Use the scientific notation calculator below to convert numbers between standard notation and scientific notation quickly and accurately!
Scientific Notation Calculator
Enter a number in standard, scientific, or E notation.
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Scientific notation is especially useful for expressing very large or very small numbers in a more manageable form. The examples below show how to convert numbers to and from scientific notation by hand.
Writing Large Numbers in Scientific Notation
Scientific notation expresses a number as a value between 1 and 10 multiplied by a power of 10.
To write 45,600,000 in scientific notation, move the decimal point until there is only one nonzero digit to its left.
\(45{,}600{,}000 \rightarrow 4.56\)
The decimal point moved 7 places to the left, so the exponent is 7.
\(4.56 \times 10^7\)
Therefore, \(45{,}600{,}000 = 4.56 \times 10^7\).
Writing Small Numbers in Scientific Notation
The same basic process works for numbers smaller than 1. Move the decimal point until the number is between 1 and 10.
For 0.0000721, move the decimal point 5 places to the right.
\(0.0000721 \rightarrow 7.21\)
Because we moved the decimal point to the right, the exponent is negative.
\(7.21 \times 10^{-5}\)
Therefore, \(0.0000721 = 7.21 \times 10^{-5}\).
Converting Scientific Notation to Standard Notation
To convert scientific notation back to standard notation, use the exponent to determine how far and in which direction to move the decimal point.
In \(6.3 \times 10^4\), the exponent is positive 4, so move the decimal point 4 places to the right.
\(6.3 \rightarrow 63 \rightarrow 630 \rightarrow 6{,}300 \rightarrow 63{,}000\)
Therefore, \(6.3 \times 10^4 = 63{,}000\).
