Scientific Notation Operations: Evaluate and express answers in scientific notation.

Let’s solve each problem step by step. 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 → 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 larger one: 10⁴)
1.11 × 10² = 0.0111 × 10⁴
Now add: 0.0111 + 2.3 = 2.3111
→ 2.3111 × 10⁴

But let’s round appropriately? The original numbers have 3 and 2 significant figures — but since it’s addition, we go by decimal places after aligning exponents. Actually, for simplicity in school math, we often keep as is unless told otherwise. Let’s write it as 2.3111 × 10⁴, but maybe they expect rounding? Wait — 2.3 has only one decimal place when written as 2.3000 × 10⁴? Hmm.

Actually, better approach: Convert both to same exponent and add carefully.

1.11 × 10² = 0.0111 × 10⁴
2.3 × 10⁴ = 2.3000 × 10⁴
Sum = 2.3111 × 10⁴

Since 2.3 has uncertainty in the tenths place, and 0.0111 is much smaller, we might round to 2.3 × 10⁴? But that would lose precision. In many textbooks, they keep all digits unless specified. Let’s check other problems — probably they want exact calculation.

Wait — actually, looking at the numbers, perhaps we should express with correct sig figs? But the instruction doesn’t say. So I’ll compute exactly and leave as is.

But let me double-check: 1.11e2 is 111, 2.3e4 is 23000, sum is 23111 → which is 2.3111 × 10⁴. Correct.

So answer: 2.3111 × 10⁴

But maybe simplify? No, scientific notation allows decimals. Okay.

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Problem 3: 1.8 × 10⁴ + 4.12 × 10²

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

Check: 18000 + 412 = 18412 → yes, 1.8412 × 10⁴

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Problem 4: 9.5 × 10⁵ + 6.2 × 10⁴

Convert 6.2 × 10⁴ to 0.62 × 10⁵
Add: 9.5 + 0.62 = 10.12
But 10.12 × 10⁵ is not proper scientific notation (coefficient must be <10).
So rewrite: 10.12 × 10⁵ = 1.012 × 10⁶

Check: 950000 + 62000 = 1,012,000 → 1.012 × 10⁶ ✔️

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Problem 5: 5.91 × 10⁴ + 6.12 × 10³

Convert 6.12 × 10³ to 0.612 × 10⁴
Add: 5.91 + 0.612 = 6.522
→ 6.522 × 10⁴

Check: 59100 + 6120 = 65220 → 6.522 × 10⁴ ✔️

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Problem 6: 3.32 × 10⁶ – 4 × 10⁶

Same power → subtract coefficients: 3.32 - 4 = -0.68
→ -0.68 × 10⁶ → not proper scientific notation.

Rewrite: -0.68 × 10⁶ = -6.8 × 10⁵

Check: 3,320,000 - 4,000,000 = -680,000 → -6.8 × 10⁵ ✔️

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Problem 7: 7.32 × 10⁷ – 3.6 × 10⁶

Convert 3.6 × 10⁶ to 0.36 × 10⁷
Subtract: 7.32 - 0.36 = 6.96
→ 6.96 × 10⁷

Check: 73,200,000 - 3,600,000 = 69,600,000 → 6.96 × 10⁷ ✔️

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Problem 8: 4.2 × 10⁴ – 3 × 10²

Convert 3 × 10² to 0.03 × 10⁴
Subtract: 4.2 - 0.03 = 4.17
→ 4.17 × 10⁴

Check: 42000 - 300 = 41700 → 4.17 × 10⁴ ✔️

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Problem 9: 1.2 × 10² – 2.3 × 10³

Convert to same power — use 10³
1.2 × 10² = 0.12 × 10³
Subtract: 0.12 - 2.3 = -2.18
→ -2.18 × 10³

Check: 120 - 2300 = -2180 → -2.18 × 10³ ✔️

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Problem 10: 2.02 × 10⁴ + 2.2 × 10⁵

Convert 2.02 × 10⁴ to 0.202 × 10⁵
Add: 0.202 + 2.2 = 2.402
→ 2.402 × 10⁵

Check: 20200 + 220000 = 240200 → 2.402 × 10⁵ ✔️

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Final Answers:

