Scientific Notation Calculator
Convert a number or a list, or calculate with two numbers and see each step.
- Decimal
- Engineering notation
Exact value
Calculation steps
Calculate with scientific notation, step by step
Choose Calculate (+ − × ÷) for two-number arithmetic. You can enter ordinary decimals, E notation, or a coefficient times a power of ten. The result includes scientific, decimal, and engineering notation, followed by the steps for your operation.
Adding and subtracting: use the same exponent
For 4 × 10^5 + 7 × 10^4, rewrite the second number as 0.7 × 10^5. Add the coefficients: (4 + 0.7) × 10^5 = 4.7 × 10^5. Subtraction follows the same rule: 5.4 × 10^3 − 2.1 × 10^3 = 3.3 × 10^3.
Multiplying: multiply coefficients and add exponents
(3.2 × 10^5) × (2 × 10^3) = (3.2 × 2) × 10^(5 + 3) = 6.4 × 10^8. If the coefficient is outside the range from 1 up to, but not including, 10 in absolute value, shift its decimal point and adjust the exponent.
Dividing: divide coefficients and subtract exponents
(6 × 10^8) ÷ (2 × 10^3) = (6 ÷ 2) × 10^(8 − 3) = 3 × 10^5. A divisor of zero is not allowed. A result such as 1 ÷ 3 keeps its exact fraction and marks its displayed decimal as approximate.
Choose display precision without rounding intermediate steps
Arithmetic mode uses the entered values exactly and rounds only the displayed result to your selected significant figures. Open Exact value to compare. This setting does not infer the precision of measured quantities: for example, an exact factor of 2 does not reduce 2 × 2.35 to one significant figure. With three figures selected, the result is 4.70.
Exact conversion before optional rounding
Every valid row first shows scientific, E, engineering, and expanded decimal notation from the entered decimal digits. The converter uses string and integer operations rather than binary floating-point, so a value such as 0.1 does not acquire extra tail digits.
Two rounding questions, two answers
In Convert numbers mode, rounding to four significant figures is not the same task as rounding to four decimal places. Each result shows both rounding options separately and leaves the exact conversion visible for comparison.
Paste a worksheet column without hiding bad rows
Use one value per line. Valid lines remain available even when another row contains an expression, malformed comma grouping, too many retained digits, or an exponent outside the documented range. Copy produces tab-separated columns for a spreadsheet.
Accepted scope
Examples include 345600, 3.456e5, 3.456 x 10^5, and 3.456 × 10⁵. Enter a single value in each arithmetic field, or one value per line in Convert numbers mode. Each input accepts up to 100 retained digits and a normalized exponent from −1000 to 1000; arithmetic results may have larger exponents. Full expressions, parentheses, fractions, general exponentiation such as 2^3, and roots are not accepted as input. Powers of ten within scientific notation are supported. Use the operation selector for addition, subtraction, multiplication, or division.
Frequently asked questions
Can this calculator add, subtract, multiply, and divide scientific notation?
Yes. Choose Calculate, enter one number in each field, select an operation, and click Calculate with steps. The Convert numbers mode still converts up to 100 values at once. Arithmetic mode calculates one pair of numbers at a time.
How do you add or subtract numbers with different exponents?
Rewrite both numbers using the same power of ten, add or subtract the coefficients, then normalize. For example, 4 × 10^5 + 7 × 10^4 = (4 + 0.7) × 10^5 = 4.7 × 10^5.
How do you multiply or divide scientific notation?
For multiplication, multiply the coefficients and add the exponents. For division, divide the coefficients and subtract the second exponent from the first. Normalize the coefficient afterward. Division by zero is undefined and returns an error.
Are arithmetic answers exact or rounded?
The calculation uses the entered decimal values exactly. The displayed scientific, decimal, and engineering formats use your selected 1–12 significant figures; an approximately-equal sign marks a rounded result. Expand Exact value to see the unrounded decimal when it terminates, or an exact fraction when it does not. Rounding happens once at the end, and halfway magnitudes round away from zero. The selected precision is a display setting, not an automatic application of measurement significant-figure rules.
How do you convert a number to scientific notation?
Move the decimal point so one nonzero digit remains to its left. The number of places moved becomes the exponent: moving left gives a positive exponent, while moving right gives a negative exponent.
What is the difference between scientific notation and E notation?
They encode the same value. For example, 5.6 × 10^-3 and 5.6e-3 are equivalent. E notation is convenient in spreadsheets, calculators, and plain text.
What is engineering notation?
Engineering notation uses an exponent that is a multiple of three. A value such as 1.234 × 10^8 becomes 123.4 × 10^6.
Are significant figures the same as decimal places?
No. Significant figures count meaningful retained digits from the first nonzero digit. Decimal places count positions to the right of the decimal point. This page calculates both settings separately so their effects are visible.
How are halfway values rounded in Convert numbers mode?
The two optional rounding views use half-up rounding: if the first discarded digit is 5 or greater, the last retained magnitude increases. The exact conversion is always shown separately before either rounding view.
How many numbers can I convert at once?
Up to 100 non-empty lines. Each value may retain up to 100 digits, and its normalized exponent must stay between -1000 and 1000. Invalid lines are identified without discarding valid rows.