How do you convert scientific notation to standard form?

Scientific notation writes a number as a coefficient times 10 raised to an exponent: for example, 4.5 times 10 to the power of minus 5 (written 4.5e-5). To convert to decimal, move the decimal point in the coefficient by the number of places indicated by the exponent. A negative exponent moves it left: 4.5e-5 becomes 0.000045. A positive exponent moves it right: 1.23e8 becomes 123,000,000.

When is scientific notation used?

Scientific notation is used whenever numbers are very large or very small, making them impractical to write in full. In chemistry you encounter Avogadro's number (6.022e23), in physics the charge of an electron (1.602e-19 coulombs), and in engineering you might see material properties like Young's modulus (2e11 Pa) or the permeability of free space (1.257e-6 H/m). It also prevents ambiguity about the number of significant figures.

What is the difference between e notation and times-10 notation?

They are the same number, just written differently. 4.5e-5 is the computer or calculator notation for 4.5 times 10 to the power of negative 5. The 'e' stands for exponent. Written in traditional mathematical notation it would be 4.5 times 10 superscript minus 5. Most calculators, programming languages, and spreadsheets accept the e notation directly.

Scientific Notation Converter

Scientific notation expresses any number as a coefficient between 1 and 10 multiplied by a power of ten. The format 4.5e-5 means 4.5 times 10 to the power of minus 5, which equals 0.000045 in standard decimal form. The notation is used throughout science and engineering to handle very large and very small quantities without writing long strings of zeros: the mass of an electron is 9.109e-31 kilograms, the speed of light is 2.998e8 metres per second, and the national debt of many countries sits in the range of tens of trillions, around 1e13 dollars. This converter is bidirectional and auto-detects which format you enter. If your input contains an 'e' followed by a number (like 4.5e-5), it is treated as scientific notation and converted to decimal. If your input is a plain number (like 0.000045 or 123000000), it is converted to scientific notation. Both the coefficient-exponent form (e.g. 4.5 times 10 to the minus 5) and the e-notation shorthand (4.5e-5) are shown. Large integers in the output are formatted with comma separators for readability. The tool handles both positive and negative numbers. If the decimal form would be longer than about 20 digits, it is shown in e notation with a note to preserve accuracy. Use this when copying values between datasheets, entering numbers into formulas, or converting between calculator output and written documents.

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Enter a number (scientific or decimal)

0.000045

standard decimal form

Scientific (e) notation4.5e-5

Times-10 form4.5 × 10&sup5;

Signed exponent-5

How it works

The input is parsed using JavaScript's parseFloat(), which accepts both plain decimal numbers and e-notation strings. The resulting number is then converted to both forms. For the decimal form, very small numbers (exponent below about -6) and very large numbers (above 10 to the 15) are displayed using JavaScript's toFixed() or toPrecision() methods to avoid exponential output in the decimal column. For the scientific form, the coefficient is computed as the number divided by 10 to the floor of log base 10 of the absolute value, giving a value between 1 and 10. The exponent is the floor of log base 10 of the absolute value.

Worked example

Enter 4.5e-5. This is 4.5 times 10 to the power of minus 5. Moving the decimal point 5 places to the left: 4.5 becomes 0.000045 in standard decimal form. The e-notation is 4.5e-5, the times-10 form is 4.5 times 10 to the minus 5, and the exponent is -5. For the reverse direction, enter 123000000: the coefficient is 1.23, the exponent is 8, giving 1.23e8 in scientific notation.

Related calculators

Stress and Strain Calculator: enter Young's modulus and second moment of area in scientific notation.
Beam Deflection Calculator: accepts moment of inertia values like 8.33e-6 in the I field.
Molar Mass Calculator: molar masses and molecular counts often appear in scientific notation.
Percent Error Calculator: compare very small or very large measured values to reference values.

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