How to Add and Subtract in Scientific Notations? (+FREE Worksheet!)

Adding and subtracting numbers in scientific notation requires one extra step that most operations don’t: the powers of 10 must match before you can combine the coefficients. Once the exponents are equal, the addition or subtraction is straightforward. This lesson walks through the method with clear examples, two video lessons, and practice exercises.

What Is Addition and Subtraction in Scientific Notation?

When numbers are in scientific notation, you can only add or subtract the coefficients if the powers of 10 are identical — just as you can only add like terms in algebra. The key skill is rewriting one number so both share the same exponent, then combining.

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How to Add or Subtract in Scientific Notation

Step 1: Match the exponents

Adjust one number so both have the same power of 10. Shift the decimal point of the smaller exponent number to make its exponent equal to the larger one.

• \(\color{blue}{4.5 \times 10^{4} + 2.3 \times 10^{3}}\): rewrite \(\color{blue}{2.3 \times 10^{3} = 0.23 \times 10^{4}}\)

Step 2: Add or subtract the coefficients

Once exponents match, combine the coefficients as normal numbers.

• \(\color{blue}{4.5 \times 10^{4} + 0.23 \times 10^{4} = 4.73 \times 10^{4}}\)

Step 3: Re-normalize if needed

Check that the coefficient is between 1 and 10. If not, adjust the exponent. For example, if you get \(\color{blue}{14.5 \times 10^{3}}\), rewrite as \(\color{blue}{1.45 \times 10^{4}}\).

Step-by-Step Summary

1. Identify the two powers of 10.
2. Rewrite the number with the smaller exponent so its exponent matches the larger one (move the decimal left; increase the exponent by the same amount).
3. Add or subtract the coefficients.
4. Keep the shared power of 10.
5. Re-normalize: make sure the coefficient satisfies \(\color{blue}{1 \le a < 10}\).

Watch: Subtracting in Scientific Notation (Video Lesson)

This Khan Academy lesson demonstrates subtracting numbers in scientific notation with exponent-matching:

Addition and Subtraction in Scientific Notation – Worked Examples

Example 1: Add \(\color{blue}{3.2 \times 10^{5} + 1.8 \times 10^{5}}\).

Same exponents. Add coefficients: \(\color{blue}{3.2 + 1.8 = 5.0}\).
Answer: \(\color{blue}{5.0 \times 10^{5}}\)

Example 2: Add \(\color{blue}{4.5 \times 10^{4} + 2.3 \times 10^{3}}\).

Different exponents. Rewrite: \(\color{blue}{2.3 \times 10^{3} = 0.23 \times 10^{4}}\).
Add: \(\color{blue}{4.5 + 0.23 = 4.73}\).
Answer: \(\color{blue}{4.73 \times 10^{4}}\)

Example 3: Subtract \(\color{blue}{6.0 \times 10^{6} – 4.0 \times 10^{5}}\).

Rewrite: \(\color{blue}{4.0 \times 10^{5} = 0.40 \times 10^{6}}\).
Subtract: \(\color{blue}{6.0 – 0.40 = 5.60}\).
Answer: \(\color{blue}{5.60 \times 10^{6}}\)

Example 4: Subtract \(\color{blue}{7.1 \times 10^{3} – 3.5 \times 10^{2}}\).

Rewrite: \(\color{blue}{3.5 \times 10^{2} = 0.35 \times 10^{3}}\).
Subtract: \(\color{blue}{7.1 – 0.35 = 6.75}\).
Answer: \(\color{blue}{6.75 \times 10^{3}}\)

More Practice: Adding and Subtracting Scientific Notation Video

This step-by-step video reviews adding and subtracting with full worked examples and exponent-matching technique:

Exercises for Addition and Subtraction in Scientific Notation

1. \(\color{blue}{5.0 \times 10^{4} + 3.0 \times 10^{4}}\)
2. \(\color{blue}{6.2 \times 10^{6} – 1.5 \times 10^{6}}\)
3. \(\color{blue}{3.4 \times 10^{3} + 2.6 \times 10^{2}}\)
4. \(\color{blue}{9.0 \times 10^{5} – 4.5 \times 10^{4}}\)
5. \(\color{blue}{2.1 \times 10^{-2} + 3.9 \times 10^{-2}}\)
6. \(\color{blue}{8.0 \times 10^{7} – 3.5 \times 10^{7}}\)

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Answers

1. \(\color{blue}{8.0 \times 10^{4}}\)
2. \(\color{blue}{4.7 \times 10^{6}}\)
3. \(\color{blue}{3.66 \times 10^{3}}\)
4. \(\color{blue}{8.55 \times 10^{5}}\)
5. \(\color{blue}{6.0 \times 10^{-2}}\)
6. \(\color{blue}{4.5 \times 10^{7}}\)

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Want More Practice?

We haven’t published a worksheet built specifically for Addition and Subtraction in Scientific Notation just yet. In the meantime, the free worksheets below cover closely related skills and concepts. If you’d like extra practice, download any that look helpful, complete the problems, and check your work — they’re a great way to reinforce what you learned on this page and strengthen the foundations this topic builds on:

• Download Properties of Exponents Worksheet

Frequently Asked Questions

Why must exponents match before adding?

Adding \(\color{blue}{a \times 10^{m} + b \times 10^{n}}\) when \(\color{blue}{m \ne n}\) is like adding apples and oranges — the units differ. You must convert to the same power of 10 first, just as you find a common denominator before adding fractions.

Which number do I adjust — the larger or the smaller?

Adjust the number with the smaller exponent: increase its exponent to match the larger one by moving its decimal point left (and decreasing the coefficient). This keeps the larger, more precise coefficient unchanged.

What if the result needs re-normalizing?

If the combined coefficient \(\color{blue}{\text{ is } \ge 10}\) or < 1, shift the decimal point and adjust the exponent: increase the exponent by 1 for every place you move the decimal left, or decrease it for moves to the right.

Related Topics

• Scientific Notation
• Multiplication and Division in Scientific Notation
• Zero and Negative Exponents
• Multiplication Property of Exponents
• Division Property of Exponents