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Let’s solve each problem one by one. We’re comparing two numbers written in scientific notation and finding how many times bigger the first is than the second — basically, we divide the first number by the second.

Remember:
When dividing powers of ten, subtract the exponents:
10^a ÷ 10^b = 10^(a−b)
And don’t forget to divide the front numbers too!

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Problem 1:
9 × 10⁵ is ______ × the value of 7 × 10²

→ Divide: (9 × 10⁵) ÷ (7 × 10²)
= (9 ÷ 7) × (10⁵ ÷ 10²)
= (9/7) × 10³
≈ 1.2857 × 1000
= 1285.7

But let’s keep it as a decimal if needed — actually, 9/7 is about 1.2857, so 1.2857 × 1000 = 1285.7 → but maybe they want exact fraction? Wait — instruction says “answer as a decimal if necessary”. Let’s compute exactly:

9 ÷ 7 = 1.285714...
Then multiply by 1000 → 1285.714...

But perhaps better to write as (9/7) × 1000 = 9000/7 ≈ 1285.7

Wait — let me check again:
Actually, 10⁵ / 10² = 10³ = 1000
So 9 × 1000 = 9000
Divide by 7 → 9000 ÷ 7 = 1285.714...

So answer is 1285.7 (rounded to one decimal) or leave as fraction? But instructions say “decimal if necessary” — so yes, use decimal.

But let’s do all problems carefully.

Actually, maybe I should just compute each as (first coefficient / second coefficient) × 10^(exponent difference)

Let’s make a table for clarity:

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1) 9×10⁵ vs 7×10²
Coefficients: 9 ÷ 7 ≈ 1.2857
Exponents: 5 - 2 = 3 → 10³ = 1000
Total: 1.2857 × 1000 = 1285.7

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2) 3×10² vs 7×10⁶
Coefficients: 3 ÷ 7 ≈ 0.4286
Exponents: 2 - 6 = -4 → 10⁻⁴ = 0.0001
Total: 0.4286 × 0.0001 = 0.00004286 → which is 4.286 × 10⁻⁵, but as decimal: 0.00004286

Wait — that seems very small. Let me double-check:

We are asking: 3×10² is how many times the value of 7×10⁶?

That means: (3×10²) / (7×10⁶) = (3/7) × 10^(2-6) = (3/7) × 10⁻⁴

3/7 ≈ 0.42857
0.42857 × 0.0001 = 0.000042857 → so 0.0000429 (rounded to 6 decimal places? Or scientific?)

But instruction says “answer as a decimal if necessary” — so we can write it as 0.0000429 or maybe in scientific? But probably decimal form.

Alternatively, perhaps they expect us to write it as a decimal without scientific notation.

Let’s continue and see pattern.

Actually, maybe I made a mistake in interpretation.

The question is: “A is ___ × the value of B” → meaning A = ? × B → so ? = A/B

Yes, correct.

So for #2: A = 3e2, B = 7e6 → A/B = 3e2 / 7e6 = 3/(7*10^4) = 3/70000 = 0.000042857...

So 0.0000429 (if rounded to 7 decimal places, but maybe keep more precision?)

But let's do exact fractions where possible and convert to decimal at end.

Perhaps better to calculate numerically for each.

Let me list all:

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1) (9e5)/(7e2) = 900000 / 700 = 9000 / 7 ≈ 1285.714 → round to 1285.7

2) (3e2)/(7e6) = 300 / 7000000 = 3 / 70000 = 0.000042857... → 0.0000429

3) (2e9)/(6e5) = 2000000000 / 600000 = 20000 / 6 = 10000 / 3 ≈ 3333.333

4) (2e5)/(9e2) = 200000 / 900 = 2000 / 9 ≈ 222.222

5) (9e2)/(5e6) = 900 / 5000000 = 9 / 50000 = 0.00018 → 0.00018

6) (2e5)/(6e3) = 200000 / 6000 = 200 / 6 = 100 / 3 ≈ 33.333

7) (2e2)/(4e2) = 200 / 400 = 0.5 → 0.5

8) (3e2)/(2e9) = 300 / 2000000000 = 3 / 20000000 = 0.00000015 → 0.00000015

9) (8e8)/(2e9) = 800000000 / 2000000000 = 8 / 20 = 0.4 → 0.4

Now let’s verify each calculation step by step to avoid errors.

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Double-checking each:

1) 9×10⁵ = 900,000; 7×10² = 700; 900,000 ÷ 700 = 9000 ÷ 7 = 1285.714... → ✔ 1285.7

2) 3×10² = 300; 7×10⁶ = 7,000,000; 300 ÷ 7,000,000 = 3 ÷ 70,000 = 0.000042857... → ✔ 0.0000429 (rounded to 7 decimal places: 0.0000429)

Actually, 3/70000 = 0.000042857142... so to 6 decimal places: 0.000043? No — 0.000042857 is closer to 0.0000429 if we take 7 decimals.

But perhaps write as 4.2857 × 10^{-5}, but instruction says decimal — so 0.0000429 is fine.

3) 2×10⁹ = 2,000,000,000; 6×10⁵ = 600,000; divide: 2e9 / 6e5 = (2/6) × 10^{4} = (1/3) × 10000 = 10000/3 ≈ 3333.333... → ✔ 3333.3

4) 2×10⁵ = 200,000; 9×10² = 900; 200,000 ÷ 900 = 2000 ÷ 9 ≈ 222.222... → ✔ 222.2

5) 9×10² = 900; 5×10⁶ = 5,000,000; 900 ÷ 5,000,000 = 9 ÷ 50,000 = 0.00018 → ✔ 0.00018

6) 2×10⁵ = 200,000; 6×10³ = 6,000; 200,000 ÷ 6,000 = 200 ÷ 6 = 100 ÷ 3 ≈ 33.333... → ✔ 33.3

7) 2×10² = 200; 4×10² = 400; 200 ÷ 400 = 0.5 → ✔ 0.5

8) 3×10² = 300; 2×10⁹ = 2,000,000,000; 300 ÷ 2e9 = 3 ÷ 20,000,000 = 0.00000015 → ✔ 0.00000015

9) 8×10⁸ = 800,000,000; 2×10⁹ = 2,000,000,000; 8e8 / 2e9 = 8/20 = 0.4 → ✔ 0.4

All calculations checked.

Now, for answers, we’ll write them as decimals, rounding reasonably — usually to 3-4 significant figures or as exact decimal if terminates.

For repeating decimals like 1/3, we can write 3333.3 or 33.3 etc., since instruction says "decimal if necessary".

Final Answers:

1) 1285.7
2) 0.0000429
3) 3333.3
4) 222.2
5) 0.00018
6) 33.3
7) 0.5
8) 0.00000015
9) 0.4

But let’s write them neatly.

Note: For #2, 0.000042857... — if we round to 6 decimal places, it’s 0.000043, but that’s less accurate. Better to write as 0.0000429 (7 decimal places) or even 4.29 × 10^{-5}, but since it says "decimal", we'll use decimal form.

Similarly, #8 is 0.00000015 — which is exact.

I think these are acceptable.

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Final Answer:
1) 1285.7
2) 0.0000429
3) 3333.3
4) 222.2
5) 0.00018
6) 33.3
7) 0.5
8) 0.00000015
9) 0.4