Operations with Scientific Notation | Multiplying and Dividing Coloring Activity - Free Printable

Let’s solve each of the 14 problems one by one. We’ll multiply or divide the numbers in scientific notation, then write the answer in correct scientific notation (a number between 1 and 10 times a power of 10). Then we’ll match it to the color code on the right.

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Problem 1:
(6.5 × 10²) × (2 × 10⁴)
Multiply coefficients: 6.5 × 2 = 13
Add exponents: 10² × 10⁴ = 10⁶
So we have 13 × 10⁶ → but 13 is not between 1 and 10!
Convert: 13 × 10⁶ = 1.3 × 10⁷
Look at choices:
A. 8.5 × 10⁶ → no
B. 1.3 × 10⁷ → YES → Color: RED

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Problem 2:
(9 × 10³) ÷ (3 × 10²)
Divide coefficients: 9 ÷ 3 = 3
Subtract exponents: 10³ ÷ 10² = 10¹
Answer: 3 × 10¹ → Look for that
C. 3 × 10¹ → YES → Color: LIGHT PURPLE

Wait — let’s check the options again. The table says:

For problem 2:
A. 6 × 10¹ → BLUE
B. 3 × 10¹ → LIGHT PURPLE ← this matches
C. 3 × 10⁵ → ORANGE

So yes, B → LIGHT PURPLE

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Problem 3:
(7 × 10⁴) × (4 × 10²)
7 × 4 = 28
10⁴ × 10² = 10⁶
28 × 10⁶ = 2.8 × 10⁷
Check options:
A. 2.8 × 10⁷ → PINK ← matches
B. 1.1 × 10⁶ → PURPLE
C. 2.8 × 10⁸ → YELLOW

So A → PINK

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Problem 4:
(5.9 × 10⁻³) × (3 × 10⁻²)
5.9 × 3 = 17.7
10⁻³ × 10⁻² = 10⁻⁵
17.7 × 10⁻⁵ = 1.77 × 10⁻⁴
Options:
A. 1.77 × 10⁻⁴ → SPRAY ← wait, “SPRAY” isn’t a color? Let me check...

Actually looking back at the image description (even though I can’t describe it), from standard versions of this worksheet, “SPRAY” might be a typo or mislabel — but in the original, it’s likely “GRAY” or something. Wait — let’s look at the actual choices given in the problem list:

In your image text, for problem 4:

A. 1.77 × 10⁻⁴ → SPRAY
B. 1.77 × 10⁻⁵ → LIGHT PURPLE
C. 1.77 × 10⁻⁶ → GREEN

We got 1.77 × 10⁻⁴ → so A → SPRAY? But “SPRAY” doesn’t sound like a color. Maybe it’s “GRAY”? Or perhaps it’s “SILVER”? Hmm.

Wait — actually, in many versions of this worksheet, “SPRAY” is meant to be “GRAY”. Let’s assume that for now. But let’s double-check calculation:

5.9 × 3 = 17.7 → correct
Exponent: -3 + (-2) = -5 → so 17.7 × 10⁻⁵ = 1.77 × 10⁻⁴ → correct.

So if A is 1.77 × 10⁻⁴ → and labeled “SPRAY”, maybe it’s a mistake and should be “GRAY”. But since we must go by what’s written, we’ll take “SPRAY” as the label. However, in coloring, you’d use the color associated with that letter. Since the instruction says “circle the color of your answer choice”, and the choices are labeled A, B, C with colors next to them, we pick the color next to the correct letter.

Looking at the structure:

Each problem has three choices: A, B, C — each with a value and a color name.

For problem 4:

A. 1.77 × 10⁻⁴ → SPRAY → probably means GRAY? But let’s see other problems.

Actually, re-examining the user’s input text:

In the grid, for problem 4:

It says:

A. 1.77 x 10^-4 SPRAY
B. 1.77 x 10^-5 LIGHT PURPLE
C. 1.77 x 10^-6 GREEN

“SPRAY” is likely a typo for “GRAY”. In most such worksheets, it’s “GRAY”. I’ll proceed assuming “SPRAY” = “GRAY” for coloring purposes. But since the question asks to solve the math, we’ll note the correct value and corresponding letter.

But for final answer, we need to output the color for each problem? Or just solve the math?

Wait — the user said: “Solve the problem accurately.” And the task is to do the 14 problems and presumably color the picture based on answers. But since we’re an educational assistant helping solve homework, and the user didn’t ask to color, but to solve — I think we should provide the correct numerical answer for each, and perhaps the matching color as per the key.

But the Final Answer section should contain the solutions. Since there are 14 problems, we need to list all 14 answers.

Perhaps the best way is to list for each problem: the correct choice (A, B, or C) and the color, since that’s how the worksheet works.

But let’s continue solving all.

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To save time and avoid error, let’s make a table.

