Chemistry worksheet focusing on scientific notation, including conversion and calculation exercises.

Let's solve each part of this chemistry worksheet step by step. I'll go through Part A, Part B, and Part C with clear explanations.

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Part A: Express each of the following in standard form

We convert scientific notation to standard (decimal) form.

1. $ 5.2 \times 10^3 $
→ Move decimal 3 places right: $ 5200 $

2. $ 8.05 \times 10^{-4} $
→ Move decimal 4 places left: $ 0.000805 $

3. $ 9.6 \times 10^5 $
→ Move decimal 5 places right: $ 960,000 $

4. $ 3.71 \times 10^0 $
→ Any number × $10^0 = $ itself: $ 3.71 $

5. $ 5.5 \times 10^1 $
→ Move decimal 1 place right: $ 55 $

6. $ 6.460 \times 10^2 $
→ Move decimal 2 places right: $ 646.0 $

7. $ 8.77 \times 10^{-3} $
→ Move decimal 3 places left: $ 0.00877 $

8. $ 9.4 \times 10^{-5} $
→ Move decimal 5 places left: $ 0.000094 $

✔ Part A Answers:
1. 5200
2. 0.000805
3. 960,000
4. 3.71
5. 55
6. 646.0
7. 0.00877
8. 0.000094

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Part B: Express each of the following in scientific notation

Convert standard numbers to scientific notation (format: $ a \times 10^n $, where $ 1 \leq a < 10 $).

1. $ 78,000 $
→ Move decimal 4 places left: $ 7.8 \times 10^4 $

2. $ 0.00053 $
→ Move decimal 4 places right: $ 5.3 \times 10^{-4} $

3. $ 200 $
→ Move decimal 2 places left: $ 2.0 \times 10^2 $

4. $ 2.657 $
→ Already between 1 and 10 → $ 2.657 \times 10^0 $

5. $ 180 $
→ Move decimal 2 places left: $ 1.8 \times 10^2 $

6. $ 0.9043 $
→ Move decimal 1 place right: $ 9.043 \times 10^{-1} $

7. $ 0.870 $
→ Move decimal 1 place right: $ 8.70 \times 10^{-1} $

8. $ 0.01054 $
→ Move decimal 2 places right: $ 1.054 \times 10^{-2} $

✔ Part B Answers:
1. $ 7.8 \times 10^4 $
2. $ 5.3 \times 10^{-4} $
3. $ 2.0 \times 10^2 $
4. $ 2.657 \times 10^0 $
5. $ 1.8 \times 10^2 $
6. $ 9.043 \times 10^{-1} $
7. $ 8.70 \times 10^{-1} $
8. $ 1.054 \times 10^{-2} $

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Part C: Use the exponent function on your calculator (Y^x or EXP) to compute the following

We will use rules of exponents and scientific notation:

- $ (a \times 10^m) \times (b \times 10^n) = (a \times b) \times 10^{m+n} $
- $ \frac{a \times 10^m}{b \times 10^n} = \left(\frac{a}{b}\right) \times 10^{m-n} $
- For powers: $ (a \times 10^m)^n = a^n \times 10^{m \times n} $

Let’s solve each one:

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1. $ (6.02 \times 10^{23})(8.00 \times 10^3) $
→ Multiply coefficients: $ 6.02 \times 8.00 = 48.16 $
→ Add exponents: $ 10^{23+3} = 10^{26} $
→ $ 48.16 \times 10^{26} $ → Convert to proper scientific notation:
→ $ 4.816 \times 10^{27} $

2. $ (6.00 \times 10^{23})(8.00 \times 10^3) $
→ $ 6.00 \times 8.00 = 48.00 $, $ 10^{23+3} = 10^{26} $
→ $ 48.00 \times 10^{26} = 4.80 \times 10^{27} $

3. $ \frac{6.00 \times 10^{23}}{8.00 \times 10^3} $
→ $ \frac{6.00}{8.00} = 0.75 $, $ 10^{23-3} = 10^{20} $
→ $ 0.75 \times 10^{20} = 7.5 \times 10^{19} $

4. $ (-4.00 \times 10^4)(7.00 \times 10^{-3}) $
→ $ -4.00 \times 7.00 = -28.00 $, $ 10^{4 + (-3)} = 10^1 $
→ $ -28.00 \times 10^1 = -2.80 \times 10^2 $

5. $ \frac{3.00 \times 10^{-2}}{6.00 \times 10^{-3}} $
→ $ \frac{3.00}{6.00} = 0.5 $, $ 10^{-2 - (-3)} = 10^{1} $
→ $ 0.5 \times 10^1 = 5.0 \times 10^0 = 5.0 $

6. $ \frac{7.66 \times 10^{48}}{6.02 \times 10^{23}} $
→ $ \frac{7.66}{6.02} \approx 1.272 $, $ 10^{48-23} = 10^{25} $
→ $ 1.272 \times 10^{25} $

7. $ (3.00 \times 10^3)^2(8.00 \times 10^4) $
First: $ (3.00 \times 10^3)^2 = 3.00^2 \times 10^{3 \times 2} = 9.00 \times 10^6 $
Then: $ (9.00 \times 10^6)(8.00 \times 10^4) = 72.0 \times 10^{10} = 7.20 \times 10^{11} $

8. $ \frac{(6.02 \times 10^{23})(1.00 \times 10^{-3})}{5.54 \times 10^3} $
Numerator: $ 6.02 \times 1.00 = 6.02 $, $ 10^{23 + (-3)} = 10^{20} $ → $ 6.02 \times 10^{20} $
Denominator: $ 5.54 \times 10^3 $
Divide: $ \frac{6.02}{5.54} \approx 1.086 $, $ 10^{20 - 3} = 10^{17} $
→ $ 1.086 \times 10^{17} $

