Perform the following operations and express the results in the correct number of significant digits or decimal places. Express all results in scientific notation. Please help me I'm so confused on how to do this!!
15. (1.71 x 10^6)(6.73 x 10^-8)/2.25 x 10
20. (533)(24)
21. (1.55 x 10^6)(3.05 x 10^-8)^2/(6.53 x 10^-9)^3
22. �ã9.74 x 10-3 + 9.65 x 10-4
You need to know the rules for significant figures. Here is a good site. Study it carefully.
http://www.chemteam.info/SigFigs/SigFigs.html
For 15: All multiplication and division. The s.f. rule is the final answer can have as many s.f. as the LOWEST number involved. All of them are 3 s.f.; therefore, you can have 3 s.f. in the answer. I didn't run the number because I think you omitted a number on the exponent of 10.
For #20. All multiplication so you can have 2 s.f. as dictated by the 24. My calculator gives 1.2792E4 so this is rounded to 1.3E4.
For 22:
In addition and subtraction you are allowed the minimum number after the decimal point, (I don't now what the a squigly line is. I'll assume that is not supposed to be there.
0.00974
+0.000965
---------------
0.010705
The first value is the least precise so you can use anything past 0.00001. So we round the final answer to
0.01070 (and I'm using the rounding rule that says round a 5 to the nearest even number).
Sure! I'll guide you through each operation step-by-step.
15. (1.71 x 10^6)(6.73 x 10^-8)/2.25 x 10
Step 1: First, let's multiply (1.71 x 10^6) by (6.73 x 10^-8):
(1.71 x 10^6) x (6.73 x 10^-8) = 11.5233 x 10^-2
Step 2: Next, let's divide the result by 2.25 x 10:
11.5233 x 10^-2 / (2.25 x 10) = 5.11346667 x 10^-3
Step 3: Now we need to express the result in scientific notation, with the correct number of significant digits or decimal places:
5.11346667 x 10^-3 can be approximated to 5.11 x 10^-3 (to three significant digits).
So, the result is 5.11 x 10^-3 in scientific notation.
Next, let's move on to the next problem.
20. (533)(24)
Step 1: Multiply 533 by 24:
533 x 24 = 12792
Step 2: The result does not require scientific notation since it is not a very large or very small number. Therefore, 12792 is the final answer.
Moving on to the next problem.
21. (1.55 x 10^6)(3.05 x 10^-8)^2/(6.53 x 10^-9)^3
Step 1: First, let's square (3.05 x 10^-8):
(3.05 x 10^-8)^2 = 9.3025 x 10^-16
Step 2: Next, let's cube (6.53 x 10^-9):
(6.53 x 10^-9)^3 = 2.36088817 x 10^-26
Step 3: Now, let's multiply (1.55 x 10^6) by (9.3025 x 10^-16) and divide the result by (2.36088817 x 10^-26):
(1.55 x 10^6) x (9.3025 x 10^-16) / (2.36088817 x 10^-26) = 617.0356915 x 10^2
Step 4: Finally, let's express the result in scientific notation:
617.0356915 x 10^2 can be approximated to 6.17 x 10^4 (to three significant digits).
So, the result is 6.17 x 10^4 in scientific notation.
Finally, let's move on to the last problem.
22. 9.74 x 10^-3 + 9.65 x 10^-4
Step 1: Add 9.74 x 10^-3 and 9.65 x 10^-4:
9.74 x 10^-3 + 9.65 x 10^-4 = 1.0635 x 10^-2
Step 2: The result does not require scientific notation since it is not a very large or very small number. Therefore, 1.0635 x 10^-2 is the final answer.
I hope this helps! Let me know if you have any more questions.
Sure! Let's go through each operation step by step.
15. (1.71 x 10^6)(6.73 x 10^-8)/2.25 x 10
To multiply two numbers in scientific notation, you multiply the coefficients and add the exponents. Then, to divide by another number in scientific notation, you subtract the exponent. Let's calculate it:
(1.71 x 10^6)(6.73 x 10^-8) = 1.71 * 6.73 * 10^6 * 10^-8 = 11.5007 x 10^-2 = 1.15 x 10^-1
Now, let's divide by 2.25 x 10:
1.15 x 10^-1 / (2.25 x 10) = 1.15 * 10^-1 / 2.25 * 10^1 = 0.5111 x 10^-2 = 5.111 x 10^-3
20. (533)(24)
This is a simple multiplication without scientific notation.
533 * 24 = 12,792
21. (1.55 x 10^6)(3.05 x 10^-8)^2/(6.53 x 10^-9)^3
For this expression, we need to square the value within the parentheses and cube another value. Let's do the calculations step by step:
(3.05 x 10^-8)^2 = (3.05^2) x (10^-8)^2 = 9.3025 x 10^-16
(6.53 x 10^-9)^3 = (6.53^3) x (10^-9)^3 = 275.635 x 10^-27
Now, let's substitute these values back into the expression:
(1.55 x 10^6) x (9.3025 x 10^-16) / (275.635 x 10^-27) = (1.55 x 9.3025 x 275.635) x (10^6 x 10^-16 / 10^-27) = 3.4417298125 x 10^7 / 10^11 = 3.4417298125 x 10^-4
22. �ã9.74 x 10-3 + 9.65 x 10-4
To add or subtract numbers in scientific notation, you need to have them expressed with the same exponent. Let's convert them to the same exponent first:
9.74 x 10^-3 + 9.65 x 10^-4 = (9.74 x 10^-3) + (9.65 x 10^-4 x 10) = 9.74 x 10^-3 + 9.65 x 10^-3 = (9.74 + 9.65) x 10^-3 = 19.39 x 10^-3 = 1.939 x 10^-2
I hope this helps you understand how to perform these operations. If you have any further questions, feel free to ask!