Questions: The technology output for -1/2^97 is -6.31088724 E-30. Write this number in scientific notation with three significant digits. The number -1/2^97 written in scientific notation with three significant digits is . (Use scientific notation. Use the multiplication symbol in the math palette as needed.)

The technology output for -1/2^97 is -6.31088724 E-30. Write this number in scientific notation with three significant digits. The number -1/2^97 written in scientific notation with three significant digits is . (Use scientific notation. Use the multiplication symbol in the math palette as needed.)

Transcript text: The technology output for $-\frac{1}{2^{97}}$ is $-6.31088724 \mathrm{E}-30$. Write this number in scientific notation with three significant digits. The number $-\frac{1}{2^{97}}$ written in scientific notation with three significant digits is $\square$ (Use scientific notation. Use the multiplication symbol in the math palette as needed.)

Solution

Solution Steps

To express the number $-6.31088724 \times 10^{-30}$ in scientific notation with three significant digits, we need to round the coefficient to three significant figures. The number is already in scientific notation, so we only need to adjust the precision of the coefficient.

Step 1: Identify the Original Number

The original number given is $ -6.31088724 \times 10^{-30} $.

Step 2: Round to Three Significant Digits

To express this number in scientific notation with three significant digits, we round the coefficient $ -6.31088724 $ to three significant figures. This gives us $ -6.31 $.

Step 3: Write in Scientific Notation

The rounded number can now be expressed in scientific notation as: \[ -6.31 \times 10^{-30} \]