Question - Converting Between Scientific Notation and Floating-Point Notation

Solution:

The mathematical concept requested in the image involves understanding and converting between scientific notation and floating-point notation. Typically, any number in scientific notation is written as \( a \times 10^n \), where \( 1 \leq |a| < 10 \) and \( n \) is an integer.

To convert from floating-point to scientific notation, we must adjust the decimal point to fit the criteria for \( a \), and then determine the appropriate exponent \( n \) that \( 10 \) must be raised to.

Looking at the options provided:

\( 20 \times 10^{-06} \) can be adjusted to \( 2.0 \times 10^{1} \times 10^{-06} = 2.0 \times 10^{-05} \)

\( 0.02 \times 10^{-03} \) can be adjusted to \( 2.0 \times 10^{-02} \times 10^{-03} = 2.0 \times 10^{-05} \)

\( 2 \times 10^{-05} \) is already in scientific notation.

Without any additional context or numerical values in the image to match the options against, all three options provided are valid representations of numbers in scientific notation adjusted from the given floating-point notation starting points.

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