Add & Subtract Scientific Notation Worksheets (printable, online ... - Free Printable

Let’s solve each problem one by one. We’ll add or subtract numbers in scientific notation by making sure the powers of 10 are the same first, then combine the coefficients.

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Problem 1: 2.9 × 10⁴ + 3.2 × 10⁴

Same power of 10 → just add coefficients:

2.9 + 3.2 = 6.1
→ 6.1 × 10⁴

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Problem 2: 1.11 × 10² + 2.3 × 10⁴

Different powers → convert to same power (use 10⁴):

1.11 × 10² = 0.0111 × 10⁴
Now add: 0.0111 + 2.3 = 2.3111
→ 2.3111 × 10⁴

But we usually round to reasonable digits — since 2.3 has 2 sig figs and 1.11 has 3, let’s keep 3 sig figs:
→ 2.31 × 10⁴

*(Note: Some teachers accept exact decimal; but for consistency with input precision, 2.31 × 10⁴ is fine.)*

Wait — actually, 2.3 × 10⁴ might be considered as having 2 significant figures, so answer should have 2? But 1.11 has 3. Let’s check standard rule: when adding, go by decimal places after converting.

Better approach: Convert both to same exponent and line up decimals.

1.11 × 10² = 111
2.3 × 10⁴ = 23000
Sum = 23111 → which is 2.3111 × 10⁴ → rounded to nearest hundred? Since 2.3 × 10⁴ is precise to hundreds place (because 2.3 means ±0.05×10⁴ = ±500), so sum should be rounded to hundreds: 23100 → 2.31 × 10⁴

We’ll go with 2.31 × 10⁴

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Problem 3: 1.8 × 10⁴ + 4.12 × 10²

Convert 4.12 × 10² to 10⁴:
4.12 × 10² = 0.0412 × 10⁴
Add: 1.8 + 0.0412 = 1.8412
→ 1.8412 × 10⁴

Round appropriately: 1.8 has 2 sig figs, 4.12 has 3 → limiting is 1.8 (tenths place in 10⁴). So round to tenths: 1.8 × 10⁴? Wait no — 1.8 is 1.80? Actually, 1.8 × 10⁴ means uncertainty in the thousands place? Let’s think numerically:

1.8 × 10⁴ = 18000
4.12 × 10² = 412
Sum = 18412 → which is 1.8412 × 10⁴

Since 1.8 × 10⁴ could be from 17500 to 18500, and 412 is small, the sum is about 18400 → so write as 1.84 × 10⁴ (keeping 3 sig figs because 4.12 adds precision)

Actually, better: When adding, look at least precise decimal place.

1.8 × 10⁴ → known to nearest 1000 (since 1.8 implies ±0.05×10⁴=±500)
4.12 × 10² → known to nearest 1 (since 4.12×100=412, ±0.005×100=±0.5)

So sum should be rounded to nearest 1000? That would be 18000 → too rough.

Standard practice in school: convert to same exponent and add, then round to least number of decimal places in the coefficient *after alignment*.

After converting:

1.8000 × 10⁴
0.0412 × 10⁴
Add: 1.8412 × 10⁴

1.8 has 1 decimal place (in coefficient), 0.0412 has 4 → so result should have 1 decimal place? But 1.8 is actually 1.80 if we consider it as two sig figs? This is messy.

In most middle/high school contexts, they expect you to compute exactly and report with reasonable sig figs — often matching the least precise term.

Here, 1.8 × 10⁴ has 2 sig figs, 4.12 × 10² has 3 → so answer should have 2 sig figs? But that would be 1.8 × 10⁴, which ignores the addition.

Actually, let's do it numerically:

18000 + 412 = 18412 → scientific notation: 1.8412 × 10⁴

To 3 significant figures: 1.84 × 10⁴ (since 18412 rounds to 18400)

I think 1.84 × 10⁴ is acceptable.

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Problem 4: 9.5 × 10⁵ + 6.2 × 10⁴

Convert 6.2 × 10⁴ to 10⁵:
6.2 × 10⁴ = 0.62 × 10⁵
Add: 9.5 + 0.62 = 10.12
→ 10.12 × 10⁵ = 1.012 × 10⁶

Now, 9.5 has 2 sig figs, 6.2 has 2 → so answer should have 2 sig figs?
1.012 × 10⁶ → to 2 sig figs: 1.0 × 10⁶

But wait: 9.5 + 0.62 = 10.12 → which is closer to 10.1 than 10.0? But sig fig rules for addition: 9.5 is precise to 0.1, 0.62 to 0.01 → so sum precise to 0.1 → 10.1 → then 1.01 × 10⁶? But 10.1 × 10⁵ = 1.01 × 10⁶

Actually, 9.5 × 10⁵ = 950000
6.2 × 10⁴ = 62000
Sum = 1,012,000 → 1.012 × 10⁶

With 2 sig figs: 1.0 × 10⁶

But some might say 1.01 × 10⁶. Let’s see inputs: 9.5 (two sig figs), 6.2 (two) → product or sum? For addition, it’s decimal places.

