Converting Forms Worksheets | Free - Distance Learning, worksheets ... - Free Printable
Educational worksheet: Converting Forms Worksheets | Free - Distance Learning, worksheets .... Download and print for classroom or home learning activities.
PNG
442×567
33.7 KB
Free · Personal Use
Quality Assured by Worksheets Library Team
Reviewed for educational accuracy and age-appropriateness
ID: #1096005
⭐
Show Answer Key & Explanations
Step-by-step solution for: Converting Forms Worksheets | Free - Distance Learning, worksheets ...
▼
Show Answer Key & Explanations
Step-by-step solution for: Converting Forms Worksheets | Free - Distance Learning, worksheets ...
To convert numbers from scientific notation to standard form, we need to understand what the exponent tells us.
The general rule is:
- If the exponent is positive, move the decimal point to the right.
- If the exponent is negative, move the decimal point to the left.
- The number of places you move the decimal equals the absolute value of the exponent.
Let’s go step by step for each problem:
---
1) 3.6 × 10²
Exponent is +2 → move decimal 2 places right.
3.6 → 36 → 360
✔ Answer: 360
---
2) 7.35 × 10⁴
Exponent is +4 → move decimal 4 places right.
7.35 → 73.5 → 735 → 7,350 → 73,500
✔ Answer: 73,500
---
3) 6 × 10⁵
Exponent is +5 → move decimal 5 places right.
6 → 60 → 600 → 6,000 → 60,000 → 600,000
✔ Answer: 600,000
---
4) 5.15 × 10⁴
Exponent is +4 → move decimal 4 places right.
5.15 → 51.5 → 515 → 5,150 → 51,500
✔ Answer: 51,500
---
5) 9.51 × 10³
Exponent is +3 → move decimal 3 places right.
9.51 → 95.1 → 951 → 9,510
✔ Answer: 9,510
---
6) 2.57 × 10²
Exponent is +2 → move decimal 2 places right.
2.57 → 25.7 → 257
✔ Answer: 257
---
7) 9.59485169 × 10⁸
Exponent is +8 → move decimal 8 places right.
Start: 9.59485169
Move 1: 95.9485169
Move 2: 959.485169
Move 3: 9,594.85169
Move 4: 95,948.5169
Move 5: 959,485.169
Move 6: 9,594,851.69
Move 7: 95,948,516.9
Move 8: 959,485,169
✔ Answer: 959,485,169
---
8) 5.39 × 10³
Exponent is +3 → move decimal 3 places right.
5.39 → 53.9 → 539 → 5,390
✔ Answer: 5,390
---
9) 1.945 × 10⁰
Any number to the power of 0 is 1 → so this is just 1.945 × 1 = 1.945
✔ Answer: 1.945
---
10) 6 × 10³
Exponent is +3 → move decimal 3 places right.
6 → 60 → 600 → 6,000
✔ Answer: 6,000
---
11) 9.94 × 10²
Exponent is +2 → move decimal 2 places right.
9.94 → 99.4 → 994
✔ Answer: 994
---
12) 0.707 × 10⁻¹
Exponent is -1 → move decimal 1 place left.
0.707 → 0.0707
✔ Answer: 0.0707
---
13) 8.91 × 10³
Exponent is +3 → move decimal 3 places right.
8.91 → 89.1 → 891 → 8,910
✔ Answer: 8,910
---
14) 0.01 × 10⁻¹
First, note: 0.01 × 10⁻¹ = 0.01 ÷ 10 = 0.001
Or: move decimal in 0.01 one place left → 0.001
✔ Answer: 0.001
---
15) 1 × 10³
Exponent is +3 → move decimal 3 places right.
1 → 10 → 100 → 1,000
✔ Answer: 1,000
---
16) 1.99008789 × 10⁵
Exponent is +5 → move decimal 5 places right.
1.99008789 → 19.9008789 → 199.008789 → 1,990.08789 → 19,900.8789 → 199,008.789
✔ Answer: 199,008.789
---
17) 9.72385865 × 10⁸
Exponent is +8 → move decimal 8 places right.
Start: 9.72385865
Move 1: 97.2385865
Move 2: 972.385865
Move 3: 9,723.85865
Move 4: 97,238.5865
Move 5: 972,385.865
Move 6: 9,723,858.65
Move 7: 97,238,586.5
Move 8: 972,385,865
✔ Answer: 972,385,865
---
18) 3.73968811 × 10⁸
Same as above — move decimal 8 places right.
3.73968811 → ... → 373,968,811
✔ Answer: 373,968,811
---
19) 5.91107 × 10⁰
Again, anything to the 0 power is 1 → so it’s just 5.91107
✔ Answer: 5.91107
---
20) 8.97 × 10⁻²
Exponent is -2 → move decimal 2 places left.
