# How do you calculate (3.6 times 10^15) × (8 × 10^21)?

May 13, 2016

$2.88 \times {10}^{37}$

#### Explanation:

$3.6 \times {10}^{15} \times 8 \times {10}^{21}$

$= 3.6 \times 8 \times {10}^{15} \times {10}^{21}$

Let's combine the $10 \text{'s}$:

$= 3.6 \times 8 \times {10}^{15 + 21}$

$= 3.6 \times 8 \times {10}^{36}$

Multiply the numbers:

$= 28.8 \times {10}^{36}$

This is NOT in the scientific form.

$\textcolor{red}{2.88 \times {10}^{n}}$ is the correct way of writing the number in the scientific notation .

Note: only 1 whole number should be on the left side of the decimal point. The remaining numbers come on the right side of the decimal point and this number is then multiplied by a power of $10$, as required.

Now, to write $28.8 \times {10}^{36}$ in scientific notation.

We can write $28.8 = 2.88 \times 10$.

Then, $28.8 \times {10}^{36}$

$= 2.88 \times 10 \times {10}^{36}$

Combine the $10 \text{'s}$

$= 2.88 \times {10}^{1 + 36}$

$\textcolor{red}{= 2.88 \times {10}^{37}}$

$\textcolor{b l u e}{\text{Some examples to understand scientific numbers: }}$

• $\textcolor{b l u e}{80000 \text{ in scientific notation will be } 8 \times {10}^{4}}$
• $\textcolor{b l u e}{1234 \text{ in scientific notation will be } 1.234 \times {10}^{3}}$
• $\textcolor{b l u e}{452.42 \text{ in scientific notation will be } 4.5242 \times {10}^{2}}$
• $\textcolor{b l u e}{0.004 \text{ in scientific notation will be } 4 \times {10}^{-} 3}$
• $\textcolor{b l u e}{0.0126 \text{ in scientific notation will be } 1.26 \times {10}^{-} 2}$