Addition And Subtraction With Scientific Notation Worksheet - Free Printable

Let’s solve each problem step by step. Remember: to add or subtract numbers in scientific notation, the powers of 10 must be the same. If they’re not, rewrite one number so both have the same exponent — then add or subtract the coefficients.

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Problem 1:
3.1 × 10³ + 4.3 × 10³
→ Same exponent (10³), so just add coefficients:
3.1 + 4.3 = 7.4
Answer: 7.4 × 10³

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Problem 2:
3 × 10¹ + 6.4 × 10²
→ Different exponents. Let’s make them both 10².
3 × 10¹ = 0.3 × 10²
Now: 0.3 × 10² + 6.4 × 10² = (0.3 + 6.4) × 10² = 6.7 × 10²
Answer: 6.7 × 10²

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Problem 3:
2.4 × 10⁴ + 5.57 × 10³
→ Make both 10⁴.
5.57 × 10³ = 0.557 × 10⁴
Now: 2.4 + 0.557 = 2.957
Answer: 2.957 × 10⁴

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Problem 4:
5 × 10⁻² + 1.6 × 10⁻³
→ Make both 10⁻².
1.6 × 10⁻³ = 0.16 × 10⁻²
Now: 5 + 0.16 = 5.16
Answer: 5.16 × 10⁻²

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Problem 5:
2.5 × 10¹ + 6.14 × 10⁴
→ Make both 10⁴.
2.5 × 10¹ = 0.0025 × 10⁴
Now: 0.0025 + 6.14 = 6.1425
Answer: 6.1425 × 10⁴

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Problem 6:
7 × 10⁻¹ + 6.4 × 10⁻⁵
→ Make both 10⁻¹.
6.4 × 10⁻⁵ = 0.000064 × 10⁻¹
Now: 7 + 0.000064 = 7.000064
Answer: 7.000064 × 10⁻¹

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Problem 7:
5 × 10⁻³ + 3.3 × 10⁻⁶
→ Make both 10⁻³.
3.3 × 10⁻⁶ = 0.0033 × 10⁻³
Now: 5 + 0.0033 = 5.0033
Answer: 5.0033 × 10⁻³

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Problem 8:
8 × 10⁻¹ + 6.9 × 10³
→ Make both 10³.
8 × 10⁻¹ = 0.0008 × 10³
Now: 0.0008 + 6.9 = 6.9008
Answer: 6.9008 × 10³

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Problem 9:
1.39 × 10⁵ – 4 × 10²
→ Make both 10⁵.
4 × 10² = 0.004 × 10⁵
Now: 1.39 – 0.004 = 1.386
Answer: 1.386 × 10⁵

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Problem 10:
2.74 × 10⁻¹ – 6.53 × 10⁻⁴
→ Make both 10⁻¹.
6.53 × 10⁻⁴ = 0.00653 × 10⁻¹
Now: 2.74 – 0.00653 = 2.73347
Answer: 2.73347 × 10⁻¹

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Problem 11:
8.14 × 10⁵ – 7.8 × 10²
→ Make both 10⁵.
7.8 × 10² = 0.0078 × 10⁵
Now: 8.14 – 0.0078 = 8.1322
Answer: 8.1322 × 10⁵

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Problem 12:
6.36 × 10³ – 5.8 × 10⁻¹
→ Make both 10³.
5.8 × 10⁻¹ = 0.00058 × 10³
Now: 6.36 – 0.00058 = 6.35942
Answer: 6.35942 × 10³

