Order Of Magnitude And Estimation

The order of magnitude of a quantity is the power of ten nearest to the number when it is written in scientific notation as a × 10^b. The rule states that if the coefficient a is less than the square root of ten, about 3.16, the order of magnitude is simply 10^b; if a is 3.16 or greater, we round up to 10^(b+1). Here the value is 1.06 × 10^-10, and the coefficient 1.06 is comfortably below 3.16, so the order of magnitude remains 10^-10. The choice 10^-9 would apply only if the coefficient exceeded 3.16, which it does not. The choice 10^-11 mistakenly rounds the coefficient down past the lower power of ten. The choice 10^-8 is off by two powers and is far too large for atomic dimensions. This estimation technique is exactly how NCERT teaches comparison of physical scales from nuclei to galaxies. A reasonableness check confirms it: atomic sizes are universally quoted in angstroms, and one angstrom equals 10^-10 metre, matching the result.