# Question #115aa

Jan 8, 2018

$8.34 \cdot {10}^{7}$ is scientific form, so we convert it to standard form by simplifying it

#### Explanation:

Standard notation is the "normal" way we write numbers, such as 23 or 450. Scientific notation is always expressed as a positive number less than 10 multiplied by 10 to the power of something. To convert back to standard notation, the scientific notation must be simplified as though it were a simple math problem.

${10}^{7}$ is 10,000,000 (10 million)

Since 8.34 is being multiplied by ${10}^{7}$, multiply it by 10,000,000.

8.34 times 1 is 8.34, but there are 7 zeros.

You can move the decimal place over by 2 so it becomes 834. 8.34 times 100 (note that there are 2 zeros) is 834. As for the remaining 5 zeros, add that on to 834. The final answer should be 83,400,000.

You could also simply move the decimal over by 7 because it was ${10}^{7}$ (adding a zero each time there isn't a digit). Since the number has two digits after the decimal, those are 2 numbers the decimal will move over. After that, a zero will be added each time.

Jan 8, 2018

$= 83 , 400 , 000$

#### Explanation:

$8.34 \times {10}^{7}$ is written in standard scientific notation with 3 significant figures. Take note that a positive exponent here indicates a large number (with zeros) and moving its decimal point to the left corresponds to a positive exponent and a negative exponent when moving it to the right.

To remove the exponent, moving the decimal point $\left(7 \times\right)$ to the right cancels the exponent; thus, the normal way of writing this number is $8. \underline{3400000.} \times {10}^{7 - 7} = 83 , 400 , 000 \times {10}^{o} = 83 , 400 , 000 \times 1 = 83 , 400 , 000 \text{ with 3 significant figures}$

Take note that any number raised to 0 is equal to 1; that is,
${a}^{o} = 1$