Scientific Notation Calculator
Convert numbers to and from scientific notation. Perform arithmetic operations and format numbers as a × 10^n where 1 ≤ |a| < 10.
Scientific Notation Calculator
Convert to/from scientific notation and perform calculations
Arithmetic in Scientific Notation
First Number
Second Number
Understanding Scientific Notation
Scientific notation is a way of expressing very large or very small numbers in a compact form. It's especially useful in science, engineering, and mathematics when dealing with measurements that span many orders of magnitude.
Format and Structure
Scientific notation expresses numbers in the form a × 10ⁿ where:
- a is the coefficient (1 ≤ |a| < 10)
- n is the exponent (can be positive or negative)
- The coefficient has one non-zero digit before the decimal point
Converting to Scientific Notation
Large Numbers (Positive Exponents)
123,000,000 = 1.23 × 10⁸
Move decimal left 8 places, exponent is +8
Small Numbers (Negative Exponents)
0.000045 = 4.5 × 10⁻⁵
Move decimal right 5 places, exponent is -5
E Notation
E notation is a computer-friendly version of scientific notation where "E" or "e" replaces "× 10". For example, 1.5 × 10⁶ becomes 1.5E6. This format is commonly used in calculators, spreadsheets, and programming.
Arithmetic Operations
Multiplication: Multiply coefficients, add exponents
(2 × 10³) × (3 × 10⁴) = 6 × 10⁷
Division: Divide coefficients, subtract exponents
(6 × 10⁸) ÷ (2 × 10³) = 3 × 10⁵
Addition/Subtraction: Convert to same exponent first
(3 × 10⁴) + (2 × 10³) = (3 × 10⁴) + (0.2 × 10⁴) = 3.2 × 10⁴
Frequently Asked Questions
Why is scientific notation useful?
Scientific notation makes it easier to work with extremely large or small numbers. It simplifies calculations, reduces writing errors, and clearly shows the order of magnitude. For example, the distance to the sun (150,000,000,000 m) is more manageable as 1.5 × 10¹¹ m.
Can the coefficient be greater than 10?
No, in proper scientific notation the coefficient must be between 1 and 10 (1 ≤ |a| < 10). If your coefficient is outside this range, adjust it by changing the exponent accordingly. For example, 15 × 10³ should be written as 1.5 × 10⁴.
How do I enter scientific notation in a calculator?
Most calculators have an EE, EXP, or E button for entering scientific notation. To enter 1.5 × 10⁶, type: 1.5, press EE, then 6. Don't manually type '× 10' - the calculator handles that automatically.
What's the difference between E6 and 10⁶?
They represent the same thing - both mean 'times 10 to the power of 6'. E6 is E notation (computer format), while 10⁶ is standard mathematical notation. For example, 2E6 = 2 × 10⁶ = 2,000,000.
How do negative exponents work?
Negative exponents indicate division by powers of 10, creating small numbers. 10⁻³ = 1/10³ = 1/1000 = 0.001. So 5 × 10⁻³ = 5/1000 = 0.005. Each negative increase moves the decimal one place left.
Is scientific notation the same as standard form?
In the US, 'scientific notation' and 'standard form' usually refer to the same thing (a × 10ⁿ). However, in the UK, 'standard form' is the term typically used instead of 'scientific notation', though they're identical in meaning and format.
Understanding Scientific Notation
Scientific notation is a standardized way to express very large or very small numbers by representing them as a product of a coefficient and a power of 10. The format is a × 10ⁿ, where 'a' is the coefficient (a number between 1 and 10, or -10 and -1 for negative numbers) and 'n' is an integer exponent.
For example, 65,000 can be written as 6.5 × 10⁴ because we move the decimal point 4 places to the left. Similarly, 0.0045 becomes 4.5 × 10⁻³ because we move the decimal point 3 places to the right (indicated by the negative exponent).
E Notation: In computer systems and calculators, scientific notation is often expressed as E notation, where 'E' represents "times ten raised to the power of." For example, 6.5E4 is equivalent to 6.5 × 10⁴, and 4.5E-3 is equivalent to 4.5 × 10⁻³.
This notation is essential in science, engineering, and mathematics because it simplifies calculations with extreme values, reduces potential for error, and makes it easy to compare magnitudes at a glance. The exponent quickly tells you the order of magnitude of a number.
How to Use the Calculator
Converting to Scientific Notation
- Enter your standard number (e.g., 123000 or 0.00456)
- The calculator automatically converts it to scientific notation format (a × 10ⁿ)
- View results in both standard scientific notation and E notation
Converting from Scientific Notation
- Enter the coefficient and exponent (e.g., 1.23 × 10⁵)
- Or use E notation format (e.g., 1.23E5)
- Get the standard decimal form instantly
Arithmetic Operations
Perform calculations directly in scientific notation:
- Multiplication: Multiply coefficients, add exponents
- Division: Divide coefficients, subtract exponents
- Addition/Subtraction: Adjust to same exponent, then add/subtract coefficients
Frequently Asked Questions
Why is scientific notation useful?
Scientific notation makes it easier to work with extremely large or small numbers. It simplifies calculations, reduces writing errors, and clearly shows the order of magnitude. For example, the distance to the sun (150,000,000,000 m) is more manageable as 1.5 × 10¹¹ m.
Can the coefficient be greater than 10?
No, in proper scientific notation the coefficient must be between 1 and 10 (1 ≤ |a| less than 10). If your coefficient is outside this range, adjust it by changing the exponent accordingly. For example, 15 × 10³ should be written as 1.5 × 10⁴.
How do I enter scientific notation in a calculator?
Most calculators have an EE, EXP, or E button for entering scientific notation. To enter 1.5 × 10⁶, type: 1.5, press EE, then 6. Don't manually type '× 10' - the calculator handles that automatically.
What's the difference between E6 and 10⁶?
They represent the same thing - both mean 'times 10 to the power of 6'. E6 is E notation (computer format), while 10⁶ is standard mathematical notation. For example, 2E6 = 2 × 10⁶ = 2,000,000.
How do negative exponents work?
Negative exponents indicate division by powers of 10, creating small numbers. 10⁻³ = 1/10³ = 1/1000 = 0.001. So 5 × 10⁻³ = 5/1000 = 0.005. Each negative increase moves the decimal one place left.
Is scientific notation the same as standard form?
In the US, 'scientific notation' and 'standard form' usually refer to the same thing (a × 10ⁿ). However, in the UK, 'standard form' is the term typically used instead of 'scientific notation', though they're identical in meaning and format.