Question

How to multiply in scientific notation `(0.00100 "mole") xx (6.02 xx 10^23 "molecules")/(1 "mole")`?

Answer 1

Convert `0.00100"mole"` to scientific notation by moving the decimal to the right 3 places. This will give the number in scientific notation as `1.00xx10^(-3)"mole"`.

Now the question becomes `1.00xx10^(-3)"mole"*(6.022xx10^23"molecules")/(1 "mole")`

Multiply the coefficients.

`1.00xx6.022=6.022`

Multiply the base `10` for each number.

`10^(-3)xx10^23=10^((-3+23))=10^20`

Put the coefficient together with the base `10`.

`6.022xx10^20`

Rewrite the problem, canceling moles.

`1.00xx10^(-3)cancel("mole")*(6.022xx10^23"molecules")/(1 cancel("mole"))=6.02xx10^20"molecules"`