Scientific Notation Calculator

About the Scientific Notation Calculator

Converts an ordinary number into scientific notation (a × 10ⁿ with 1 ≤ |a| < 10) and back, and reports the order of magnitude.

How to use this calculator

1. Enter the number you want to convert, or enter a value already written in scientific notation.
2. Choose whether you want standard form to scientific notation, or scientific notation to standard form.
3. Check the coefficient, which should be a number between 1 and 10 for scientific notation.
4. Read the converted result and, if needed, use the exponent to see how many places the decimal moves.

The formula explained

Scientific notation writes a number as \( a \times 10^n \), where \(a\) is the coefficient and \(n\) is the exponent. This form shows how many times the number is scaled by powers of 10.

• a = the coefficient, a number with absolute value from 1 to 10 when written in scientific notation
• n = the exponent on 10, which tells how many places the decimal moves

Step by step method

1. Write the number so the decimal point is placed after the first nonzero digit.
2. Count how many places the decimal moved, and use that count as the exponent.
3. If the original number is large, the exponent is positive, if it is a small decimal, the exponent is negative.

Worked example

Problem. Convert 48,300 to scientific notation.

1. Move the decimal 4 places left so the number becomes 4.83.
2. Because the decimal moved left, the exponent is positive 4.
3. Write the result as 4.83 × 10^4.

Tips and common mistakes

• Make sure the coefficient is at least 1 and less than 10, otherwise it is not in proper scientific notation.
• If the decimal moves right, the exponent is negative, for example 0.00056 = 5.6 × 10^-4.

Frequently asked questions