Question

is each number written correctly in scientific notation? choose yes or no.
a. $8.0 \times 10^3$ \bigcirc yes \bigcirc no
b. $0.6 \times 10^6$ \bigcirc yes \bigcirc no
c. $7.1 \times 10^{-3}$ \bigcirc yes \bigcirc no
d. $93 \times 10^{-10}$ \bigcirc yes \bigcirc no

Explanation:

Part a

Step1: Recall scientific notation rule

Scientific notation is in the form \(a\times10^{n}\) where \(1\leq|a|\lt10\) and \(n\) is an integer. For \(8.0\times10^{3}\), \(a = 8.0\) which satisfies \(1\leq8.0\lt10\) and \(n = 3\) (an integer).

Step1: Check the coefficient

For \(0.6\times10^{6}\), the coefficient \(a = 0.6\) which is less than \(1\). In scientific notation, the coefficient should satisfy \(1\leq|a|\lt10\). So this is not in correct scientific notation.

Step1: Verify the form

For \(7.1\times10^{- 3}\), the coefficient \(a=7.1\) satisfies \(1\leq7.1\lt10\) and the exponent \(n=-3\) is an integer. So it is in correct scientific notation.

Answer:

a. Yes

Part b