Writing Numbers in Scientific Notation (A) Worksheet | 8th Grade ... - Free Printable
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Step-by-step solution for: Writing Numbers in Scientific Notation (A) Worksheet | 8th Grade ...
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Show Answer Key & Explanations
Step-by-step solution for: Writing Numbers in Scientific Notation (A) Worksheet | 8th Grade ...
Let's solve this step-by-step. The task is to convert numbers from scientific notation into standard (number) form.
---
A number in scientific notation is written as:
$$
a \times 10^n
$$
Where:
- $ a $ is a number between 1 and 10 (inclusive of 1, exclusive of 10),
- $ n $ is an integer (positive or negative).
To convert to standard form:
- If $ n > 0 $: move the decimal point right by $ n $ places.
- If $ n < 0 $: move the decimal point left by $ |n| $ places.
---
## ✔ Section A: Convert from Scientific Notation to Number Form (Positive Exponents)
We’ll go through each one:
1. $ 8.2 \times 10^4 $
→ Move decimal 4 places right:
$ 8.2 \rightarrow 82000 $
✔ 82,000
2. $ 9.1 \times 10^3 $
→ Move decimal 3 places right:
$ 9.1 \rightarrow 9100 $
✔ 9,100
3. $ 7.3 \times 10^2 $
→ Move decimal 2 places right:
$ 7.3 \rightarrow 730 $
✔ 730
4. $ 6.5 \times 10^8 $
→ Move decimal 8 places right:
$ 6.5 \rightarrow 650,000,000 $
✔ 650,000,000
5. $ 4.9 \times 10^4 $
→ Move decimal 4 places right:
$ 4.9 \rightarrow 49,000 $
✔ 49,000
6. $ 5.6 \times 10^2 $
→ Move decimal 2 places right:
$ 5.6 \rightarrow 560 $
✔ 560
7. $ 8.21 \times 10^3 $
→ Move decimal 3 places right:
$ 8.21 \rightarrow 8,210 $
✔ 8,210
8. $ 6.13 \times 10^4 $
→ Move decimal 4 places right:
$ 6.13 \rightarrow 61,300 $
✔ 61,300
9. $ 7.09 \times 10^8 $
→ Move decimal 8 places right:
$ 7.09 \rightarrow 709,000,000 $
✔ 709,000,000
---
10. $ 5.345 \times 10^4 $
→ Move decimal 4 places right:
$ 5.345 \rightarrow 53,450 $
✔ 53,450
11. $ 6.902 \times 10^3 $
→ Move decimal 3 places right:
$ 6.902 \rightarrow 6,902 $
✔ 6,902
12. $ 2.003 \times 10^2 $
→ Move decimal 2 places right:
$ 2.003 \rightarrow 200.3 $
✔ 200.3
13. $ 1.98 \times 10^8 $
→ Move decimal 8 places right:
$ 1.98 \rightarrow 198,000,000 $
✔ 198,000,000
14. $ 4.012 \times 10^4 $
→ Move decimal 4 places right:
$ 4.012 \rightarrow 40,120 $
✔ 40,120
15. $ 7.087 \times 10^2 $
→ Move decimal 2 places right:
$ 7.087 \rightarrow 708.7 $
✔ 708.7
16. $ 8.5245 \times 10^9 $
→ Move decimal 9 places right:
$ 8.5245 \rightarrow 8,524,500,000 $
✔ 8,524,500,000
17. $ 7.6909 \times 10^7 $
→ Move decimal 7 places right:
$ 7.6909 \rightarrow 76,909,000 $
✔ 76,909,000
18. $ 7.1156 \times 10^8 $
→ Move decimal 8 places right:
$ 7.1156 \rightarrow 711,560,000 $
✔ 711,560,000
---
## ✔ Section B: Convert from Scientific Notation to Standard Form (Negative Exponents)
Now we handle negative exponents, which means moving the decimal left.