8.97 → 0.897 → 0.0897
✔ Answer: 0.0897
---
Final Answer:
1. 360
2. 73,500
3. 600,000
4. 51,500
5. 9,510
6. 257
7. 959,485,169
8. 5,390
9. 1.945
10. 6,000
11. 994
12. 0.0707
13. 8,910
14. 0.001
15. 1,000
16. 199,008.789
17. 972,385,865
18. 373,968,811
19. 5.91107
20. 0.0897
The general rule is:
- If the exponent is positive, move the decimal point to the right.
- If the exponent is negative, move the decimal point to the left.
- The number of places you move the decimal equals the absolute value of the exponent.
Let’s go step by step for each problem:
---
1) 3.6 × 10²
Exponent is +2 → move decimal 2 places right.
3.6 → 36 → 360
✔ Answer: 360
---
2) 7.35 × 10⁴
Exponent is +4 → move decimal 4 places right.
7.35 → 73.5 → 735 → 7,350 → 73,500
✔ Answer: 73,500
---
3) 6 × 10⁵
Exponent is +5 → move decimal 5 places right.
6 → 60 → 600 → 6,000 → 60,000 → 600,000
✔ Answer: 600,000
---
4) 5.15 × 10⁴
Exponent is +4 → move decimal 4 places right.
5.15 → 51.5 → 515 → 5,150 → 51,500
✔ Answer: 51,500
---
5) 9.51 × 10³
Exponent is +3 → move decimal 3 places right.
9.51 → 95.1 → 951 → 9,510
✔ Answer: 9,510
---
6) 2.57 × 10²
Exponent is +2 → move decimal 2 places right.
2.57 → 25.7 → 257
✔ Answer: 257
---
7) 9.59485169 × 10⁸
Exponent is +8 → move decimal 8 places right.
Start: 9.59485169
Move 1: 95.9485169
Move 2: 959.485169
Move 3: 9,594.85169
Move 4: 95,948.5169
Move 5: 959,485.169
Move 6: 9,594,851.69
Move 7: 95,948,516.9
Move 8: 959,485,169
✔ Answer: 959,485,169
---
8) 5.39 × 10³
Exponent is +3 → move decimal 3 places right.
5.39 → 53.9 → 539 → 5,390
✔ Answer: 5,390
---
9) 1.945 × 10⁰
Any number to the power of 0 is 1 → so this is just 1.945 × 1 = 1.945
✔ Answer: 1.945
---
10) 6 × 10³
Exponent is +3 → move decimal 3 places right.
6 → 60 → 600 → 6,000
✔ Answer: 6,000
---
11) 9.94 × 10²
Exponent is +2 → move decimal 2 places right.
9.94 → 99.4 → 994
✔ Answer: 994
---
12) 0.707 × 10⁻¹
Exponent is -1 → move decimal 1 place left.
0.707 → 0.0707
✔ Answer: 0.0707
---
13) 8.91 × 10³
Exponent is +3 → move decimal 3 places right.
8.91 → 89.1 → 891 → 8,910
✔ Answer: 8,910
---
14) 0.01 × 10⁻¹
First, note: 0.01 × 10⁻¹ = 0.01 ÷ 10 = 0.001
Or: move decimal in 0.01 one place left → 0.001
✔ Answer: 0.001
---
15) 1 × 10³
Exponent is +3 → move decimal 3 places right.
1 → 10 → 100 → 1,000
✔ Answer: 1,000
---
16) 1.99008789 × 10⁵
Exponent is +5 → move decimal 5 places right.
1.99008789 → 19.9008789 → 199.008789 → 1,990.08789 → 19,900.8789 → 199,008.789
✔ Answer: 199,008.789
---
17) 9.72385865 × 10⁸
Exponent is +8 → move decimal 8 places right.
Start: 9.72385865
Move 1: 97.2385865
Move 2: 972.385865
Move 3: 9,723.85865
Move 4: 97,238.5865
Move 5: 972,385.865
Move 6: 9,723,858.65
Move 7: 97,238,586.5
Move 8: 972,385,865
✔ Answer: 972,385,865
---
18) 3.73968811 × 10⁸
Same as above — move decimal 8 places right.
3.73968811 → ... → 373,968,811
✔ Answer: 373,968,811
---
19) 5.91107 × 10⁰
Again, anything to the 0 power is 1 → so it’s just 5.91107
✔ Answer: 5.91107
---
20) 8.97 × 10⁻²
Exponent is -2 → move decimal 2 places left.
8.97 → 0.897 → 0.0897
✔ Answer: 0.0897
---
Final Answer:
1. 360
2. 73,500
3. 600,000
4. 51,500
5. 9,510
6. 257
7. 959,485,169
8. 5,390
9. 1.945
10. 6,000
11. 994
12. 0.0707
13. 8,910
14. 0.001
15. 1,000
16. 199,008.789
17. 972,385,865
18. 373,968,811
19. 5.91107
20. 0.0897
Parent Tip: Review the logic above to help your child master the concept of scientific notation to standard form worksheet.
