Question

rewrite the following statement using a number in scientific notation. the diameter of a certain atom is about 0.76 nanometers. (recall that nano - means \billionth.\) the diameter of a certain atom is about 7.6×16^(-10) meters. (type your answer in scientific notation, using the appropriate symbol from the math palette for any multiplication.)

Explanation:

Step1: Recall the conversion of nano - to base unit

1 nanometer = $1\times10^{-9}$ meters.

Step2: Convert 0.76 nanometers to meters

$0.76\times1\times10^{-9}$ meters.

Step3: Rewrite 0.76 in scientific - notation form

$0.76 = 7.6\times10^{-1}$, so $0.76\times10^{-9}=(7.6\times10^{-1})\times10^{-9}$.

Step4: Use the exponent rule $a^m\times a^n=a^{m + n}$

$(7.6\times10^{-1})\times10^{-9}=7.6\times(10^{-1}\times10^{-9})=7.6\times10^{-1+( - 9)}=7.6\times10^{-10}$ meters.

Answer:

$7.6\times10^{-10}$ meters