1. $ 8.2 \times 10^{-4} $
→ Move decimal 4 places left:
$ 8.2 \rightarrow 0.00082 $
✔ 0.00082
2. $ 9.1 \times 10^{-3} $
→ Move decimal 3 places left:
$ 9.1 \rightarrow 0.0091 $
✔ 0.0091
3. $ 7.3 \times 10^{-2} $
→ Move decimal 2 places left:
$ 7.3 \rightarrow 0.073 $
✔ 0.073
4. $ 6.5 \times 10^{-8} $
→ Move decimal 8 places left:
$ 6.5 \rightarrow 0.000000065 $
✔ 0.000000065
5. $ 4.9 \times 10^{-4} $
→ Move decimal 4 places left:
$ 4.9 \rightarrow 0.00049 $
✔ 0.00049
6. $ 5.6 \times 10^{-2} $
→ Move decimal 2 places left:
$ 5.6 \rightarrow 0.056 $
✔ 0.056
7. $ 8.21 \times 10^{-3} $
→ Move decimal 3 places left:
$ 8.21 \rightarrow 0.00821 $
✔ 0.00821
8. $ 4.62 \times 10^{-7} $
→ Move decimal 7 places left:
$ 4.62 \rightarrow 0.000000462 $
✔ 0.000000462
9. $ 8.03 \times 10^{-8} $
→ Move decimal 8 places left:
$ 8.03 \rightarrow 0.0000000803 $
✔ 0.0000000803
---
10. $ 5.345 \times 10^{-4} $
→ Move decimal 4 places left:
$ 5.345 \rightarrow 0.0005345 $
✔ 0.0005345
11. $ 6.902 \times 10^{-3} $
→ Move decimal 3 places left:
$ 6.902 \rightarrow 0.006902 $
✔ 0.006902
12. $ 2.003 \times 10^{-2} $
→ Move decimal 2 places left:
$ 2.003 \rightarrow 0.02003 $
✔ 0.02003
13. $ 1.981 \times 10^{-8} $
→ Move decimal 8 places left:
$ 1.981 \rightarrow 0.00000001981 $
✔ 0.00000001981
14. $ 4.012 \times 10^{-4} $
→ Move decimal 4 places left:
$ 4.012 \rightarrow 0.0004012 $
✔ 0.0004012
15. $ 7.087 \times 10^{-2} $
→ Move decimal 2 places left:
$ 7.087 \rightarrow 0.07087 $
✔ 0.07087
16. $ 8.5245 \times 10^{-9} $
→ Move decimal 9 places left:
$ 8.5245 \rightarrow 0.0000000085245 $
✔ 0.0000000085245
17. $ 7.6909 \times 10^{-7} $
→ Move decimal 7 places left:
$ 7.6909 \rightarrow 0.00000076909 $
✔ 0.00000076909
18. $ 7.1156 \times 10^{-8} $
→ Move decimal 8 places left:
$ 7.1156 \rightarrow 0.000000071156 $
✔ 0.000000071156
---
## ✔ Final Answer Table
| Number Form | Scientific Notation |
|--------------------|--------------------------|
| 82,000 | $ 8.2 \times 10^4 $ |
| 9,100 | $ 9.1 \times 10^3 $ |
| 730 | $ 7.3 \times 10^2 $ |
| 650,000,000 | $ 6.5 \times 10^8 $ |
| 49,000 | $ 4.9 \times 10^4 $ |
| 560 | $ 5.6 \times 10^2 $ |
| 8,210 | $ 8.21 \times 10^3 $ |
| 61,300 | $ 6.13 \times 10^4 $ |
| 709,000,000 | $ 7.09 \times 10^8 $ |
| 53,450 | $ 5.345 \times 10^4 $ |
| 6,902 | $ 6.902 \times 10^3 $ |
| 200.3 | $ 2.003 \times 10^2 $ |
| 198,000,000 | $ 1.98 \times 10^8 $ |
| 40,120 | $ 4.012 \times 10^4 $ |
| 708.7 | $ 7.087 \times 10^2 $ |
| 8,524,500,000 | $ 8.5245 \times 10^9 $ |
| 76,909,000 | $ 7.6909 \times 10^7 $ |
