(This is just an example)
A proton has a size of 1.23x10^-11 and an electron has a size of 1.4x10^-8. How many times smaller is and electron than a proton?
Now the part I need help with the which scientific notation goes in the numerator? Is it 1.23x10^-11 or the 1.4x10^-8?
This means: how many times larger is a proton then an electron?
Thus we put the proton on the numerator and the electron on the denominator.
From pure chemical science, a proton is wayyy bigger (and heavier) than an electron. Thus, if you get an answer that is really small then you know you are wrong.
Okay thank you. But would 0.000000000123 be 1.23x10^-11?
Actually, that would be 1.23 x 10^-10. Move it over one more place. Count 11 places from 1.23. From 1.23 to 0.123 there is one jump.
Would that mean that my answer would be 0.88x10^-18?
To determine how many times smaller an electron is compared to a proton, we can calculate the ratio between their sizes. The scientific notation that goes in the numerator depends on which particle's size we want to compare.
In this case, we want to find out how many times smaller the electron is than the proton. So, the numerator should be the electron's size, which is 1.4x10^-8.
To calculate the ratio, we divide the electron's size by the proton's size:
Ratio = Electron's Size / Proton's Size
Ratio = (1.4x10^-8) / (1.23x10^-11)
Now, we can simplify the expression by dividing the coefficients and subtracting the exponents:
Ratio = (1.4 / 1.23) * (10^-8 / 10^-11)
Ratio = 1.1382114 * 10^-8-(-11)
Ratio = 1.1382114 * 10^3
Therefore, the electron is approximately 1.1382114 * 10^3 times smaller than the proton.