Scientific Notation Operations Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

medium
Compute (3.2×105)×(4.0×10−3)(3.2 \times 10^5) \times (4.0 \times 10^{-3}) and express in scientific notation.

Solution

  1. 1
    Multiply the coefficients: 3.2×4.0=12.83.2 \times 4.0 = 12.8.
  2. 2
    Multiply the powers of 1010: 105×10−3=105+(−3)=10210^5 \times 10^{-3} = 10^{5+(-3)} = 10^2.
  3. 3
    Combine: 12.8×10212.8 \times 10^2.
  4. 4
    Adjust to proper scientific notation (coefficient must satisfy 1≤c<101 \leq c < 10): 12.8=1.28×10112.8 = 1.28 \times 10^1, so 12.8×102=1.28×10312.8 \times 10^2 = 1.28 \times 10^3.

Answer

1.28×1031.28 \times 10^3
To multiply in scientific notation: multiply the coefficients, add the exponents (using 10a×10b=10a+b10^a \times 10^b = 10^{a+b}), then adjust so the coefficient is between 11 and 1010. This mirrors the exponent rules for powers of the same base.

About Scientific Notation Operations

Performing addition, subtraction, multiplication, and division on numbers expressed in scientific notation.

Learn more about Scientific Notation Operations →

More Scientific Notation Operations Examples

Example 2 hard

Compute [formula] and [formula], expressing both in scientific notation.

Example 3 easy

Compute [formula]. Express your answer in scientific notation.

Example 4 medium

The mass of the Earth is [formula] kg. The mass of the Moon is [formula] kg. How many times heavier

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