| 711,560,000 | $ 7.1156 \times 10^8 $ |
---
| Number Form | Scientific Notation |
|------------------------|----------------------------|
| 0.00082 | $ 8.2 \times 10^{-4} $ |
| 0.0091 | $ 9.1 \times 10^{-3} $ |
| 0.073 | $ 7.3 \times 10^{-2} $ |
| 0.000000065 | $ 6.5 \times 10^{-8} $ |
| 0.00049 | $ 4.9 \times 10^{-4} $ |
| 0.056 | $ 5.6 \times 10^{-2} $ |
| 0.00821 | $ 8.21 \times 10^{-3} $ |
| 0.000000462 | $ 4.62 \times 10^{-7} $ |
| 0.0000000803 | $ 8.03 \times 10^{-8} $ |
| 0.0005345 | $ 5.345 \times 10^{-4} $ |
| 0.006902 | $ 6.902 \times 10^{-3} $ |
| 0.02003 | $ 2.003 \times 10^{-2} $ |
| 0.00000001981 | $ 1.981 \times 10^{-8} $ |
| 0.0004012 | $ 4.012 \times 10^{-4} $ |
| 0.07087 | $ 7.087 \times 10^{-2} $ |
| 0.0000000085245 | $ 8.5245 \times 10^{-9} $ |
| 0.00000076909 | $ 7.6909 \times 10^{-7} $ |
| 0.000000071156 | $ 7.1156 \times 10^{-8} $ |
---
## 📌 Summary of Key Concepts
- Positive exponent: Move decimal to the right.
- Negative exponent: Move decimal to the left.
- Always count the number of places equal to the exponent.
- Add zeros if needed to fill in empty spaces.
This skill is essential for working with very large or very small numbers in science and engineering!
Let me know if you'd like this formatted as a printable answer sheet!
---
🔷 Scientific Notation Review
A number in scientific notation is written as:
$$
a \times 10^n
$$
Where:
- $ a $ is a number between 1 and 10 (inclusive of 1, exclusive of 10),
- $ n $ is an integer (positive or negative).
To convert to standard form:
- If $ n > 0 $: move the decimal point right by $ n $ places.
- If $ n < 0 $: move the decimal point left by $ |n| $ places.
---
## ✔ Section A: Convert from Scientific Notation to Number Form (Positive Exponents)
We’ll go through each one:
Left Column:
1. $ 8.2 \times 10^4 $
→ Move decimal 4 places right:
$ 8.2 \rightarrow 82000 $
✔ 82,000
2. $ 9.1 \times 10^3 $
→ Move decimal 3 places right:
$ 9.1 \rightarrow 9100 $
✔ 9,100
3. $ 7.3 \times 10^2 $
→ Move decimal 2 places right:
$ 7.3 \rightarrow 730 $
✔ 730
4. $ 6.5 \times 10^8 $
→ Move decimal 8 places right:
$ 6.5 \rightarrow 650,000,000 $
✔ 650,000,000
5. $ 4.9 \times 10^4 $
→ Move decimal 4 places right:
$ 4.9 \rightarrow 49,000 $
✔ 49,000
6. $ 5.6 \times 10^2 $
→ Move decimal 2 places right:
$ 5.6 \rightarrow 560 $
✔ 560
7. $ 8.21 \times 10^3 $
→ Move decimal 3 places right:
$ 8.21 \rightarrow 8,210 $
✔ 8,210
8. $ 6.13 \times 10^4 $
→ Move decimal 4 places right:
$ 6.13 \rightarrow 61,300 $
✔ 61,300
9. $ 7.09 \times 10^8 $
→ Move decimal 8 places right:
$ 7.09 \rightarrow 709,000,000 $
