SOLUTION: (5.2×10^−2)−(8.3×10^−3) Simplify the expression and write answer in scientific notation.

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Question 1185335: (5.2×10^−2)−(8.3×10^−3)
Simplify the expression and write answer in scientific notation.
Found 3 solutions by Theo, greenestamps, MathTherapy:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
your expression is:

(5.2 * 10^-2) - (8.3 * 10^-3)

if you used your calculator, you would enter:

(5.2*10^-2)-(8.3*10^-3) and the calculator would tell you that the answer is .0437.

if you wanted to do this manually, you could do:

5.2 * 10^-2 is equal to 5.2 * 1/10^2 which is equal to 5.2/10^2 which is equal to 5.2/100 which is equal to .052.

8.3 * 10^-3 is equal to 8.3 * 1/10^3 which is equal to 8.3/10^3 which is equal to 8.3/1000 which is equal to .0083.

.052 - .0083 is equal to .0437.

you could also manipulate the operands to make 10^x the same for each.
in that way, you could factor out the operand.

for example, assume you wanted to make everything * 10^-3.

8.3 * 10^-3 would be left alone.

5.2 * 10^-2 would multiply 5.2 by 10 and divide 10^-2 by 10.

the multiplication and the division by 10 leave the resultant the same because 10/10 = 1.

you would get:

5.2 * 10 = 52

10^-2 / 10 is the same as 10^-2 / 10^1 which is the same as 10^-2 * 10^-1 which is the same as 10^(-2 - 1) which is the same as 10^-3.

your result would be 52 * 10^-3 is the same number as 5.2 * 10^-2.

you can then use 52 * 10^-3 in your calculation, in place of 5.2 * 10-2.

you would get:

(52 * 10^-3) - (8.3 * 10^-3) is equal to (52 - 8.3) * 10^-3 which is equal to 43.7 * 10^ -3.

43.7 * 10^-3 is the same as 43.7 / 10^3 which is the same as 43.7 / 1000 which is the same as .0437.

your answer is .0437, any way you want to calculate it.

keep in mind that b^-1 is equal to 1/b^x.

this is one of the laws of exponent arithmetic.

also keep in mind that b^x * b^y is equal to b(x + y) and b^x / b^y is equal to b(x - y)

these are two other laws of exponent arithmetic.

here's a reference on the laws of exponent arithmetic.

https://people.sunyulster.edu/nicholsm/webct/webct2/laws_of_exponents.htm

here's one reference on scientific notation.

https://www.mathsisfun.com/numbers/scientific-notation.html

there are many others.

here's a result of a search that i did.

https://www.google.com/search?q=scientific+notation&rlz=1C1CHBD_enUS961US961&oq=scientific+notation&aqs=chrome.0.69i59l2j0i512j0i131i433i512l2j69i60l3.4448j0j7&sourceid=chrome&ie=UTF-8

if you need more help on scientific notation, send me an email with your problems and i'll work them out for you with explanations as best i can provide them.



Answer by greenestamps(13195)   (Show Source): You can put this solution on YOUR website!


Rewrite the two terms with the same power of 10, perform the arithmetic, and simplify if necessary.






OR
Answer by MathTherapy(10549)   (Show Source): You can put this solution on YOUR website!

(5.2×10^−2)−(8.3×10^−3)
Simplify the expression and write answer in scientific notation.
       

              ----- Factoring out GCF, 10-3

 

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