1. 6.1 × 10⁴
2. 2.3111 × 10⁴
3. 1.8412 × 10⁴
4. 1.012 × 10⁶
5. 6.522 × 10⁴
6. -6.8 × 10⁵
7. 6.96 × 10⁷
8. 4.17 × 10⁴
9. -2.18 × 10³
10. 2.402 × 10⁵

Wait — for Problem 2, should we round? Let's see the inputs: 1.11 (three sig figs), 2.3 (two sig figs). When adding, the result should be rounded to the least precise decimal place. After converting to same exponent:

1.11 × 10² = 0.0111 × 10⁴
2.3 × 10⁴ = 2.3000 × 10⁴ → but 2.3 implies uncertainty in the tenths place, so 2.3 means ±0.05? Actually, in addition, we look at decimal places of the aligned numbers.

Aligned:

0.0111 × 10⁴
2.3000 × 10⁴ → but 2.3 has only one decimal place if we consider it as 2.3, meaning it’s precise to the nearest 0.1 in the coefficient when exponent is 10⁴? This is tricky.

In many middle/high school contexts, they don't strictly enforce sig fig rules for these operations unless specified. Since the problem says "evaluate and give the answer", and no mention of rounding, I'll keep the full value.

But let me check online or standard practice — actually, for consistency, perhaps we should present answers with reasonable precision. However, looking at the other answers, like 6.522, 4.17, etc., they kept decimals. So I think it's fine.

Alternatively, for Problem 2, since 2.3 has two significant figures and 1.11 has three, but in addition, the limiting factor is the position of the last digit. 2.3 × 10⁴ is known to the nearest 1000 (since 0.1 × 10⁴ = 1000), while 1.11 × 10² is known to the nearest 1. So the sum should be rounded to the nearest 1000, which is 23000, so 2.3 × 10⁴? But that seems too rough.

Actually, 2.3 × 10⁴ could be from 22500 to 23500, and 1.11 × 10² is 111, so sum is between 22611 and 23611, so best to report as 2.31 × 10⁴? I'm overcomplicating.

Given that this is likely a basic worksheet, and other answers have multiple decimals, I'll stick with 2.3111 × 10⁴. But let me see if there's a pattern.

Looking back at the image, all numbers are given with up to 3 significant figures, and answers probably expected similarly. For Problem 2, 2.3111 has 6 sig figs — too many. Perhaps round to 2.31 × 10⁴? Because 2.3 has two decimal places in the sense that when added to 0.0111, the result should have two decimal places? No.

Standard rule: for addition/subtraction, the result should have the same number of decimal places as the measurement with the fewest decimal places.

After aligning exponents:

1.11 × 10² = 0.0111 × 10⁴ → this has 4 decimal places in the coefficient? But it's derived.

Better to think in terms of absolute precision.

2.3 × 10⁴ has an implied uncertainty of ±0.05 × 10⁴ = ±500
1.11 × 10² has uncertainty ±0.005 × 10² = ±0.5? No, typically ±0.005 × 100 = ±0.5, but that's small.

The dominant uncertainty is from 2.3 × 10⁴, which is ±500. So the sum is 23111 ±500, so we can report as 23100 or 2.31 × 10⁴.

Similarly, in many textbooks, they would write 2.31 × 10⁴ for this.

Let me adjust for consistency.

For Problem 2: 1.11e2 + 2.3e4 = 23111 → rounded to nearest hundred? Since 2.3e4 suggests precision to thousands? 2.3e4 means 23000, with the '3' being the hundreds place? I'm confused.

Perhaps for this level, they expect exact calculation without rounding. I'll keep it as 2.3111 × 10⁴, but note that some might prefer 2.31 × 10⁴.

To match the style of other answers, like 6.522, which is exact, I'll keep it.

But let's list all final answers clearly.

Final Answer:
1. \( 6.1 \times 10^{4} \)
2. \( 2.3111 \times 10^{4} \)
3. \( 1.8412 \times 10^{4} \)
4. \( 1.012 \times 10^{6} \)
5. \( 6.522 \times 10^{4} \)
6. \( -6.8 \times 10^{5} \)
7. \( 6.96 \times 10^{7} \)
8. \( 4.17 \times 10^{4} \)
9. \( -2.18 \times 10^{3} \)
10. \( 2.402 \times 10^{5} \)

I think that's accurate based on direct calculation.