9.5 × 10⁵ → the '5' is in the ten-thousands place? 950,000 — uncertain in the ten-thousands? Actually, 9.5 × 10⁵ means between 945,000 and 955,000.

6.2 × 10⁴ = 62,000 — between 61,500 and 62,500.

Sum between 1,006,500 and 1,017,500 → so best to report as 1.01 × 10⁶? Or 1.0 × 10⁶?

I think for this level, they expect 1.012 × 10⁶, but rounded to 3 sig figs since 9.5 has two but when added, the result has more digits.

Looking at common textbook approach: they often don't strictly enforce sig figs in these problems unless specified. So I'll compute exactly and present with 3 or 4 digits as needed.

For consistency, let's keep 3 significant figures where possible.

So 1.012 × 10⁶ → 1.01 × 10⁶ (if rounding to 3 sig figs)

But 9.5 has only 2, so perhaps 1.0 × 10⁶

I recall: in addition, the result should be reported with the same precision as the least precise measurement.

9.5 × 10⁵ is precise to the nearest 10,000 (since 0.1 × 10⁵ = 10,000)
6.2 × 10⁴ is precise to the nearest 1,000 (0.1 × 10⁴ = 1,000)

So the sum should be precise to the nearest 10,000.

1,012,000 rounded to nearest 10,000 is 1,010,000 → 1.01 × 10⁶

Yes, that makes sense.

So 1.01 × 10⁶

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This is taking too long per problem. Let me speed up with a consistent method:

For each pair:
- If exponents same, add/subtract coefficients.
- If different, convert smaller exponent to match larger one by moving decimal left.
- Then add/subtract.
- Adjust to proper scientific notation (coefficient between 1 and 10).
- Round to reasonable digits — typically 3 sig figs unless inputs suggest otherwise.

Let me redo all quickly with this method.

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1. 2.9e4 + 3.2e4 = (2.9+3.2)e4 = 6.1e4 → 6.1 × 10⁴

2. 1.11e2 + 2.3e4 = 0.0111e4 + 2.3e4 = 2.3111e4 → 2.31 × 10⁴ (rounded to 3 sig figs)

3. 1.8e4 + 4.12e2 = 1.8e4 + 0.0412e4 = 1.8412e4 → 1.84 × 10⁴

4. 9.5e5 + 6.2e4 = 9.5e5 + 0.62e5 = 10.12e5 = 1.012e6 → 1.01 × 10⁶

5. 5.91e4 + 6.12e3 = 5.91e4 + 0.612e4 = 6.522e4 → 6.52 × 10⁴

6. 3.32e6 - 4e6 = (3.32 - 4)e6 = -0.68e6 = -6.8 × 10⁵

7. 7.32e7 - 3.6e6 = 7.32e7 - 0.36e7 = 6.96e7 → 6.96 × 10⁷

8. 4.2e4 - 3e2 = 4.2e4 - 0.03e4 = 4.17e4 → 4.17 × 10⁴

9. 1.2e2 - 2.3e3 = 0.12e3 - 2.3e3 = -2.18e3 → -2.18 × 10³

10. 2.02e4 + 2.2e5 = 0.202e5 + 2.2e5 = 2.402e5 → 2.40 × 10⁵

Now, let's verify a few calculations:

Problem 6: 3.32 - 4 = -0.68 → -0.68 × 10⁶ = -6.8 × 10⁵ ✓

Problem 9: 1.2 × 10² = 120, 2.3 × 10³ = 2300, 120 - 2300 = -2180 = -2.18 × 10³ ✓

Problem 10: 2.02 × 10⁴ = 20200, 2.2 × 10⁵ = 220000, sum = 240200 = 2.402 × 10⁵ → rounded to 3 sig figs: 2.40 × 10⁵ ✓

All seem correct.

Final Answers:

1. 6.1 × 10⁴
2. 2.31 × 10⁴
3. 1.84 × 10⁴
4. 1.01 × 10⁶
5. 6.52 × 10⁴
6. -6.8 × 10⁵
7. 6.96 × 10⁷
8. 4.17 × 10⁴
9. -2.18 × 10³
10. 2.40 × 10⁵

I think that's accurate for school level.

Final Answer:
6.1 × 10⁴, 2.31 × 10⁴, 1.84 × 10⁴, 1.01 × 10⁶, 6.52 × 10⁴, -6.8 × 10⁵, 6.96 × 10⁷, 4.17 × 10⁴, -2.18 × 10³, 2.40 × 10⁵