Scientific Notation Calculator

How to use the scientific notation calculator

1. Choose the calculation: convert a number (either way), or multiply, divide, add, subtract or raise to a power.
2. Type the number the way you would write it: 0.00052, 2500000, 2,500,000, 6.022e23, 3.2 × 10^5 (or 3.2x10^5, 3.2*10^-5) or 1.5 million.
3. Pick how to give the answer: keep every digit, or round to a number of significant figures.
4. You get the answer, the worked solution step by step (the decimal point moving one place at a time), a check, and the number in decimal form, E-notation and engineering notation.

What is scientific notation?

Scientific notation writes a number as a number between 1 and 10 multiplied by a power of ten:

• a is the coefficient (also called the mantissa or significand). It has exactly one non-zero digit before the decimal point.
• n is the exponent. It is positive for numbers of 10 or more, negative for numbers less than 1, and 0 for numbers from 1 to 10.

It makes very large and very small numbers short and easy to compare: the distance to the Sun, about 150,000,000 km, is 1.5 \times 10^{8} km, and the width of a red blood cell, about 0.000008 m, is 8 \times 10^{-6} m.

How to write a number in scientific notation

1. Find the coefficient: put the decimal point just after the first non-zero digit. For 0.00052 that gives 5.2; for 2,500,000 it gives 2.5 (zeros at the end are only placeholders).
2. Count the places the decimal point moved to get there.
3. Choose the sign: if the point moved left (a big number) the exponent is positive; if it moved right (a number less than 1) the exponent is negative.
4. Write coefficient × 10^exponent, and check by multiplying back.

Example 1: 2,500,000. The decimal point moves 6 places to the left (2,500,000 → 250,000 → 25,000 → 2,500 → 250 → 25 → 2.5), so

Example 2: 0.00052. The decimal point moves 4 places to the right (0.00052 → 0.0052 → 0.052 → 0.52 → 5.2), so the exponent is negative:

How to convert scientific notation to a decimal number

Do the moves backwards: a positive exponent moves the decimal point to the right (the number gets bigger), a negative exponent moves it to the left (the number gets smaller). Fill empty places with zeros.

• 3.2 \times 10^{5}: move the point 5 places right → 320,000.
• 7.06 \times 10^{-3}: move the point 3 places left → 0.00706.
• E-notation works the same way: 6.022E23 means 6.022 \times 10^{23}, and 1.6E-19 means 1.6 \times 10^{-19}.

Numbers in scientific notation

The numbers people look up most often. Select one to see the full working.

Famous numbers in scientific notation

Multiplying and dividing in scientific notation

• Multiply: multiply the coefficients and add the exponents. (3 \times 10^{4}) \times (5 \times 10^{6}) = 15 \times 10^{10} = 1.5 \times 10^{11}
• Divide: divide the coefficients and subtract the exponents. (8 \times 10^{5}) \div (2 \times 10^{-3}) = 4 \times 10^{8}
• Power: raise the coefficient to the power and multiply the exponents. (3 \times 10^{4})^{2} = 9 \times 10^{8}
• If the new coefficient is 10 or more, move its decimal point left and add to the exponent; if it is less than 1, move it right and subtract.

Adding and subtracting in scientific notation

The coefficients can only be added or subtracted when the powers of ten are the same. Rewrite the number with the smaller exponent first:

Significant figures

• All non-zero digits count: 4.56 has 3 significant figures.
• Zeros between non-zero digits count: 2.05 has 3.
• Zeros in front never count: 0.0052 has 2.
• Zeros at the end count after a decimal point (2.50 has 3), but in a whole number like 2,500,000 they may or may not. Scientific notation removes the doubt: 2.5 \times 10^{6} has 2, 2.500 \times 10^{6} has 4.
• To round, look at the first digit you drop: 5 or more rounds up, less than 5 leaves the kept digits as they are.

Powers of ten and their names

“Standard form” means different things

• In the UK, India and many other countries, “standard form” is scientific notation: 2.5 × 10⁶.
• In the US, “standard form” usually means the ordinary way of writing a number: 2,500,000.
• The answer shows both, clearly labelled, so you can use whichever your class or textbook means.

E-notation and engineering notation

• E-notation is how calculators, spreadsheets and programming languages show scientific notation: 5.2E-4 = 5.2 \times 10^{-4}.
• Engineering notation uses only powers that are multiples of 3, matching the prefixes kilo, mega, milli and micro: 0.00052 = 520 \times 10^{-6} (520 micro).

Converting between lakh, crore, million and billion? Use the number converter. To write a number in words, use number to words.

Frequently asked questions