What is scientific notation?

Scientific notation is a way to write numbers as a product of two parts: a coefficient between 1 and 10, and a power of ten. For example, 300 = 3 × 10². Scientists and engineers use it to make very large or very small numbers easier to read and calculate.

How do you write a number in scientific notation?

Move the decimal point until exactly one non-zero digit sits to the left of the decimal. Count the moves. If you moved the decimal left, the exponent is positive. If you moved it right, the exponent is negative. Write the result as a × 10ⁿ. Example: 5,400,000 → move decimal 6 places left → 5.4 × 10⁶.

What does the exponent mean in scientific notation?

The exponent tells you how many places to move the decimal point. A positive exponent means the number is large (decimal moves right when converting back). A negative exponent means the number is small (decimal moves left). For example, 10³ = 1,000 and 10⁻³ = 0.001.

How do you convert scientific notation back to a regular number?

Move the decimal point the number of places shown by the exponent. If the exponent is positive, move right and add zeros as needed. If negative, move left and add leading zeros. Example: 2.3 × 10⁻⁴ → move decimal 4 places left → 0.00023.

How do you multiply numbers in scientific notation?

Multiply the coefficients and add the exponents. If the resulting coefficient is not between 1 and 10, adjust by moving the decimal one place and changing the exponent accordingly. Example: (3 × 10⁴) × (2 × 10³) = (3 × 2) × 10^(4+3) = 6 × 10⁷.

How do you divide numbers in scientific notation?

Divide the first coefficient by the second, then subtract the second exponent from the first. Adjust the result to standard form if needed. Example: (6 × 10⁸) ÷ (2 × 10³) = (6 ÷ 2) × 10^(8−3) = 3 × 10⁵.

What is the difference between scientific notation and engineering notation?

Scientific notation uses any integer power of ten. Engineering notation restricts exponents to multiples of three (10³, 10⁶, 10⁹, etc.) to match SI prefixes like kilo, mega, and giga. Engineering notation makes it easier to read measurements in standard units.

Why is scientific notation used in science?

Scientific notation makes arithmetic easier on very large or very small numbers. Writing 0.000000001 meters is error-prone; 1 × 10⁻⁹ meters is clearer. It also shows significant figures at a glance, which matters in experimental work where precision must be communicated explicitly.

Scientific Notation Calculator — Convert and Calculate in Scientific Notation

Convert any number to scientific notation or back to standard form. Multiply and divide numbers in scientific notation. Steps shown.

[PLACEHOLDER — Premium Content Writer will supply this intro paragraph. It should describe the tool in 2-3 sentences, mention the three modes (convert to scientific notation, convert back to standard form, and multiply/divide), and explain who uses it: students, scientists, and engineers working with very large or very small numbers.]

How this tool works

Pick a mode at the top. To convert a regular number, type it in and get the scientific notation result with steps. To convert scientific notation back, enter the coefficient and exponent. To multiply or divide two numbers already in scientific notation, choose the operation, fill in both numbers, and the calculator multiplies or divides the coefficients and adds or subtracts the exponents. Results update as you type. Share any calculation by copying the URL — all inputs are saved in the address bar.

Worked examples

Large number to scientific notation: 5,400,000
Move the decimal 6 places left: 5,400,000 → 5.4. Count: 6 moves left means a positive exponent. Answer: 5.4 × 10⁶.
Small number to scientific notation: 0.00023
Move the decimal 4 places right: 0.00023 → 2.3. Count: 4 moves right means a negative exponent. Answer: 2.3 × 10⁻⁴.
Scientific notation back to standard form: 6.02 × 10²³
Move the decimal 23 places right. This gives 602,000,000,000,000,000,000,000 — Avogadro's number, used in chemistry to count atoms and molecules.
Multiply in scientific notation: (3 × 10⁴) × (2 × 10³)
Multiply coefficients: 3 × 2 = 6. Add exponents: 4 + 3 = 7. Result: 6 × 10⁷ = 60,000,000.

