The value of one atomic mass unit

Question

In my textbook, it is given:

1 atomic mass unit equals $1/12$th mass of one carbon 12-atom. Since mass of $6.02 * 10^{26}$ atoms of carbon-12 is $12\space\text{kg}$. Thus,

$$1 \text{ a.m.u (or u)} = \frac{1}{12} * \frac{12}{6.02 * 10^{26}} \text{ kg}$$

This makes sense to me. But what follows is that they make this value equal to:

$$1.66 * 10^{-27} \text{ kg}$$

Which goes against the value that I had thought. I thought that the $12$s would cancel out resulting in only:

$$(6.02*10^{26})^{-1} \text{ kg}$$

Please help my out in figuring where did I go wrong.

Answer 1

Both your answers are same.

$1.66\times 10^{-27} = (6.02\times 10^{26})^{-1}$

Hope that helps...

Answer 2

Both of you are right for 1.66∗10−27 kg=(6.02∗1026)−1 kg. NB: 1 amu=1/12 of 1 (one) C-12 atom mass (weight); 1 C-12 atom weight = 1.9926 x 10^-23 gr (please see the Avogadro number and mole unit)= 1.9926 x 10^-23 gr x 1Kg/10^3 gr=1.9926 x 10^-26 Kg therefore 1 amu=1/12 x 1.99 10^-26 Kg= 1.6666 x 10^-27 Kg.