Scientific Notation Operations Math Example 2

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

Example 2

hard
Compute 6.0×1082.4×10−2\dfrac{6.0 \times 10^8}{2.4 \times 10^{-2}} and (5.0×103)+(3.0×102)(5.0 \times 10^3) + (3.0 \times 10^2), expressing both in scientific notation.

Solution

  1. 1
    Division: 6.02.4=2.5\dfrac{6.0}{2.4} = 2.5 and 10810−2=108−(−2)=1010\dfrac{10^8}{10^{-2}} = 10^{8-(-2)} = 10^{10}. Result: 2.5×10102.5 \times 10^{10}.
  2. 2
    Addition: align exponents to the larger one (10310^3). Convert: 3.0×102=0.3×1033.0 \times 10^2 = 0.3 \times 10^3.
  3. 3
    Add coefficients: (5.0+0.3)×103=5.3×103(5.0 + 0.3) \times 10^3 = 5.3 \times 10^3.

Answer

Division: 2.5×10102.5 \times 10^{10}; Addition: 5.3×1035.3 \times 10^3.
Division in scientific notation: divide coefficients and subtract exponents. Addition/subtraction requires matching exponents first (like aligning decimal points), then combining coefficients. Addition is trickier than multiplication because of the alignment step.

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 1 medium

Compute [formula] and express 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

← All Scientific Notation Operations Examples Scientific Notation Operations Concept