Scientific Notation Calculator

Convert any number to scientific notation, engineering notation and E notation, or add, subtract, multiply and divide two numbers written in scientific notation, with the steps shown. Example: 0.000345 = 3.45 × 10⁻⁴, and (3.2 × 10⁵) × (4 × 10³) = 1.28 × 10⁹.

How to use the Scientific Notation Calculator

1. Pick a mode: convert a number, calculate with two numbers in scientific notation, or turn coefficient × 10^exponent back into a plain number.
2. For converting, type the number. For very large or very small numbers use E notation, such as 6.02e23.
3. For calculating, enter each number as a coefficient and an exponent and pick the operation.
4. Optional: set a number of significant figures to round the result.
5. Press Calculate and open Show steps.

Formula and method

N = a × 10ⁿ, with 1 ≤ |a| < 10 and n an integer.

Multiply: (a×10^m)(b×10ⁿ) = (ab) × 10^m+n. Divide: (a÷b) × 10^m−n. Add or subtract: first give both the same exponent, then add or subtract the coefficients.

If the new coefficient is not between 1 and 10, move the decimal and adjust the exponent.

Example: (3.2×10⁵)(4×10³) = 12.8 × 10⁸ = 1.28 × 10⁹.

What is scientific notation?

Scientific notation writes a number as a coefficient between 1 and 10 times a power of ten. It makes very large and very small numbers easier to write and compare, such as the speed of light (3.00 × 10⁸ m/s) or the mass of an electron (9.11 × 10⁻³¹ kg).

How to convert to scientific notation

Move the decimal point until one non-zero digit is to its left. Count the moves: moving left gives a positive exponent, moving right a negative exponent. 45,600 becomes 4.56 × 10⁴; 0.00072 becomes 7.2 × 10⁻⁴.

Scientific vs engineering vs E notation

Engineering notation uses exponents that are multiples of 3, matching SI prefixes such as kilo, mega and micro.

Significant figures

The digits of the coefficient are the significant figures. 3.20 × 10⁵ has three, and 3.2 × 10⁵ has two. Use the significant-figures box to round results to the precision your measurement supports.

Adding and subtracting

Exponents must match first. 3.5 × 10⁴ + 6 × 10³ becomes 3.5 × 10⁴ + 0.6 × 10⁴ = 4.1 × 10⁴. The calculator does this alignment for you.

Common mistakes

Forgetting that a negative exponent means a small number, not a negative number. Adding exponents when adding numbers (only add them when multiplying). Leaving a coefficient such as 12.8 un-normalised.

Where scientific notation is used

Astronomy (distances), chemistry (Avogadro’s number 6.022 × 10²³), computing (file sizes), and any lab report with measurements across many orders of magnitude.

Accuracy and limits

JavaScript doubles hold about 15 to 17 digits, so results with more digits are rounded. Extremely large exponents beyond 10³⁰⁸ overflow.

Frequently asked questions

How do I write a number in scientific notation?

Move the decimal point so one non-zero digit is in front, count the moves, and use that as the power of ten.

What does E notation mean?

The letter E stands for ×10 to the power. 6.02e23 means 6.02 × 10^23.

How do I multiply numbers in scientific notation?

Multiply the coefficients and add the exponents, then normalise.

What is engineering notation?

Scientific notation restricted to exponents that are multiples of 3.

How many significant figures does 3.20 × 10^5 have?

Three: 3, 2 and 0.

Sources

• Scientific notation (Wikipedia)
• Significant figures (Wikipedia)

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