Scientific Notation Calculator
Convert numbers to and from scientific notation and perform arithmetic.
Enter a positive, negative, large, small, or decimal number.
Scientific notation
4.5 × 10⁴
Compact a × 10ⁿ form.
Standard decimal form
45,000
Ordinary written number.
Coefficient / mantissa
4.5
Exponent
4
E notation
4.5E4
Engineering notation
45 × 10³
Order of magnitude
10⁴
Method
Standard to scientific notation
Scientific Notation Formulas and Rules
Scientific Notation
N = a × 10ⁿ
Normalized Coefficient
1 ≤ |a| < 10, when N ≠ 0
Standard Form
a × 10ⁿ = move decimal n places
Positive Exponent
a × 10ⁿ moves decimal n places to the right
Negative Exponent
a × 10⁻ⁿ moves decimal n places to the left
Multiplication
(a × 10ᵐ)(b × 10ⁿ) = (a × b) × 10ᵐ⁺ⁿ
Division
(a × 10ᵐ) ÷ (b × 10ⁿ) = (a ÷ b) × 10ᵐ⁻ⁿ
Variable Explanations
N
Original number.
a
Coefficient or mantissa.
n
Exponent or power of 10.
10ⁿ
Power of ten.
Normalized form
Coefficient between 1 and 10.
E notation
Computer format for ×10ⁿ.
Engineering notation
Notation where exponent is a multiple of 3.
What Scientific Notation Means
Compact form
Scientific notation writes very large or very small numbers compactly.
Power of 10
It uses a coefficient multiplied by a power of 10.
Science and engineering
Common in astronomy, chemistry, physics, engineering, and data work.
Readable scale
It makes numbers easier to read, compare, and calculate.
Decimal movement
The exponent shows how many decimal places the number moves.
Zero exception
Zero is simply written as 0.
Worked Examples
Convert 45,000
Rule: Move decimal 4 places left
Answer: 45,000 = 4.5 × 10⁴
Positive exponent because the number is large.
Convert 0.0032
Rule: Move decimal 3 places right
Answer: 0.0032 = 3.2 × 10⁻³
Negative exponent because the number is small.
7.89 × 10⁵ to standard form
Rule: Move decimal 5 places right
Answer: 789,000
Positive exponent moves right.
4.2 × 10⁻⁴ to standard form
Rule: Move decimal 4 places left
Answer: 0.00042
Negative exponent moves left.
Convert -52,000
Rule: Keep the negative sign and move decimal
Answer: -5.2 × 10⁴
The sign stays with the coefficient.
Normalize 45 × 10³
Rule: 45 becomes 4.5 and exponent increases by 1
Answer: 4.5 × 10⁴
Normalized coefficient is between 1 and 10.
Multiply 3 × 10⁴ by 2 × 10²
Rule: Multiply coefficients and add exponents
Answer: 6 × 10⁶
3 × 2 = 6 and 4 + 2 = 6.
Divide 8 × 10⁶ by 2 × 10³
Rule: Divide coefficients and subtract exponents
Answer: 4 × 10³
8 ÷ 2 = 4 and 6 − 3 = 3.
E notation 1.23E5
Rule: E means ×10 raised to a power
Answer: 123,000
Useful in calculators and spreadsheets.
Engineering notation
Rule: Use exponent multiple of 3
Answer: 12,300 = 12.3 × 10³
Engineering notation aligns with prefixes like kilo and mega.
Standard Form, Scientific Notation, and Engineering Notation
Standard
12,300
Ordinary decimal number.
Scientific
1.23 × 10⁴
One non-zero digit before the decimal.
E notation
1.23E4
Calculator and spreadsheet shorthand.
Engineering
12.3 × 10³
Exponent is a multiple of 3.
Operations with Scientific Notation
Multiplication
Multiply coefficients and add exponents.
Division
Divide coefficients and subtract exponents.
Addition
Match exponents first, then add coefficients.
Subtraction
Match exponents first, then subtract coefficients.
Normalize
After operations, adjust the coefficient to be between 1 and 10.
Check both forms
Use scientific notation and standard form together when possible.
Common Use Cases
Common Scientific Notation Mistakes
Understanding Your Result
Scientific notation
Compact a × 10ⁿ form.
Standard decimal form
Ordinary written number.
Coefficient
Leading number multiplied by the power of 10.
Exponent
Number of decimal places moved.
E notation
Spreadsheet and calculator-friendly format.
Engineering notation
Exponent grouped by multiples of 3.
Order of magnitude
Approximate power-of-10 scale.
Frequently Asked Questions
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