Question #115aa

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.

#8.34xx10^7# 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 #(7xx)# to the right cancels the exponent; thus, the normal way of writing this number is #8.ul3400000.xx10^(7-7)=83,400,000xx10^o=83,400,000xx1=83,400,000 " with 3 significant figures"#

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