9. $ \frac{(6.02 \times 10^{23})(1.00 \times 10^{-3})}{5.54 \times 10^3} $
→ Same as #8 → $ 1.086 \times 10^{17} $

10. $ \frac{(6.02 \times 10^{23})(1.00 \times 10^{-3})}{5.54 \times 10^3} $
→ Again same → $ 1.086 \times 10^{17} $

Wait — looks like #8, #9, #10 are identical? Possibly typo in worksheet. But assuming it's correct:

Let’s recheck #8, #9, #10:

Actually, looking again:

#8: $ \frac{(6.02 \times 10^{23})(1.00 \times 10^{-3})}{5.54 \times 10^3} $ → already done → $ 1.086 \times 10^{17} $

#9: $ \frac{(6.02 \times 10^{23})(1.00 \times 10^{-3})}{5.54 \times 10^3} $ → same → $ 1.086 \times 10^{17} $

#10: $ \frac{(6.02 \times 10^{23})(1.00 \times 10^{-3})}{5.54 \times 10^3} $ → same → $ 1.086 \times 10^{17} $

So likely a copy-paste error in the worksheet.

But let's proceed with what's written.

Now continue:

11. $ \frac{(6.02 \times 10^{23})(1.00 \times 10^{-3})}{5.54 \times 10^3} $ → again same → $ 1.086 \times 10^{17} $

Wait — no, actually, the next ones are different:

Looking at the original image text:

11. $ \frac{(6.02 \times 10^{23})(1.00 \times 10^{-3})}{5.54 \times 10^3} $ → same as above → $ 1.086 \times 10^{17} $

12. $ (6.02 \times 10^{23})(1.00 \times 10^{-3}) $
→ $ 6.02 \times 1.00 = 6.02 $, $ 10^{23 - 3} = 10^{20} $ → $ 6.02 \times 10^{20} $

13. $ \frac{1.00 \times 10^{-3}}{7.00 \times 10^{-3}} $
→ $ \frac{1.00}{7.00} \approx 0.14286 $, $ 10^{-3 - (-3)} = 10^0 $ → $ 0.14286 $ → $ 1.4286 \times 10^{-1} $

14. $ \frac{(1.00 \times 10^{-3})(1.00 \times 10^{-3})}{6.02 \times 10^{-3}} $
Numerator: $ 1.00 \times 1.00 = 1.00 $, $ 10^{-3 + (-3)} = 10^{-6} $ → $ 1.00 \times 10^{-6} $
Divide: $ \frac{1.00 \times 10^{-6}}{6.02 \times 10^{-3}} = \frac{1.00}{6.02} \times 10^{-6 - (-3)} = 0.166 \times 10^{-3} = 1.66 \times 10^{-4} $

15. $ (7.00 \times 10^4)^3(3.00 \times 10^{-3})(6.02 \times 10^{23}) $
Step-by-step:
- $ (7.00 \times 10^4)^3 = 7.00^3 \times 10^{4 \times 3} = 343 \times 10^{12} = 3.43 \times 10^{14} $
- Now multiply: $ (3.43 \times 10^{14})(3.00 \times 10^{-3}) = 10.29 \times 10^{11} = 1.029 \times 10^{12} $
- Then: $ (1.029 \times 10^{12})(6.02 \times 10^{23}) = 6.19458 \times 10^{35} \approx 6.19 \times 10^{35} $

✔ Part C Answers:

1. $ 4.816 \times 10^{27} $
2. $ 4.80 \times 10^{27} $
3. $ 7.5 \times 10^{19} $
4. $ -2.80 \times 10^2 $
5. $ 5.0 $
6. $ 1.272 \times 10^{25} $
7. $ 7.20 \times 10^{11} $
8. $ 1.086 \times 10^{17} $
9. $ 1.086 \times 10^{17} $
10. $ 1.086 \times 10^{17} $
11. $ 1.086 \times 10^{17} $
12. $ 6.02 \times 10^{20} $
13. $ 1.4286 \times 10^{-1} $
14. $ 1.66 \times 10^{-4} $
15. $ 6.19 \times 10^{35} $

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✔ Final Answer Summary

#### Part A: Standard Form
1. 5200
2. 0.000805
3. 960,000
4. 3.71
5. 55
6. 646.0
7. 0.00877
8. 0.000094

#### Part B: Scientific Notation
1. $ 7.8 \times 10^4 $
2. $ 5.3 \times 10^{-4} $
3. $ 2.0 \times 10^2 $
4. $ 2.657 \times 10^0 $
5. $ 1.8 \times 10^2 $
6. $ 9.043 \times 10^{-1} $
7. $ 8.70 \times 10^{-1} $
8. $ 1.054 \times 10^{-2} $

#### Part C: Calculations
1. $ 4.816 \times 10^{27} $
2. $ 4.80 \times 10^{27} $
3. $ 7.5 \times 10^{19} $
4. $ -2.80 \times 10^2 $
5. $ 5.0 $
6. $ 1.272 \times 10^{25} $
7. $ 7.20 \times 10^{11} $
8. $ 1.086 \times 10^{17} $
9. $ 1.086 \times 10^{17} $
10. $ 1.086 \times 10^{17} $
11. $ 1.086 \times 10^{17} $
12. $ 6.02 \times 10^{20} $
13. $ 1.4286 \times 10^{-1} $
14. $ 1.66 \times 10^{-4} $
15. $ 6.19 \times 10^{35} $

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