The atomic weight of aluminum is 26.982 u, how many aluminum atoms are there in a 4.55g sample of aluminum?

The key to this problem is the correct interpretation of what atomic weight means.

Notice that aluminium is said to have an atomic mass of #"26.982 u"#. The unit used here is the unified atomic mass unit, #u#.

The unified atomic mass unit is defined as #1/12"th"# of the mass of a neutral carbon-12 atom and is approximately equal to the mass of one nucleon, as in the mass of one proton or one neutron. Also, you should know that you have

#"1 u" color(white)(x) = color(white)(x)"1 g/mol"#

This means that the mass of one mole of aluminium atoms will be #"26.982 g"#.

As you know, one mole of any element contains exactly #6.022 * 10^(23)# atoms of that element.

This means that if you know how many moles of aluminium you have in #"4.55 g"#, you can use Avogadro's number to find the number of atoms.

#4.55 color(red)(cancel(color(black)("g"))) * "1 mole Al"/(26.982color(red)(cancel(color(black)("g")))) = "0.168631 moles Al"#

Therefore, you will have

#0.168631color(red)(cancel(color(black)("moles of Al"))) * (6.022 * 10^(23)"atoms of Al")/(1color(red)(cancel(color(black)("mole Al")))) = color(green)(1.02 * 10^(23)"atoms of Al")#

The answer is rounded to three sig figs, the number of isg figs you gave for the mass of the sample.