✏️ Expressions & Equations
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Scientific Notation

Scientific notation compactly expresses very large or very small numbers using powers of 10.

Scientific notation writes a number in the form a × 10ⁿ, where 1 ≤ |a| < 10 and n is an integer. You can add, subtract, multiply, and divide in scientific notation by combining the coefficient and the power of 10 separately.

a×10nwhere 1≤∣a∣<10,  n∈Za \times 10^n \quad \text{where } 1 \leq |a| < 10, \; n \in \mathbb{Z}
🌍Converting to scientific notation
Earth's mass ≈ 5,970,000,000,000,000,000,000,000 kg
= 5.97 × 10²⁴ kg

A bacterium's diameter ≈ 0.000002 m
= 2 × 10⁻⁶ m
(3×104)×(2×103)=6×107(3 \times 10^4) \times (2 \times 10^3) = 6 \times 10^7
8×1064×102=2×104\frac{8 \times 10^6}{4 \times 10^2} = 2 \times 10^4
➕Adding in scientific notation
3.2 × 10⁵ + 4 × 10⁴

Adjust to same power: 3.2 × 10⁵ + 0.4 × 10⁵ = 3.6 × 10⁵

Both terms must share the same power of 10 before adding.
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Remember This!

To compare numbers in scientific notation, first compare the exponents. Larger exponent = larger number. If exponents match, compare the coefficients.

✏️ Try It!

Multiply: (4 × 10³) × (3 × 10⁵). What is the result in scientific notation?

Practice with CalcVerse
🔬Scientific Notation
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