Q.A $12$ g sample of carbon-12 contains exactly one mole of atoms, i.e. Avogadro's number of atoms, $6.022\times10^{23}$. State the order of magnitude of this number, explaining the rounding rule you use.

[!TLDR] Round the coefficient of the scientific-notation form up or down to the nearest power of ten. [!ANSWER] Since $6.022 \ge 5$, …

Avogadro's number is $6.022\times10^{23}$, already in scientific notation $a\times10^{b}$ with $a=6.022$ and $b=23$.

The order-of-magnitude rounding rule states: if the coefficient $a \le 5$, the order of magnitude is $10^{b}$; if $a > 5$, the order of magnitude is rounded up to $10^{b+1}$.

Here $a = 6.022$, which is greater than $5$, so the coefficient rounds up to $10$, carrying the power up by one: the order of magnitude is $10^{23+1} = 10^{24}$. …

Write the number in scientific notation $a\times10^b$, then apply the rule: order of magnitud …

• Simply keeping the power of ten already present in the scientific notation ($10^{23}$) without checking whether the coefficient requires rounding the power up …