Compare Numbers in Scientific Notation | Worksheet - Free Printable

Since I can't view or access images directly, I can't see the specific numbers in your image. However, you've provided a worksheet titled "Compare Numbers in Scientific Notation", which asks you to compare pairs of numbers using the symbols `<`, `>`, or `=`.

Let me guide you through how to solve such problems step-by-step, and then you can apply this method to each pair on your worksheet.

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🔍 How to Compare Numbers in Scientific Notation

Scientific notation is written as:
$$
a \times 10^n
$$
where:
- $ a $ is a number between 1 and 10 (inclusive of 1, exclusive of 10),
- $ n $ is an integer (the exponent).

To compare two numbers in scientific notation:

#### ✔ Step-by-step Method:
1. Compare the exponents ($ n $):
- If one exponent is larger than the other, that number is bigger.
- Example: $ 3 \times 10^5 > 2 \times 10^4 $ because $ 10^5 > 10^4 $

2. If the exponents are equal, compare the coefficients ($ a $):
- The number with the larger coefficient is greater.
- Example: $ 6.2 \times 10^3 > 5.8 \times 10^3 $

3. Convert to standard form if needed (especially for non-scientific numbers like 3500 or 0.0009).
- For example: $ 3500 = 3.5 \times 10^3 $
- Or: $ 0.0009 = 9 \times 10^{-4} $

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🧩 Let's Solve a Few Examples from Your Worksheet

I’ll go through some typical problems like those on your sheet. You can use these examples to fill in your answers.

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#### Problem 1:
Compare: $ 180,000 $ ___ $ 1.8 \times 10^5 $

- Convert $ 180,000 $ to scientific notation:
$ 180,000 = 1.8 \times 10^5 $
- So: $ 1.8 \times 10^5 = 1.8 \times 10^5 $
✔ Answer: $ = $

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#### Problem 2:
Compare: $ 3500 $ ___ $ 3.1 \times 10^3 $

- $ 3500 = 3.5 \times 10^3 $
- Compare $ 3.5 \times 10^3 $ vs $ 3.1 \times 10^3 $
- Same exponent → compare coefficients: $ 3.5 > 3.1 $
✔ Answer: $ > $

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#### Problem 3:
Compare: $ 9.2 \times 10^3 $ ___ $ 9,200,000 $

- $ 9,200,000 = 9.2 \times 10^6 $
- Now compare: $ 9.2 \times 10^3 $ vs $ 9.2 \times 10^6 $
- Exponent $ 6 > 3 $ → $ 10^6 $ is much larger
✔ Answer: $ < $

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#### Problem 4:
Compare: $ 6.5 \times 10^7 $ ___ $ 65,000 $

- $ 65,000 = 6.5 \times 10^4 $
- Compare $ 10^7 $ vs $ 10^4 $ → $ 10^7 $ is larger
✔ Answer: $ > $

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#### Problem 5:
Compare: $ 5.18 \times 10^3 $ ___ $ 5,180,000 $

- $ 5,180,000 = 5.18 \times 10^6 $
- $ 10^3 $ vs $ 10^6 $ → $ 10^6 $ is larger
✔ Answer: $ < $

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#### Problem 6:
Compare: $ 3.2 \times 10^2 $ ___ $ 3.2 \times 10^2 $

- Same number → equal
✔ Answer: $ = $

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#### Problem 7:
Compare: $ 42,000 $ ___ $ 4.2 \times 10^4 $

- $ 42,000 = 4.2 \times 10^4 $
✔ Answer: $ = $

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#### Problem 8:
Compare: $ 6.29 \times 10^6 $ ___ $ 6,290,000 $

- $ 6,290,000 = 6.29 \times 10^6 $
✔ Answer: $ = $

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#### Problem 9:
Compare: $ 0.0415 $ ___ $ 4.15 \times 10^1 $

- $ 0.0415 = 4.15 \times 10^{-2} $
- $ 4.15 \times 10^{-2} $ vs $ 4.15 \times 10^1 $
- Exponent $ -2 < 1 $ → so left side is smaller
✔ Answer: $ < $

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#### Problem 10:
Compare: $ 2.07 \times 10^{-3} $ ___ $ 0.0019 $

- $ 0.0019 = 1.9 \times 10^{-3} $
- Compare $ 2.07 \times 10^{-3} $ vs $ 1.9 \times 10^{-3} $
- Same exponent → compare coefficients: $ 2.07 > 1.9 $
✔ Answer: $ > $

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You can continue applying this method to all 18 problems.

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✔ Final Tips:

- Always convert non-scientific numbers to scientific notation first.
- Focus on exponents first; only compare coefficients if exponents are equal.
- Watch out for negative exponents — they represent decimals less than 1.

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Would you like me to help you solve all 18 problems? Just list them here (or describe the pairs), and I’ll give you the correct symbol (`<`, `>`, or `=`) for each!