Write 7.5625 as a mixed number.

Answer 1

To convert the decimal \( 7.5625 \) into a mixed number, we can follow these steps:

1. Separate the whole number from the decimal part: The whole number part is \( 7 \).

2. Convert the decimal part \( 0.5625 \) into a fraction:

   • \( 0.5625 \) can be expressed as \( \frac{5625}{10000} \) since there are four decimal places.
   • We can simplify this fraction by finding the greatest common divisor (GCD) of \( 5625 \) and \( 10000 \).

   First, let's factor both numbers:

   • \( 5625 = 5^4 \times 9 = 5^4 \times 3^2 \)
   • \( 10000 = 10^4 = 2^4 \times 5^4 \)

   The GCD of \( 5625 \) and \( 10000 \) is \( 5^4 = 625 \).

   Now we divide both the numerator and the denominator by \( 625 \): \[ \frac{5625 \div 625}{10000 \div 625} = \frac{9}{16} \]

3. Combine the whole number and the fraction: Now that we have \( 7 \) as the whole number and \( \frac{9}{16} \) as the fraction, we can write the mixed number: \[ 7 \frac{9}{16} \]

Therefore, \( 7.5625 \) as a mixed number is \( 7 \frac{9}{16} \).