Scientific Notation
Express very large and small numbers
Start with the basics and progress through 6 lessons. Each lesson builds on the previous one.
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In This Topic (6 lessons)
Scientific Notation
Learn how to write very large and very small numbers using scientific notation.
Writing Numbers in Scientific Notation
Learn how to convert large and small numbers into scientific notation and understand when to use this format.
Converting from Scientific Notation
Learn to turn a number like 3.2 × 10⁻⁴ back into an ordinary decimal number by moving the decimal point and filling in zeros.
Comparing Numbers in Scientific Notation
Learn to compare and order numbers in scientific notation: exponents first, then coefficients, and how many times bigger one number is.
Multiplying in Scientific Notation
Learn to multiply numbers in scientific notation: multiply the coefficients, add the exponents and normalize the result.
Dividing in Scientific Notation
Divide numbers in scientific notation: divide the coefficients, subtract the exponents, then normalize the result so the coefficient is between 1 and 10.
Scientific notation provides a concise way to express very large or very small numbers using powers of 10. Instead of writing 299,792,458 (the speed of light in m/s), scientists write $2.998 \times 10^8$. For tiny numbers like 0.000000001 (a nanometer in meters), we write $1 \times 10^{-9}$. This notation makes calculations with extreme values manageable.
In scientific notation, numbers are written as a coefficient between 1 and 10 multiplied by a power of 10. This standardized format is essential in physics, chemistry, astronomy, and engineering where measurements span enormous ranges from subatomic particles to galaxies.
What You'll Learn
- Convert numbers between standard form and scientific notation
- Compare and order numbers expressed in scientific notation
- Perform addition, subtraction, multiplication, and division with scientific notation
- Apply scientific notation to solve real-world science problems
- Understand significant figures in scientific notation
Frequently Asked Questions
Why do scientists use scientific notation?
It makes extremely large or small numbers manageable, reduces writing errors, clearly shows the scale of measurements, and simplifies calculations involving many zeros.
What does a negative exponent mean in scientific notation?
A negative exponent indicates a small number less than 1. For example, $10^{-3} = 0.001$. The exponent tells you how many places to move the decimal point left.
How do you multiply numbers in scientific notation?
Multiply the coefficients and add the exponents. For example: $(2 \times 10^3) \times (3 \times 10^4) = 6 \times 10^7$.