Let’s solve each problem step by step. We’re adding or subtracting numbers in scientific notation. Remember: to add or subtract, the exponents must be the same. If they’re not, we adjust one number so both have the same exponent — then we add or subtract the coefficients (the front numbers) and keep the exponent.
We’ll go one by one.
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1. 3.0 × 10⁴ + 4.0 × 10⁴
Same exponent → just add coefficients:
3.0 + 4.0 = 7.0
Answer:
7.0 × 10⁴
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2. 5.0 × 10³ + 6.8 × 10²
Exponents different! Change 6.8 × 10² to match 10³:
6.8 × 10² = 0.68 × 10³
Now add: 5.0 + 0.68 = 5.68
Answer:
5.68 × 10³
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3. 2.0 × 10⁵ + 3.7 × 10⁴
Change 3.7 × 10⁴ to 0.37 × 10⁵
Add: 2.0 + 0.37 = 2.37
Answer:
2.37 × 10⁵
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4. 9.0 × 10⁻² + 2.2 × 10⁻³
Change 2.2 × 10⁻³ to 0.22 × 10⁻²
Add: 9.0 + 0.22 = 9.22
Answer:
9.22 × 10⁻²
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5. 1.20 × 10⁶ - 4.0 × 10⁵
Change 4.0 × 10⁵ to 0.40 × 10⁶
Subtract: 1.20 - 0.40 = 0.80
But 0.80 × 10⁶ is not proper scientific notation → move decimal:
0.80 × 10⁶ = 8.0 × 10⁵
Answer:
8.0 × 10⁵
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6. 8.50 × 10⁷ - 7.0 × 10⁶
Change 7.0 × 10⁶ to 0.70 × 10⁷
Subtract: 8.50 - 0.70 = 7.80
Answer:
7.80 × 10⁷
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7. 9.0 × 10⁻³ + 8.30 × 10⁻⁴
Change 8.30 × 10⁻⁴ to 0.830 × 10⁻³
Add: 9.0 + 0.830 = 9.830
Answer:
9.830 × 10⁻³
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8. 7.0 × 10⁻¹ + 6.8 × 10⁻²
Change 6.8 × 10⁻² to 0.68 × 10⁻¹
Add: 7.0 + 0.68 = 7.68
Answer:
7.68 × 10⁻¹
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9. 8.0 × 10⁻² + 6.0 × 10⁻³
Change 6.0 × 10⁻³ to 0.60 × 10⁻²
Add: 8.0 + 0.60 = 8.60
Answer:
8.60 × 10⁻²
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10. 2.70 × 10⁻¹ - 4.20 × 10⁻²
Change 4.20 × 10⁻² to 0.420 × 10⁻¹
Subtract: 2.70 - 0.420 = 2.280
Answer:
2.280 × 10⁻¹
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11. 6.50 × 10⁸ - 3.0 × 10⁷
Change 3.0 × 10⁷ to 0.30 × 10⁸
Subtract: 6.50 - 0.30 = 6.20
Answer:
6.20 × 10⁸
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12. 6.50 × 10⁹ - 3.0 × 10⁸
Change 3.0 × 10⁸ to 0.30 × 10⁹
Subtract: 6.50 - 0.30 = 6.20
Answer:
6.20 × 10⁹
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13. 9.0 × 10⁻ + 8.30 × 10⁻⁶
Change 8.30 × 10⁻⁶ to 0.830 × 10⁻⁵
Add: 9.0 + 0.830 = 9.830
Answer:
9.830 × 10⁻⁵
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14. 2.0 × 10⁻² - 6.070 × 10⁻³
Change 6.070 × 10⁻³ to 0.6070 × 10⁻²
Subtract: 2.0 - 0.6070 = 1.3930
Answer:
1.3930 × 10⁻²
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Final Answer:
1. 7.0 × 10⁴
2. 5.68 × 10³
3. 2.37 × 10⁵
4. 9.22 × 10⁻²
5. 8.0 × 10⁵
6. 7.80 × 10⁷
7. 9.830 × 10⁻³
8. 7.68 × 10⁻¹
9. 8.60 × 10⁻²
10. 2.280 × 10⁻¹
11. 6.20 × 10⁸
12. 6.20 × 10⁹
13. 9.830 × 10⁻⁵
14. 1.3930 × 10⁻²
Parent Tip: Review the logic above to help your child master the concept of algebra 1 scientific notation worksheet.
