How to simplify 12 times 18 times 10^23 in scientific notation?

Nov 15, 2015

$2.16 \cdot {10}^{25}$

Explanation:

The scientific notation asks you to put numbers in the form

${a}_{0} , {a}_{1} {a}_{2} {a}_{3.} . . \cdot {10}^{k}$

So, $12$ becomes $1.2 \cdot 10$ and $18$ becomes $1.8 \cdot 10$.

The whole multiplication becomes

$1.2 \cdot 10 \cdot 1.8 \cdot 10 \cdot {10}^{23} = 1.2 \cdot 1.8 \cdot 10 \cdot 10 \cdot {10}^{23}$

The numeric part is multiplied as usual: $1.2 \cdot 1.8 = 2.16$
Powers of $10$ are multiplied summing the exponents:
$10 \cdot 10 \cdot {10}^{23} = {10}^{1 + 1 + 23} = {10}^{25}$.