Questions: The technology output for 1/2^53 is 1.11022302 E-16. Write this number in scientific notation with three significant digits. The number 1/2^53 written in scientific notation with three significant digits is .

The technology output for 1/2^53 is 1.11022302 E-16. Write this number in scientific notation with three significant digits. The number 1/2^53 written in scientific notation with three significant digits is .
Transcript text: The technology output for $\frac{1}{2^{53}}$ is $1.11022302 E-16$. Write this number in scientific notation with three significant digits. The number $\frac{1}{2^{53}}$ written in scientific notation with three significant digits is $\square$ .
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Solution

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Solution Steps

To convert the given number \(\frac{1}{2^{53}}\) into scientific notation with three significant digits, we need to:

  1. Calculate the value of \(\frac{1}{2^{53}}\).
  2. Convert this value into scientific notation.
  3. Round the result to three significant digits.
Step 1: Calculate the Value of \(\frac{1}{2^{53}}\)

We start by calculating the value of \(\frac{1}{2^{53}}\). This value is approximately \(1.1102230246251565 \times 10^{-16}\).

Step 2: Convert to Scientific Notation

Next, we convert this value into scientific notation. The value \(1.1102230246251565 \times 10^{-16}\) in scientific notation with three significant digits is \(1.110 \times 10^{-16}\).

Final Answer

The number \(\frac{1}{2^{53}}\) written in scientific notation with three significant digits is: \[ \boxed{1.110 \times 10^{-16}} \]

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