How do you evaluate 0.028\times ( 3.4\times 10^ { 4} )?

Mar 2, 2018

Use BEDMAS; brackets, exponents, division/multiplication, addition/subtraction. (All in order)

Explanation:

-Begin with the brackets. Within the brackets, there is an exponent. Evaluate. It should give 10,000.

-Then multiply this number by 3.4 because it's in the brackets. You should get 34,000.

-Finish by multiplying this by 0.028. You should get 952

Mar 2, 2018

If the decimals are giving you a problem use the type of approach demonstrated.

$9.52 \times {10}^{2}$

Explanation:

Lets get rid of the decimals for now and then put them back at the end

$3.4$ is the same as $34 \times \frac{1}{10}$

So $3.4 \times {10}^{4}$ is the same as $34 \times \frac{1}{10} \times {10}^{4} \textcolor{w h i t e}{\text{dd") =color(white)("dd}} 34 \times {10}^{3}$

$0.028$ is the same as $28 \times \frac{1}{1000} = 28 \times \frac{1}{10} ^ 3$
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$\textcolor{b l u e}{\text{Putting it all together}}$

$28 \times \frac{1}{10} ^ 3 \times 34 \times {10}^{3}$

$28 \times 34 \times {10}^{3} / {10}^{3}$

$28 \times 34 = 952$

Choosing to put this into the same format as in part of the question $\left(3.4 \times {10}^{4}\right)$ we have:

$952 \to 9.52 \times {10}^{2}$

Mar 2, 2018

Answer is $952$

Explanation:

$0.028 \cdot \left(3.4 \cdot {10}^{4}\right)$ Given Equation

$3.4 \cdot {10}^{4}$ In a way, this is just scientific notation, meaning that the number just by looking at it would be $34 , 000$.

However, if you are not familiar with scientific equation, you can first look at ${10}^{4}$. Well, what is $10 \cdot 10 \cdot 10 \cdot 10$? It would be $10 , 000$.

Now that you have that part, we can continue looking inside the brackets. Giving us $3.4 \cdot 10 , 000$. The way I would solve this is by, looking at the ONLY numbers that are not $0$.

So, really we are looking at $3.4 \cdot 1$, which is $3.4$. Now we add the left over zeros, since $10 , 000$ has a total of $4$ zeros, add $4$ zeros to $3.4$.

So $\left(3.4 \cdot {10}^{4}\right) = 34 , 000$. Great! Now to solve the rest.

$0.028 \cdot 34 , 000$ Is now leftover. Could solve this like a regular multiplication problem.

$34 \cdot 28 = 952$, I would add the $3$ zeros from $34 , 000$, however since $0.028$ has $3$ numbers behind the decimal point, that would cancel everything out. Making the answer be $952$.