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Question 501623: my question is ...
Which of the following is equal to 3.4 times 10 to the negative 4th power?
1. 0.34
2. 0.034
3. 0.0034
4. 0.00034
5. 3.4
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the rules are:
each time you shift the decimal point one position to the right, you need to subtract 1 from the exponent of 10.
conversely, each time you subtract 1 from the exponent of 10, you need to shift the decimal point one position to the right.
each time you shift the decimal point one position to the left, you need to add 1 to the exponent of 10.
conversely, each time you add 1 to the exponent of 10, you need to shift the decimal point one position to the left.
10^0 = 1
100.0 is equivalent to 100.0 * 10^0
shift the decimal point to the right one place and you have to subtract 1 from the exponent of 10. the number becomes 1000.0 * 10^-1
add 1 to the exponent of 10 and the decimal point has to be shifted to the left one time. the number becomes 100 * 10^0.
decimal notation of a number would be:
537.66329
non-standard scientific notation of that same number without shifting any decimal points would be:
537.66329 * 10^0
any number in decimal notation format will be equivalent to that number * 10^0 in non-standard scientific notation format.
the standard format of the scientific notation of any number is always 1 digit to the left of the decimal point and the rest of the digits to the right of the decimal point.
the number 357.66329 in decimal notation format needs to be converted to the standard scientific notation format by following the rules for shifting decimal places.
we start with 537.66329 in decimal notation format.
we multiply it by 10^0 to get it into non-standard scientific notation format.
the number becomes:
537.66329 * 10^0
we need to move the decimal 2 places to the left.
this means we also have to add 2 to the exponent of the 10.
the standard scientific notation format of the number becomes:
5.3766329 * 10^2
537.66329 in decimal notation format = 5.3766329 * 10^2 in standard scientific notation format.
use your calculator to confirm that these 2 number are equivalent.
you don't really need a calculator.
10^2 is equal to 100.
5.3766329 * 100 is equal to 537.66329
your problem starts out as:
3.4 * 10^-4
the number is in scientific notation format.
you want to convert the number to decimal notation format.
you need to get the 10^-4 to become 10^0 by adding 4 to the exponent.
if you add 4 to the exponent of 10, you have to shift the decimal point 4 places to the left.
you will wind up with .00034 * 10^0 which will become:
.00034
you may use your calculator to confirm that .00034 is equal to 3.4 * 10^-4.
a good reference to help you understand this better can be found here:
http://www.purplemath.com/modules/exponent3.htm
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