Scientific Notation & Magnitude
Aligned to 8.EE.A.3 — Common Core State Standards for Mathematics.
What this lesson teaches
Scientific notation writes a number as a × 10^n, where 1 ≤ a < 10 and n is an integer. A positive n means a large number; a negative n means a small number. Comparing exponents tells you how many times larger one quantity is than another.
Worked example
The Sun's mass is about 2 × 10^30 kg and Earth's is about 6 × 10^24 kg. Compare: 10^30 ÷ 10^24 = 10^6, and 2 ÷ 6 ≈ 0.33, so the Sun is about 0.33 × 10^6 = 3.3 × 10^5 — roughly 330,000 times heavier than Earth.
Practice questions
- Write 0.00047 in scientific notation.
- Write 5.2 × 10^7 in standard form.
- About how many times larger is 8 × 10^9 than 4 × 10^5?
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Notación Científica y Magnitud
La notación científica escribe un número como a × 10^n, donde 1 ≤ a < 10 y n es un entero. Un n positivo indica un número grande; un n negativo, uno pequeño. Comparar los exponentes te dice cuántas veces mayor es una cantidad que otra.
Ejemplo: La masa del Sol es de unos 2 × 10^30 kg y la de la Tierra, unos 6 × 10^24 kg. Compara: 10^30 ÷ 10^24 = 10^6, y 2 ÷ 6 ≈ 0.33, así que el Sol es unas 0.33 × 10^6 = 3.3 × 10^5 — cerca de 330,000 veces más pesado que la Tierra.
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