Operations with Scientific Notation: Part 1

Multiply, Divide, Add, and Subtract

In this lesson:

• Multiply and divide numbers in scientific notation
• Add and subtract numbers in scientific notation

What You Will Learn Today

By the end of this lesson, you should be able to:

1. Multiply and divide in scientific notation using exponent rules, then adjust the result to proper form
2. Add and subtract in scientific notation by matching powers of 10 first, then combining the coefficients

Hook: How Long Does Sunlight Travel?

The Sun is about km from Earth.

Light travels at about km per second.

How long does sunlight take to reach Earth?

We'll solve this — but first we need the tools.

Multiplication: Regroup Coefficients and Powers

• Multiply the coefficients
• Add the exponents

Examples: Multiply — No Adjustment Needed

Step 1: Multiply coefficients:

Step 2: Add exponents:

Verify: ✓

Examples: Multiply — Coefficient Too Large

, : result is

Not proper form — . Adjust:

Examples: Multiply — Using Negative Exponents

Step 1: , , so result is

Is this proper form? No —

Adjust:

Division: Divide Coefficients, Subtract Exponents

Apply the same grouping strategy — but subtract exponents:

• Divide the coefficients
• Subtract the exponents

Examples: Divide — Clean Result, No Adjustment

Step 1: Divide coefficients:

Step 2: Subtract exponents:

Examples: Divide — Coefficient Less Than One

, : result is

Not proper form — . Adjust:

Sunlight Travels About 500 Seconds

≈ 8.3 minutes — light from the Sun takes about 8 minutes to reach Earth.

Try It: Compute and Adjust the Result

Compute and express in proper scientific notation:

Pause and try before the next slide.

Answer: Result Is

Step 1: , , result is

Adjust:

Warning: Addition Uses a Different Approach

What if we add exponents during addition?

Check with standard form:

Adding exponents gives the wrong answer!

Addition Rule: Match Powers of Ten First

Like terms must share the same unit before combining:

• ✓ — same power
• — must convert first

Rule: Match powers of 10, then add or subtract coefficients only.

Examples: Add — Same Power of Ten

Both numbers have the same power of 10: ✓

Add the coefficients only:

Coefficient is between 1 and 10 — no adjustment needed.

Examples: Add — Convert to Match Powers

Convert:

Add:

Verify: ✓

Examples: Subtract — Convert Before Subtracting

Step 1: Convert to match :

Step 2: Subtract the coefficients:

Examples: Add — Then Adjust the Coefficient

Powers already match — add directly:

Is this proper form? No —

Adjust:

Real-World Example: US and Canada Population

The US population is about .

Canada's population is about .

What is the combined population?

Step 1: Convert

Step 2: Add:

About 369 million people.

Try It: Add Numbers with Different Powers

Compute and express in proper scientific notation:

Show the conversion step — then combine.

Answer: Convert First, Then Add Coefficients

Convert:

Add:

Coefficient check: ✓

Key Takeaways: Two Different Procedures

Multiply/Divide: operate on coefficients and exponents directly

Add/Subtract: match powers of 10 first, then combine coefficients

• After every operation: check and adjust the coefficient
• When exponent increases by 1, coefficient divides by 10

Coming Up Next: Part Two Preview

In Part 2, you will:

• Work with mixed notation — one number in scientific notation, one in decimal form
• Read calculator displays — what does "3.5E8" mean?
• Choose appropriate units for very large and very small measurements
• Tackle multi-step real-world problems using all four operations