Question #115aa

2 Answers
Jan 8, 2018

#8.34*10^7# is scientific form, so we convert it to standard form by simplifying it


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



#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,