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Problem 13:
5.1 × 10⁻¹ + 0.38 × 10⁴
→ First, write 0.38 × 10⁴ as 3.8 × 10³? Wait — better to match exponents.
Let’s convert both to 10⁴.
5.1 × 10⁻¹ = 0.00051 × 10⁴
0.38 × 10⁴ stays same.
Now: 0.00051 + 0.38 = 0.38051 → but that’s not proper scientific notation.
Wait — let’s do it differently:
Convert 5.1 × 10⁻¹ to 0.00051 × 10⁴? Actually, easier:
Make both 10³? Or 10⁴? Let’s use 10⁴.
5.1 × 10⁻¹ = 0.00051 × 10⁴
0.38 × 10⁴ = 0.38 × 10⁴
Sum: 0.38051 × 10⁴ → which is 3.8051 × 10³? No — wait:
Actually, 0.38051 × 10⁴ = 3.8051 × 10³? That’s wrong.
Hold on — 0.38051 × 10⁴ = 3805.1 → which is 3.8051 × 10³? No!
Wait — 0.38051 × 10⁴ = 3.8051 × 10³? Let me calculate:
0.38051 × 10000 = 3805.1 → yes, and 3805.1 = 3.8051 × 10³? No — 3.8051 × 10³ = 3805.1 → YES.
But we want answer in scientific notation with coefficient between 1 and 10.
So 0.38051 × 10⁴ is NOT standard — we should write it as 3.8051 × 10³? But that changes the exponent.
Actually, better approach:
Original: 5.1 × 10⁻¹ + 0.38 × 10⁴
First, write 0.38 × 10⁴ as 3.8 × 10³? Still different from 10⁻¹.
Better: Convert everything to 10⁴.
5.1 × 10⁻¹ = 5.1 × 10⁻¹ = ? × 10⁴ → move decimal 5 places right → divide by 10⁵ → no.
To go from 10⁻¹ to 10⁴, multiply by 10⁵ → so coefficient becomes 5.1 × 10⁻⁵?
Yes:
5.1 × 10⁻¹ = 5.1 × 10⁻¹ × (10⁵ / 10⁵) = (5.1 × 10⁻⁵) × 10⁴
So: 5.1 × 10⁻⁵ × 10⁴ + 0.38 × 10⁴ = (0.000051 + 0.38) × 10⁴ = 0.380051 × 10⁴
Now convert to proper scientific notation: 0.380051 × 10⁴ = 3.80051 × 10³
Wait — that’s inconsistent. Let me recalculate numerically:

5.1 × 10⁻¹ = 0.51
0.38 × 10⁴ = 3800
Sum = 0.51 + 3800 = 3800.51
Now write 3800.51 in scientific notation: 3.80051 × 10³
Answer: 3.80051 × 10³

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Problem 14:
5.9 × 10⁻² – 0.078 × 10³
First, simplify 0.078 × 10³ = 78
5.9 × 10⁻² = 0.059
So: 0.059 – 78 = -77.941
Now write in scientific notation: -7.7941 × 10¹
But let’s do it properly with exponents.

Write both with same exponent. Let’s use 10³.
5.9 × 10⁻² = 0.0059 × 10³
0.078 × 10³ = 0.078 × 10³
Now: 0.0059 – 0.078 = -0.0721 × 10³
Convert to proper scientific notation: -0.0721 × 10³ = -7.21 × 10¹
Check numerically:
5.9e-2 = 0.059
0.078e3 = 78
0.059 - 78 = -77.941 → which is -7.7941 × 10¹? Wait, inconsistency.

Wait — I think I made a mistake here.

Original: 5.9 × 10⁻² – 0.078 × 10³

Note: 0.078 × 10³ is already 78, but let's keep it as is for calculation.

Better: Write both terms with exponent 10³.

5.9 × 10⁻² = 5.9 × 10⁻² = ? × 10³ → since 10⁻² to 10³ is multiplying by 10⁵, so coefficient divided by 10⁵ → 5.9 × 10⁻⁵ × 10³

So: 5.9 × 10⁻⁵ × 10³ – 0.078 × 10³ = (0.000059 – 0.078) × 10³ = (-0.077941) × 10³

Now convert to proper scientific notation: -0.077941 × 10³ = -7.7941 × 10¹

Numerical check:
5.9 × 10⁻² = 0.059
0.078 × 10³ = 78
0.059 - 78 = -77.941 = -7.7941 × 10¹ → matches.

Answer: -7.7941 × 10¹

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Final Answers:

1) 7.4 × 10³
2) 6.7 × 10²
3) 2.957 × 10⁴
4) 5.16 × 10⁻²
5) 6.1425 × 10⁴
6) 7.000064 × 10⁻¹
7) 5.0033 × 10⁻³
8) 6.9008 × 10³
9) 1.386 × 10⁵
10) 2.73347 × 10⁻¹
11) 8.1322 × 10⁵
12) 6.35942 × 10³
13) 3.80051 × 10³
14) -7.7941 × 10¹