✔ 709,000,000
---
Right Column:
10. $ 5.345 \times 10^4 $
→ Move decimal 4 places right:
$ 5.345 \rightarrow 53,450 $
✔ 53,450
11. $ 6.902 \times 10^3 $
→ Move decimal 3 places right:
$ 6.902 \rightarrow 6,902 $
✔ 6,902
12. $ 2.003 \times 10^2 $
→ Move decimal 2 places right:
$ 2.003 \rightarrow 200.3 $
✔ 200.3
13. $ 1.98 \times 10^8 $
→ Move decimal 8 places right:
$ 1.98 \rightarrow 198,000,000 $
✔ 198,000,000
14. $ 4.012 \times 10^4 $
→ Move decimal 4 places right:
$ 4.012 \rightarrow 40,120 $
✔ 40,120
15. $ 7.087 \times 10^2 $
→ Move decimal 2 places right:
$ 7.087 \rightarrow 708.7 $
✔ 708.7
16. $ 8.5245 \times 10^9 $
→ Move decimal 9 places right:
$ 8.5245 \rightarrow 8,524,500,000 $
✔ 8,524,500,000
17. $ 7.6909 \times 10^7 $
→ Move decimal 7 places right:
$ 7.6909 \rightarrow 76,909,000 $
✔ 76,909,000
18. $ 7.1156 \times 10^8 $
→ Move decimal 8 places right:
$ 7.1156 \rightarrow 711,560,000 $
✔ 711,560,000
---
## ✔ Section B: Convert from Scientific Notation to Standard Form (Negative Exponents)
Now we handle negative exponents, which means moving the decimal left.
Left Column:
1. $ 8.2 \times 10^{-4} $
→ Move decimal 4 places left:
$ 8.2 \rightarrow 0.00082 $
✔ 0.00082
2. $ 9.1 \times 10^{-3} $
→ Move decimal 3 places left:
$ 9.1 \rightarrow 0.0091 $
✔ 0.0091
3. $ 7.3 \times 10^{-2} $
→ Move decimal 2 places left:
$ 7.3 \rightarrow 0.073 $
✔ 0.073
4. $ 6.5 \times 10^{-8} $
→ Move decimal 8 places left:
$ 6.5 \rightarrow 0.000000065 $
✔ 0.000000065
5. $ 4.9 \times 10^{-4} $
→ Move decimal 4 places left:
$ 4.9 \rightarrow 0.00049 $
✔ 0.00049
6. $ 5.6 \times 10^{-2} $
→ Move decimal 2 places left:
$ 5.6 \rightarrow 0.056 $
✔ 0.056
7. $ 8.21 \times 10^{-3} $
→ Move decimal 3 places left:
$ 8.21 \rightarrow 0.00821 $
✔ 0.00821
8. $ 4.62 \times 10^{-7} $
→ Move decimal 7 places left:
$ 4.62 \rightarrow 0.000000462 $
✔ 0.000000462
9. $ 8.03 \times 10^{-8} $
→ Move decimal 8 places left:
$ 8.03 \rightarrow 0.0000000803 $
✔ 0.0000000803
---
Right Column:
10. $ 5.345 \times 10^{-4} $
→ Move decimal 4 places left:
$ 5.345 \rightarrow 0.0005345 $
✔ 0.0005345
11. $ 6.902 \times 10^{-3} $
→ Move decimal 3 places left:
$ 6.902 \rightarrow 0.006902 $
✔ 0.006902
12. $ 2.003 \times 10^{-2} $
→ Move decimal 2 places left:
$ 2.003 \rightarrow 0.02003 $
✔ 0.02003
13. $ 1.981 \times 10^{-8} $
→ Move decimal 8 places left:
$ 1.981 \rightarrow 0.00000001981 $
✔ 0.00000001981
14. $ 4.012 \times 10^{-4} $
→ Move decimal 4 places left:
$ 4.012 \rightarrow 0.0004012 $
✔ 0.0004012
15. $ 7.087 \times 10^{-2} $
→ Move decimal 2 places left:
