Question

(a) the signal from a certain satellite takes approximately 0.0029 seconds to reach earth. write this number in scientific notation
(b) the total surface area of africa is approximately $1.17 \times 10^7$ square miles. write this number in standard notation.
(a) \boxed{} seconds
(b) \boxed{} square miles

Explanation:

Part (a)

Step1: Recall scientific notation rules

Scientific notation is \(a\times10^{n}\) where \(1\leq|a|\lt10\) and \(n\) is an integer. For a number less than 1, \(n\) is negative, equal to the number of places we move the decimal to the right to get a number between 1 and 10.

Step2: Convert 0.0029 to scientific notation

For \(0.0029\), move the decimal point 3 places to the right to get \(2.9\). So \(n = - 3\). Thus, \(0.0029=2.9\times10^{-3}\).

Part (b)

Step1: Recall standard notation from scientific notation

To convert \(a\times10^{n}\) to standard notation, if \(n\) is positive, move the decimal point \(n\) places to the right.

Step2: Convert \(1.17\times10^{7}\) to standard notation

For \(1.17\times10^{7}\), move the decimal point 7 places to the right. \(1.17\times10^{7}=11700000\).

Answer:

s:
(a) \(2.9\times10^{-3}\) seconds
(b) \(11700000\) square miles