Question 875486: Express the number in normalized scientific notation:
0.045 x 10^7
Answer: 4.5 x 10^9
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! .045 * 10^7
you need to get the number into scientific notation form which means 1 digit to the left of the decimal point and the rest of the dibits to the right of the decimal point.
your standard notation for will be 4.5 * something.
in order to get 4.5 to be equivalent to .045, you have to divide it by 100.
you get 4.5 / 100 = .045
since 100 is the same as 10^2, you get:
4.5 / 10^2 = .045
since 4.5 / 10^2 is the same as 4.5 * 1/10^2, you get:
4.5 * 1 / 10^2 = .045
since 1/10^2 is equivalent to 10^-2, you get:
4.5 * 10^-2 = .045
your original expression is .045 * 10^7
replace .045 with 4.5 * 10^-2 and you will get:
4.5 * 10^-2 * 10^7
since 10^-2 * 10^7 = 10^(-2+7) = 10^5, then your expression becomes:
4.5 * 10^5
use your calculator to see that 4.5 * 10^5 = 450,000
use you calculator to see that .045 * 10^7 = 450,000
this confirms that .045 * 10^7 is the same number as as 4.5 * 10^5.
you were correct that .045 * 10^2 is equal to 4.5, but you went the wrong way.
what you needed to do was figure out what you had to do to 4.5 in order to make it equivalent to the original number of .045.
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