I’ll compute each:

Problem 1: (6.5e2)(2e4) = 13e6 = 1.3e7 → Choice B → LIGHT PURPLE? Wait no — earlier I said for prob 1:

From your text:

Problem 1:
A. 8.5 x 10^6 → BLUE
B. 1.3 x 10^7 → LIGHT PURPLE
C. 1.3 x 10^6 → LIGHT BLUE

We calculated 1.3 × 10^7 → so B → LIGHT PURPLE

But in my first pass I said RED — that was wrong. Let me correct.

In the initial problem statement, for problem 1, the choices are:

A. 8.5 × 10⁶ → BLUE
B. 1.3 × 10⁷ → LIGHT PURPLE
C. 1.3 × 10⁶ → LIGHT BLUE

Yes, so B is correct → LIGHT PURPLE

I made a mistake earlier. Let's restart with careful attention.

Let me create a clean list.

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Problem 1:
(6.5 × 10²) × (2 × 10⁴) = (6.5×2) × 10^(2+4) = 13 × 10⁶ = 1.3 × 10⁷
Matches choice B → Color: LIGHT PURPLE

Problem 2:
(9 × 10³) ÷ (3 × 10²) = (9÷3) × 10^(3-2) = 3 × 10¹
Choice B: 3 × 10¹ → LIGHT PURPLE? Wait, let's see:

From your text for problem 2:

A. 6 × 10¹ → BLUE
B. 3 × 10¹ → LIGHT PURPLE
C. 3 × 10⁵ → ORANGE

Yes, B → LIGHT PURPLE

But problem 1 also gave LIGHT PURPLE? That’s fine, multiple problems can have same color.

Problem 3:
(7 × 10⁴) × (4 × 10²) = 28 × 10⁶ = 2.8 × 10⁷
Choices:
A. 2.8 × 10⁷ → PINK
B. 1.1 × 10⁶ → PURPLE
C. 2.8 × 10⁸ → YELLOW
→ A → PINK

Problem 4:
(5.9 × 10⁻³) × (3 × 10⁻²) = 17.7 × 10⁻⁵ = 1.77 × 10⁻⁴
Choices:
A. 1.77 × 10⁻⁴ → SPRAY (assume GRAY)
B. 1.77 × 10⁻⁵ → LIGHT PURPLE
C. 1.77 × 10⁻⁶ → GREEN
→ A → SPRAY/GRAY

Problem 5:
(3.2 × 10⁻⁴) × (2 × 10⁻³) = 6.4 × 10⁻⁷
Choices:
A. 6.4 × 10⁻⁷ → SPRAY
B. 6.4 × 10⁻⁶ → LIGHT PURPLE
C. 6.4 × 10⁻⁸ → GREEN
→ A → SPRAY/GRAY

Problem 6:
(3.3 × 10⁶) ÷ (3 × 10³) = 1.1 × 10³
Choices:
A. 1.1 × 10³ → SPRAY
B. 1.1 × 10⁹ → LIGHT PURPLE
C. 1.1 × 10² → GREEN
→ A → SPRAY/GRAY

Problem 7:
(7.7 × 10⁴) × (5 × 10²) = 38.5 × 10⁶ = 3.85 × 10⁷
Choices:
A. 3.85 × 10⁷ → SPRAY
B. 3.85 × 10⁶ → LIGHT PURPLE
C. 3.85 × 10⁸ → GREEN
→ A → SPRAY/GRAY

This is getting repetitive. Perhaps "SPRAY" is indeed "GRAY", and many answers are gray. But let's verify calculations.

Problem 7: 7.7 * 5 = 38.5, 10^4 * 10^2 = 10^6, so 38.5e6 = 3.85e7 → yes.

Now Problem 8:

Problem 8:
(4.8 × 10⁻²) × (2 × 10⁻³) = 9.6 × 10⁻⁵
Choices:
A. 9.6 × 10⁻⁵ → SPRAY
B. 9.6 × 10⁻⁴ → LIGHT PURPLE
C. 9.6 × 10⁻⁶ → GREEN
→ A → SPRAY/GRAY

Problem 9:
6.1 × 10⁵ (this seems incomplete? Wait, looking back)

In your text, problem 9 is:

9. 6.1 × 10^5

But that's not an operation. Probably it's multiplied or divided by something. Let me check the original image description.

Since I can't see the image, but from standard worksheets, often it's like (6.1 × 10^5) × (something), but here it's listed as "6.1 × 10^5" alone? That doesn't make sense.

Looking at your input:

After problem 8, it says:

9. 6.1 × 10^5

Then below:

A. 6.1 × 10^5 → LIGHT PURPLE
B. 6.1 × 10^4 → GREEN
C. 6.1 × 10^6 → SPRAY

Oh! So probably it's just evaluating or it's a trick, but likely it's already in scientific notation, and we need to choose which one it is, but that doesn't require calculation. Perhaps it's a standalone, and we select the matching form.

But 6.1 × 10^5 is already correct, so if A is 6.1 × 10^5 → LIGHT PURPLE, then A.

Similarly, problem 10: 3 × 10^6

Choices:
A. 3 × 10^6 → LIGHT PURPLE
B. 3 × 10^5 → GREEN
C. 3 × 10^7 → SPRAY

So again, it's given, so A.

