Adding And Subtracting In Scientific Notation Worksheet, Practice ... - Free Printable

Let’s solve each problem step by step. We’re adding or subtracting numbers in scientific notation. The key rule: you can only add or subtract if the powers of 10 are the same. If they’re not, you must rewrite one number so both have the same exponent.

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Problem 1: 9 × 10⁹ - 2 × 10⁹

Same power of 10 → just subtract the coefficients:

9 - 2 = 7
So answer is 7 × 10⁹

✔ Check: 9 billion minus 2 billion = 7 billion → correct.

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Problem 2: 3.6 × 10⁷ + 2.1 × 10⁷

Same power → add coefficients:

3.6 + 2.1 = 5.7
Answer: 5.7 × 10⁷

✔ Check: 36 million + 21 million = 57 million → yes.

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Problem 3: 7.73 × 10⁵ - 5.3 × 10⁴

Different exponents! Need to make them the same.

Convert 5.3 × 10⁴ to match 10⁵:

5.3 × 10⁴ = 0.53 × 10⁵ (move decimal left one place → increase exponent by 1)

Now subtract:

7.73 × 10⁵ - 0.53 × 10⁵ = (7.73 - 0.53) × 10⁵ = 7.20 × 10⁵

We can write it as 7.2 × 10⁵ (drop trailing zero).

✔ Check: 773,000 - 53,000 = 720,000 → which is 7.2 × 10⁵ → correct.

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Problem 4: 4.9 × 10¹⁰ + 5.5 × 10⁹

Different exponents. Convert 5.5 × 10⁹ to match 10¹⁰:

5.5 × 10⁹ = 0.55 × 10¹⁰

Now add:

4.9 × 10¹⁰ + 0.55 × 10¹⁰ = (4.9 + 0.55) × 10¹⁰ = 5.45 × 10¹⁰

✔ Check: 49 billion + 5.5 billion = 54.5 billion → 5.45 × 10¹⁰ → correct.

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Problem 5: 5 × 10¹² + 8 × 10¹²

Same exponent → add coefficients:

5 + 8 = 13
But 13 × 10¹² is NOT proper scientific notation (coefficient must be between 1 and 10).

Rewrite: 13 × 10¹² = 1.3 × 10¹³

✔ Check: 5 trillion + 8 trillion = 13 trillion = 1.3 × 10¹³ → correct.

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Problem 6: 9.8 × 10¹⁴ + 3.7 × 10¹³

Different exponents. Convert 3.7 × 10¹³ to match 10¹⁴:

3.7 × 10¹³ = 0.37 × 10¹⁴

Add:

9.8 × 10¹⁴ + 0.37 × 10¹⁴ = (9.8 + 0.37) × 10¹⁴ = 10.17 × 10¹⁴

Not proper scientific notation → convert:

10.17 × 10¹⁴ = 1.017 × 10¹⁵

✔ Check: 980 trillion + 37 trillion = 1,017 trillion = 1.017 × 10¹⁵ → correct.

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Final Answer:
1) 7 × 10⁹
2) 5.7 × 10⁷
3) 7.2 × 10⁵
4) 5.45 × 10¹⁰
5) 1.3 × 10¹³
6) 1.017 × 10¹⁵