Question

answer the following.
(a) the signal from a certain satellite takes approximately 0.0037 seconds to reach earth. write this number in scientific notation.
(b) the total surface area of asia is approximately $1.72 \times 10^7$ square miles. write this number in standard notation.
(a) \\(\square\\) seconds
(b) \\(\square\\) square miles

Explanation:

Part (a)

Step 1: Recall scientific notation rules

Scientific notation is of the form \( a \times 10^n \), where \( 1 \leq |a| < 10 \) and \( n \) is an integer. For a number less than 1, we move the decimal point to the right until we get a number between 1 and 10, and the exponent \( n \) is negative (equal to the number of places we moved the decimal).

Step 2: Convert 0.0037 to scientific notation

For \( 0.0037 \), we move the decimal point 3 places to the right to get \( 3.7 \). Since we moved the decimal 3 places to the right, the exponent \( n=- 3 \). So, \( 0.0037 = 3.7\times10^{-3} \).

Part (b)

Step 1: Recall standard notation from scientific notation

To convert \( a\times10^{n} \) (where \( n>0 \)) to standard notation, we move the decimal point \( n \) places to the right.

Step 2: Convert \( 1.72\times 10^{7} \) to standard notation

For \( 1.72\times10^{7} \), we move the decimal point 7 places to the right. \( 1.72\times10^{7}=17200000 \) (we add 5 more zeros after moving the decimal 2 places from 1.72 to 172 and then 5 more zeros to make a total of 7 places moved).

Answer:

(a) \( 3.7\times 10^{-3} \) seconds
(b) \( 17200000 \) square miles