Question

answer the following.
(a) the signal from a certain satellite takes approximately 0.061 seconds to reach earth. write this number in scientific notation.
(b) the total surface area of south america is approximately $6.89 \times 10^6$ square miles. write this number in standard notation.
(a) \\(\square\\) seconds
(b) \\(\square\\) square miles

Explanation:

Part (a)

Step1: Recall scientific notation rules

Scientific notation is in the form \( a \times 10^n \), where \( 1 \leq |a| < 10 \) and \( n \) is an integer. For \( 0.061 \), we move the decimal point to the right until we get a number between 1 and 10.

Step2: Determine \( a \) and \( n \)

Moving the decimal point 2 places to the right gives \( 6.1 \). Since we moved the decimal to the right, \( n=-2 \). So \( 0.061 = 6.1 \times 10^{-2} \).

Step1: Recall standard notation from scientific notation

To convert \( 6.89 \times 10^6 \) to standard notation, we move the decimal point 6 places to the right (because the exponent of 10 is 6).

Step2: Perform the decimal movement

\( 6.89 \times 10^6 = 6890000 \) (we add zeros as needed when moving the decimal).

Answer:

\( 6.1 \times 10^{-2} \)

Part (b)