To solve this problem, we can use the Pythagorean theorem.
Keith rode 2 miles down one road and then made a 90-degree turn to ride another 2 miles down a different road. This forms a right triangle where the two roads correspond to the two legs (each 2 miles), and the direct route he would have taken to the grocery store is the hypotenuse of the triangle.
We can use the Pythagorean theorem, which states:
\[ a^2 + b^2 = c^2 \]
where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the other two sides.
In Keith's case, both \( a \) and \( b \) are 2 miles.
Calculating the hypotenuse \( c \):
\[ c^2 = 2^2 + 2^2 \] \[ c^2 = 4 + 4 \] \[ c^2 = 8 \] \[ c = \sqrt{8} \approx 2.828 \]
Thus, the direct distance he could have traveled to the grocery store is approximately 2.8 miles.
Now, to find out how much distance he saved:
The total distance he rode turning is 2 miles + 2 miles = 4 miles.
So, the distance saved by riding directly to the store instead is:
\[ \text{Distance saved} = \text{Distance ridden} - \text{Direct distance} = 4 - 2.828 \approx 1.2 \text{ miles} \]
So the answer is 1.2 miles.