Scientific Notation Calculator

Q: How do you convert a decimal number to scientific notation?

Move the decimal point until only one non-zero digit remains to its left, forming a coefficient between 1 and 10. Count how many places you moved the decimal point - that count becomes the exponent of 10, positive if you moved left (the original number was 10 or larger) and negative if you moved right (the original number was between 0 and 1). For example, 1,234,000 becomes 1.234 x 10^6, and 0.0000456 becomes 4.56 x 10^-5.

Q: How do you add or subtract numbers written in scientific notation?

Unlike multiplication and division, addition and subtraction require the exponents to match first. Rewrite one number so both share the same power of 10, then add or subtract the coefficients directly and keep that exponent. Afterward, renormalize the result so the coefficient falls back between 1 and 10, adjusting the exponent if needed - this calculator's arithmetic mode does that renormalization automatically and shows each step.

What do you want to do?

Number

Scientific Notation (use e for ×10^)

Decimal Places for Coefficient

Standard (Decimal) Form

Scientific Notation

E Notation

How Scientific Notation Works

Scientific notation writes any number as a × 10ⁿ, where the coefficient a satisfies 1 ≤ |a| < 10 and the exponent n is an integer. To convert a decimal number, you shift the decimal point until exactly one non-zero digit remains to its left, then count how many places you moved: moving left gives a positive exponent (large numbers like 1,234,000 = 1.234 × 10⁶), moving right gives a negative exponent (small numbers like 0.0000456 = 4.56 × 10^-5). This calculator also accepts "E notation" (e.g. 4.56e-5), the plain-text form used by calculators and programming languages, which means exactly the same thing.

Multiplying and Dividing in Scientific Notation

To multiply two numbers in scientific notation, multiply the coefficients and add the exponents: (a × 10^m) × (b × 10ⁿ) = (a × b) × 10^m+n. To divide, divide the coefficients and subtract the exponents. Addition and subtraction are trickier — the exponents must first be made equal (by rewriting one number so both share the same power of 10) before you add or subtract the coefficients directly. After any operation, the result is renormalized so the coefficient falls back into the 1-10 range, adjusting the exponent accordingly. If you only need the exponent rules in isolation, the exponent calculator covers those laws in more depth.

Why Scientists Use It

Scientific notation avoids writing out long strings of zeros for very large numbers (Avogadro's number, 6.022 × 10²³) or very small ones (the mass of an electron, 9.109 × 10^-31 kg), and it makes the number of significant figures unambiguous — something 0.0000456 doesn't show clearly but 4.56 × 10^-5 does. If your work also involves logarithms of these magnitudes, the log calculator is a natural companion.

Frequently Asked Questions

How do you convert a decimal number to scientific notation?

Move the decimal point until only one non-zero digit remains to its left, forming a coefficient between 1 and 10. Count how many places you moved the decimal point - that count becomes the exponent of 10, positive if you moved left (the original number was 10 or larger) and negative if you moved right (the original number was between 0 and 1). For example, 1,234,000 becomes 1.234 x 10^6, and 0.0000456 becomes 4.56 x 10^-5.

How do you add or subtract numbers written in scientific notation?

Unlike multiplication and division, addition and subtraction require the exponents to match first. Rewrite one number so both share the same power of 10, then add or subtract the coefficients directly and keep that exponent. Afterward, renormalize the result so the coefficient falls back between 1 and 10, adjusting the exponent if needed - this calculator's arithmetic mode does that renormalization automatically and shows each step.