Standard Form of Numbers
Expressing very large or very small numbers compactly using scientific notation with powers of ten.
Definition
The standard form of a number, also known as scientific notation, expresses extremely large or extremely small numbers as a decimal number between 1 and 10 multiplied by a power of 10. This format standardizes numerical representation to make calculations and comparisons much easier. Every non-zero number can be written in the form k \times 10^n, where 1 \le |k| < 10 and n is an integer.
Key formula
k \times 10^n
Worked examples
Express 85,000 in standard form by moving the decimal 4 places to the left, resulting in 8.5 \times 10^4.
Write 0.000042 in standard form by moving the decimal 5 places to the right, yielding 4.2 \times 10^{-5}.
Convert 300,000,000 to standard form to get 3 \times 10^8.
Common mistakes
- • Placing a number greater than 10 or less than 1 as the coefficient, such as writing 85 \times 10^3 instead of 8.5 \times 10^4.
- • Confusing the sign of the exponent of 10, using a positive exponent for small decimal numbers or a negative exponent for large whole numbers.
Introduction to Rational Numbers
Rational Numbers
Properties of Rational Numbers
Rational Numbers
Representation on Number Line
Rational Numbers
Rational Numbers Between Two Rational Numbers
Rational Numbers
Algebraic Expressions and Equations
Linear Equations in One Variable
Solving Equations with Variables on Both Sides
Linear Equations in One Variable