Sure, let’s break down the process of converting the number 6.375 into different forms:
### 1. Convert to a Mixed Fraction
First, we recognize that 6.375 can be separated into its integer and fractional parts:
[tex]\[ 6.375 = 6 + 0.375 \][/tex]
Next, we focus on the fractional part, 0.375. We can express it as a fraction:
[tex]\[ 0.375 = \frac{375}{1000} \][/tex]
Simplifying this fraction, the greatest common divisor (GCD) of 375 and 1000 is 125:
[tex]\[ \frac{375 \div 125}{1000 \div 125} = \frac{3}{8} \][/tex]
Therefore:
[tex]\[ 6.375 = 6 \frac{3}{8} \][/tex]
### 2. Convert to a Percentage
To convert 6.375 into a percentage, we multiply by 100:
[tex]\[ 6.375 \times 100 = 637.5 \% \][/tex]
### 3. Convert to an Improper Fraction
We already know that 6.375 is [tex]\( 6 \frac{3}{8} \)[/tex]. To convert this mixed fraction into an improper fraction, follow these steps:
[tex]\[ 6 \frac{3}{8} \][/tex]
[tex]\[ 6 \times 8 + 3 = 48 + 3 = 51 \][/tex]
Thus:
[tex]\[ 6 \frac{3}{8} = \frac{51}{8} \][/tex]
### Conclusion
Given the three choices, the equivalent forms of 6.375 are:
[tex]\[ 6 \frac{3}{8}, 637.5 \%, \frac{51}{8} \][/tex]
So the correct answer is:
[tex]\[ 6 \frac{3}{8}, 637.5 \%, \frac{51}{8} \][/tex]
