a percent, follow these steps:
- Understand the concept:
- A percent is a ratio expressed as a fraction of 100. To convert a fraction into a percent, multiply it by 100.
- Apply the formula:
[
\text{Percent} = \left( \frac{\text{Numerator}}{\text{Denominator}} \right) \times 100
] - Substitute the values:
[
\text{Percent} = \left( \frac{3}{400} \right) \times 100
] - Simplify the fraction:
- Divide (3) by (400):
( 3 \div 400 = 0.0075 ).
- Multiply by 100 to get the percent:
[
0.0075 \times 100 = 0.75\%
]
Final Answer:
( \frac{3}{400} = 0.75\% )
Detailed Explanation (300 Words):
To convert a fraction into a percent, it is important to understand the relationship between fractions and percentages. Percentages represent a part of 100. When you multiply a fraction by 100, you scale the ratio to fit into this context.
In this problem, ( \frac{3}{400} ) represents a fraction where 3 is the numerator (part) and 400 is the denominator (whole). To express this fraction as a percentage, we use the formula:
[
\text{Percent} = \left( \frac{\text{Numerator}}{\text{Denominator}} \right) \times 100
]
Start by dividing the numerator by the denominator. Performing the calculation ( 3 \div 400 ), we obtain 0.0075. This decimal value represents the proportion of 3 in 400. Next, multiply this decimal by 100 to convert it into a percent:
[
0.0075 \times 100 = 0.75\%
]
The multiplication by 100 shifts the decimal point two places to the right, giving the final percentage value.
Understanding this step-by-step process helps in tackling similar problems. Fractions with larger denominators like 400 can be intimidating, but breaking the calculation into parts—dividing first and then multiplying—makes the process straightforward.
In conclusion, ( \frac{3}{400} ) as a percent is 0.75%. This method works universally for any fraction, making it a valuable skill for interpreting ratios and proportions in percentage terms.