Answer:
Convert each of the following into scientific notation:
a. 727 -----> 7.27 x 10^2
b. 172000 -----> 1.72 x 10^5
c. 0.000984 -----> 9.84 x 10^-4
d. 200.0 -----> 2 x 10^2 ? How does the extra decimal place affect the answer - is it more certain?
If you're told that a value is 200.0, then that is more precise than saying 200. What if the true value is a little bit more than 200? If I just say 200, then that could mean 200.1 or 200.2 or 200.3 or 200.36 or 200.25 or 200.14 ... it could mean a lot of things. By saying 200.0, I narrow down the error. Now the value is known with more precision -- it could be 200.01 or 200.02 or 200.03 ...
200.01 shows more precision than 200.1
2.000 x 10^2 shows more precision than 2.00 x 10^2
YOU WROTE 2 x 10^2 Note: 2 x 10^2 is not scientific notation
Since you show NO decimal places at all, the resulting precision is so low that the true value could be 221 or 238 or 209 or 241 or ...
e 0.014 -----> 1.4 x 10^-2
f. 2560000000000000000000000000000000 (use 4 sig. figs) -----> 2.560 x 10^33 Is there a reason for using 4 significant figures, or is that arbitrary?
Same situation as above because 2.560 is more precise than 2.56
By seeing the zero in 2.560 x 10^33, I know that the true value has a zero for its fourth digit.
If you write 2.56 x 10^33 instead, then I can't be sure what the fourth digit is.
2564000000000000000000000000000000, for example.
Convert each into decimal form:
a. 1.56 x 10^4 ----->15600
b. 2.6 x 10^-2 -----> .036 This is correct to me only if you intended to type 0.026
c. 736.9 x 10^5 -----> 73690000 Note: 736.9 x 10^5 is not scientific notation, and neither are the next two exercises.
d. 0.0059 x 10^5 -----> 590
e. 0.00059 x 10^-1 -----> .000059
Calculate the following:
a. 2.34 x 10^65 + 9.2 x 10^66 ------> I don't know what to do here. Should I change 2.34 x 10^65 to .234 x 10^66 and add them to get 9.4 x 10^66?
PERFECTION!
b. 313.0 - 1.2 x 10^3 -----> -.877 x 10^3 ? Same question as in a.
Firstly, -0.877 x 10^3 is not scientific notation.
Secondly, we can't write -8.77 x 10^2 either.
We are subtracting something close to 1200 from something close to 313.0
1.2 x 10^3 could be anything from 1200 through 1249, for example.
313.0 could be anything from 313.0 through 313.04, for example.
So, the difference could be anything from about -936 to about -877. We just don't know. Therefore, with respect to precision, we have to settle on -900.
How would you round your answer and express it in scientific notation to indicate the correct number of significant digits? Try again.
Calculate the following. Give the answer in correct scientific notation with the correct number of significant figures:
a. 8.95 x 10^76/1.25 x 10^56 -----> 7.16 x 10^20
b. (4.5 x 10^29)(2.45 x 10^100) -----> I'm not sure here. Do I multiply the individual components of the terms of the whole terms?
Do you remember the Commutative Property of Multiplication?
We are allowed to multiply a string of factors in ANY order we wish.
(A * B) * (C * D) = (A) * (B) * (C) * (D) = (A) * (C) * (B) * (D), if we like ...
Try again, and keep the multiplication rule for significant digits in mind when rounding your result and writing it in scientific notation.