Question

the average diameter of an atoms nucleus is about ( 1 \times 10^{-14} ) meter. the diameter of a proton is about ( 1 \times 10^{-15} ) meter. which is larger, the diameter of a nucleus or the diameter of a proton?

Explanation:

Step1: Compare the exponents

Compare the exponents of \(10\) in \(1\times10^{-14}\) and \(1\times 10^{-15}\).
The exponent in \(1\times10^{-14}\) is \(- 14\), and the exponent in \(1\times10^{-15}\) is \(-15\).
Since \(-14>-15\), and when the coefficient (in this case \(1\)) is the same for two numbers in scientific notation \(a\times10^{n}\), the number with the larger exponent of \(10\) is larger.

Step2: Conclusion

So, \(1\times10^{-14}>1\times10^{-15}\)

Answer:

The diameter of a nucleus (\(1\times10^{-14}\text{ m}\)) is larger than the diameter of a proton (\(1\times10^{-15}\text{ m}\))