Frequently asked questions

What is scientific notation?
Scientific notation is a way to write numbers as a product of two parts: a coefficient between 1 and 10, and a power of ten. For example, 300 = 3 × 10². Scientists and engineers use it to make very large or very small numbers easier to read and calculate.
How do you write a number in scientific notation?
Move the decimal point until exactly one non-zero digit sits to the left of the decimal. Count the moves. If you moved the decimal left, the exponent is positive. If you moved it right, the exponent is negative. Write the result as a × 10ⁿ. Example: 5,400,000 → move decimal 6 places left → 5.4 × 10⁶.
What does the exponent mean in scientific notation?
The exponent tells you how many places to move the decimal point. A positive exponent means the number is large (decimal moves right when converting back). A negative exponent means the number is small (decimal moves left). For example, 10³ = 1,000 and 10⁻³ = 0.001.
How do you convert scientific notation back to a regular number?
Move the decimal point the number of places shown by the exponent. If the exponent is positive, move right and add zeros as needed. If negative, move left and add leading zeros. Example: 2.3 × 10⁻⁴ → move decimal 4 places left → 0.00023.
How do you multiply numbers in scientific notation?
Multiply the coefficients and add the exponents. If the resulting coefficient is not between 1 and 10, adjust by moving the decimal one place and changing the exponent accordingly. Example: (3 × 10⁴) × (2 × 10³) = (3 × 2) × 10^(4+3) = 6 × 10⁷.
How do you divide numbers in scientific notation?
Divide the first coefficient by the second, then subtract the second exponent from the first. Adjust the result to standard form if needed. Example: (6 × 10⁸) ÷ (2 × 10³) = (6 ÷ 2) × 10^(8−3) = 3 × 10⁵.
What is the difference between scientific notation and engineering notation?
Scientific notation uses any integer power of ten. Engineering notation restricts exponents to multiples of three (10³, 10⁶, 10⁹, etc.) to match SI prefixes like kilo, mega, and giga. Engineering notation makes it easier to read measurements in standard units.
Why is scientific notation used in science?
Scientific notation makes arithmetic easier on very large or very small numbers. Writing 0.000000001 meters is error-prone; 1 × 10⁻⁹ meters is clearer. It also shows significant figures at a glance, which matters in experimental work where precision must be communicated explicitly.

Related tools

Writing very big and very small numbers

The distance to the sun is about 149,600,000 kilometers. A red blood cell is around 0.000007 meters wide. Counting zeros in numbers like those is slow and easy to get wrong. Scientific notation fixes that.

A number is written as a value between 1 and 10 times a power of ten. So 149,600,000 becomes 1.496 x 10^8, and 0.000007 becomes 7 x 10^-6. The calculator converts both ways and does arithmetic on them.

What the exponent tells you

A positive exponent says how many places the decimal moves to the right. A negative one says how many places it moves left. 10^3 is 1,000, and 10^-3 is 0.001.

To write a number in this form, move the decimal until one non-zero digit sits in front of it. Count the moves. That count is your exponent. Move left, it's positive. Move right, it's negative.

Multiplying and dividing

Multiply the front numbers and add the exponents. (3 x 10^4) x (2 x 10^5) is 6 x 10^9. If the front number goes past 10, fix it. (5 x 10^3) x (4 x 10^2) is 20 x 10^5, which becomes 2 x 10^6.

For division, divide the front numbers and subtract the exponents. (8 x 10^7) / (2 x 10^3) is 4 x 10^4.

Addition and subtraction are fussier. The exponents have to match first. The tool handles that step and shows the result.

Scientific versus engineering notation

Engineering notation is a cousin. The exponent is always a multiple of three, so it lines up with units like kilo, mega, milli and micro. 4.7 x 10^4 ohms becomes 47 x 10^3, or 47 kilohms. It's popular with electricians and engineers for that reason.

Scientific notation is more common in school and research. Use whichever fits your field.

Why bother

It keeps big numbers readable. It shows how many significant figures you really have. And calculators and programs use it internally, with an e in the middle: 1.5e8 means 1.5 x 10^8. If you see that in a spreadsheet, now you know.

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