How many significant digits are in 26.048 13 ?

$3584 \approx 3600$
$2065 \approx 2100$

The estimated difference is $\boxed{\mathbf{1500}}$.

6. How many significant digits are in 26.04813?

The non-zero digits are 2, 6, 4, 8, 1, 3. These are all significant.

The zero between 6 and 4 is significant.

All digits (2, 6, 0, 4, 8, 1, 3) are significant. There are 7 significant digits.

There are $\boxed{\mathbf{7}}$ significant digits.

7. What answer does the calculator give when performing this operation? $6 \wedge 3 - 4 + (-) 7 =$

The operation represents $6^3 - 4 + (-7)$.

The calculator gives the answer $\boxed{\mathbf{205}}$.

8. Perform this operation, and write your answer correct to four significant figures: $\sqrt{50} - 3 \wedge 3 =$

The operation represents $\sqrt{50} - 3^3$.

The first four significant figures are 1, 9, 9, 2. The fifth significant figure is 8, so we round up the fourth digit (2) to 3.

The answer correct to four significant figures is $\boxed{\mathbf{-19.93}}$.

9. Round-off 0.38569 to the nearest hundredths.

In 0.38569, the hundredths digit is 8.

The digit to the right of 8 is 5.

Since 5 is 5 or greater, round up the hundredths digit (8) to 9. Drop all digits after the hundredths place.

The number rounded to the nearest hundredths is $\boxed{\mathbf{0.39}}$.