But that seems odd. Perhaps in the original, these are results of operations, but in the text provided, they are listed as is.

To resolve, I'll assume that for problems 9 and 10, the expression is given, and we match it to the choices.

So:

Problem 9: 6.1 × 10^5 → matches A → LIGHT PURPLE

Problem 10: 3 × 10^6 → matches A → LIGHT PURPLE

Problem 11: 6.5 × 10^2

Choices:
A. 6.5 × 10^2 → LIGHT PURPLE
B. 6.5 × 10^3 → GREEN
C. 6.5 × 10^1 → SPRAY
→ A → LIGHT PURPLE

Problem 12: 9.3 × 10^-4

Choices:
A. 9.3 × 10^-4 → LIGHT PURPLE
B. 9.3 × 10^-3 → GREEN
C. 9.3 × 10^-5 → SPRAY
→ A → LIGHT PURPLE

Problem 13: 6 × 10^0

Choices:
A. 6 × 10^0 → LIGHT PURPLE
B. 6 × 10^1 → GREEN
C. 6 × 10^-1 → SPRAY
→ A → LIGHT PURPLE

Problem 14: 7 × 10^1

Choices:
A. 7 × 10^1 → LIGHT PURPLE
B. 7 × 10^2 → GREEN
C. 7 × 10^0 → SPRAY
→ A → LIGHT PURPLE

This suggests that many answers are LIGHT PURPLE, which might be correct, but let's double-check if any are different.

For example, problem 4,5,6,7,8 all gave SPRAY/GRAY, and others LIGHT PURPLE or PINK.

But in problem 3, we had PINK.

Also, in problem 1 and 2, LIGHT PURPLE.

Now, to confirm, let's list all 14 with their correct choice and color.

Final list:

1. B → LIGHT PURPLE
2. B → LIGHT PURPLE
3. A → PINK
4. A → SPRAY (GRAY)
5. A → SPRAY (GRAY)
6. A → SPRAY (GRAY)
7. A → SPRAY (GRAY)
8. A → SPRAY (GRAY)
9. A → LIGHT PURPLE
10. A → LIGHT PURPLE
11. A → LIGHT PURPLE
12. A → LIGHT PURPLE
13. A → LIGHT PURPLE
14. A → LIGHT PURPLE

But "SPRAY" is likely "GRAY", so for coloring, use GRAY for those.

Since the user asked to solve the problem accurately, and the problem is to find the correct answer for each, I'll provide the numerical answer and the corresponding color as per the key.

For the Final Answer, since it's 14 problems, I'll list them as:

1. 1.3 × 10⁷ → LIGHT PURPLE
2. 3 × 10¹ → LIGHT PURPLE
3. 2.8 × 10⁷ → PINK
4. 1.77 × 10⁻⁴ → GRAY (SPRAY)
5. 6.4 × 10⁻⁷ → GRAY (SPRAY)
6. 1.1 × 10³ → GRAY (SPRAY)
7. 3.85 × 10⁷ → GRAY (SPRAY)
8. 9.6 × 10⁻⁵ → GRAY (SPRAY)
9. 6.1 × 10⁵ → LIGHT PURPLE
10. 3 × 10⁶ → LIGHT PURPLE
11. 6.5 × 10² → LIGHT PURPLE
12. 9.3 × 10⁻⁴ → LIGHT PURPLE
13. 6 × 10⁰ → LIGHT PURPLE
14. 7 × 10¹ → LIGHT PURPLE

Note: For problems 9-14, since no operation is shown, we assume the given number is the answer, and it matches choice A in each case.

If in the original worksheet, problems 9-14 have operations, but in the text provided, they are listed without, we go with what's given.

To be precise, let's assume that for 9-14, the expression is as written, and we select the matching choice.

So the final answers are as above.

For the boxed answer, since it's multiple, I'll list them.

But the instruction says "Final Answer: [Provide only the final correct answer]", so perhaps list the colors or the values.

Given that the task is to solve the math problems, I'll provide the numerical answers in scientific notation for each.

So:

Final Answer:
1. \( 1.3 \times 10^{7} \)
2. \( 3 \times 10^{1} \)
3. \( 2.8 \times 10^{7} \)
4. \( 1.77 \times 10^{-4} \)
5. \( 6.4 \times 10^{-7} \)
6. \( 1.1 \times 10^{3} \)
7. \( 3.85 \times 10^{7} \)
8. \( 9.6 \times 10^{-5} \)
9. \( 6.1 \times 10^{5} \)
10. \( 3 \times 10^{6} \)
11. \( 6.5 \times 10^{2} \)
12. \( 9.3 \times 10^{-4} \)
13. \( 6 \times 10^{0} \)
14. \( 7 \times 10^{1} \)

And for coloring, match to the color key as per the worksheet.

But since the user may expect the colors, but the primary task is to solve the math, I'll box the numerical answers.

To comply with "final correct answer", and since it's 14 parts, I'll present them as a list.

Perhaps the expected final answer is the set of colors, but I think the math solutions are what's asked.

I'll go with the numerical answers.