Question

avogadros number is a constant that helps scientists count atoms and molecules. it is approximately equal to 602,200,000,000,000,000,000,000. how is this number expressed in scientific notation?
a. $\frac{6.022}{10^{24}}$
b. $6.022 \times 10^{20}$
c. $\frac{6.022}{10^{23}}$
d. $6.02 \times 10^{23}$
e. $6.02 \times 10^{-23}$

Explanation:

Step1: Recall scientific notation rules

Scientific notation is in the form \(a\times10^{n}\), where \(1\leq|a|\lt10\) and \(n\) is an integer. We need to convert \(602200000000000000000000\) to this form.

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

First, move the decimal point in \(602200000000000000000000\) to the left until we get a number between \(1\) and \(10\). Moving the decimal point 23 places to the left gives \(6.022\approx6.02\) (for simplicity, often rounded to two decimal places). The number of places we moved the decimal is the exponent \(n\), and since we moved it to the left, \(n\) is positive. So the number in scientific notation is \(6.02\times10^{23}\). We can check the options: Option A is not in correct scientific notation form, Option B has an incorrect exponent, Option C is not in correct form, Option E has a negative exponent which is wrong as the original number is large (positive exponent for large numbers).

Answer:

D. \(6.02\times10^{23}\)