$ 7.087 \rightarrow 0.07087 $
✔ 0.07087
16. $ 8.5245 \times 10^{-9} $
→ Move decimal 9 places left:
$ 8.5245 \rightarrow 0.0000000085245 $
✔ 0.0000000085245
17. $ 7.6909 \times 10^{-7} $
→ Move decimal 7 places left:
$ 7.6909 \rightarrow 0.00000076909 $
✔ 0.00000076909
18. $ 7.1156 \times 10^{-8} $
→ Move decimal 8 places left:
$ 7.1156 \rightarrow 0.000000071156 $
✔ 0.000000071156
---
## ✔ Final Answer Table
Section A: Positive Exponents
| Number Form | Scientific Notation |
|--------------------|--------------------------|
| 82,000 | $ 8.2 \times 10^4 $ |
| 9,100 | $ 9.1 \times 10^3 $ |
| 730 | $ 7.3 \times 10^2 $ |
| 650,000,000 | $ 6.5 \times 10^8 $ |
| 49,000 | $ 4.9 \times 10^4 $ |
| 560 | $ 5.6 \times 10^2 $ |
| 8,210 | $ 8.21 \times 10^3 $ |
| 61,300 | $ 6.13 \times 10^4 $ |
| 709,000,000 | $ 7.09 \times 10^8 $ |
| 53,450 | $ 5.345 \times 10^4 $ |
| 6,902 | $ 6.902 \times 10^3 $ |
| 200.3 | $ 2.003 \times 10^2 $ |
| 198,000,000 | $ 1.98 \times 10^8 $ |
| 40,120 | $ 4.012 \times 10^4 $ |
| 708.7 | $ 7.087 \times 10^2 $ |
| 8,524,500,000 | $ 8.5245 \times 10^9 $ |
| 76,909,000 | $ 7.6909 \times 10^7 $ |
| 711,560,000 | $ 7.1156 \times 10^8 $ |
---
Section B: Negative Exponents
| Number Form | Scientific Notation |
|------------------------|----------------------------|
| 0.00082 | $ 8.2 \times 10^{-4} $ |
| 0.0091 | $ 9.1 \times 10^{-3} $ |
| 0.073 | $ 7.3 \times 10^{-2} $ |
| 0.000000065 | $ 6.5 \times 10^{-8} $ |
| 0.00049 | $ 4.9 \times 10^{-4} $ |
| 0.056 | $ 5.6 \times 10^{-2} $ |
| 0.00821 | $ 8.21 \times 10^{-3} $ |
| 0.000000462 | $ 4.62 \times 10^{-7} $ |
| 0.0000000803 | $ 8.03 \times 10^{-8} $ |
| 0.0005345 | $ 5.345 \times 10^{-4} $ |
| 0.006902 | $ 6.902 \times 10^{-3} $ |
| 0.02003 | $ 2.003 \times 10^{-2} $ |
| 0.00000001981 | $ 1.981 \times 10^{-8} $ |
| 0.0004012 | $ 4.012 \times 10^{-4} $ |
| 0.07087 | $ 7.087 \times 10^{-2} $ |
| 0.0000000085245 | $ 8.5245 \times 10^{-9} $ |
| 0.00000076909 | $ 7.6909 \times 10^{-7} $ |
| 0.000000071156 | $ 7.1156 \times 10^{-8} $ |
---
## 📌 Summary of Key Concepts
- Positive exponent: Move decimal to the right.
- Negative exponent: Move decimal to the left.
- Always count the number of places equal to the exponent.
- Add zeros if needed to fill in empty spaces.
This skill is essential for working with very large or very small numbers in science and engineering!
Let me know if you'd like this formatted as a printable answer sheet!
Parent Tip: Review the logic above to help your child master the concept of scientific notation worksheet for seventh grade.
