Simplify 5554/1024 and write it as a mixed number and a decimal.

Step-by-step solution

1. 1

   Cancel the common factors of 2. Both $5554$ and $1024$ are even, so divide each by $2$:

   $\frac{5554}{1024}=\frac{2777}{512}$

   Since $1024=2^{10}$, its only prime factor is $2$ — so the reduction can continue only while the numerator stays even.

2. 2

   Check whether the reduction can go further. $2777$ is odd, so it shares no factor of $2$ with $512=2^{9}$. As $2$ is the only prime available in the denominator, the greatest common divisor is $1$ and the fraction is already in lowest terms. A gcd computation confirms $\gcd(2777,512)=1$ ✓.

3. 3

   Convert to a mixed number by dividing out. How many whole $512$s fit into $2777$?

   $512\times5=2560,\qquad2777-2560=217$

   Since $217<512$, the quotient is $5$ with remainder $217$:

   $\frac{2777}{512}=5\frac{217}{512}$

   Check: $5\times512+217=2560+217=2777$ ✓.

4. 4

   Convert to a decimal — and note it terminates. A fraction terminates exactly when its reduced denominator has only $2$s and $5$s as prime factors. Here the denominator is $2^{9}$, so it terminates after at most $9$ decimal places:

   $\frac{2777}{512}=5.423828125$

   This is exact, not rounded — $217/512=0.423828125$ precisely.

5. 5

   Verify all three forms agree. $2777/512=5.423828125$ and $5554/1024=5.423828125$ ✓, computed in exact rational arithmetic. So $\frac{5554}{1024}=\frac{2777}{512}=5\frac{217}{512}=5.423828125$, four names for one number.