Scientific Notation (e.g., 1.2345e+4)
Standard Notation (e.g., 12345)
Enter a number to see the result.
Understanding Scientific Notation
Scientific notation is a standardized way of writing numbers that are too large or too small to be conveniently written in standard decimal form. It is commonly used in science, engineering, and mathematics. A number in scientific notation is expressed as a coefficient (a number between 1 and 10, inclusive of 1 but exclusive of 10) multiplied by a power of 10.
The general form is: a × 10n
a (the coefficient) is a real number such that 1 ≤ |a| < 10.
n (the exponent) is an integer, indicating how many places the decimal point must be moved.
How to Convert to Scientific Notation
To convert a standard number to scientific notation:
Locate the decimal point in the number.
Move the decimal point to the right or left until there is only one non-zero digit to its left. This forms the coefficient (a).
If you moved the decimal point to the left, the exponent (n) is positive and equal to the number of places you moved it.
If you moved the decimal point to the right, the exponent (n) is negative and equal to the number of places you moved it.
If the original number was zero, the scientific notation is 0 × 100 or simply 0.
Example: To convert 123,450,000 to scientific notation:
Move the decimal point 8 places to the left: 1.23450000
The coefficient is 1.2345.
The exponent is +8 (since we moved left).
So, 123,450,000 = 1.2345 × 108.
Example: To convert 0.0000789 to scientific notation:
Move the decimal point 5 places to the right: 000007.89
The coefficient is 7.89.
The exponent is -5 (since we moved right).
So, 0.0000789 = 7.89 × 10-5.
How to Convert from Scientific Notation
To convert a number from scientific notation (a × 10n) back to standard form:
Take the coefficient (a).
If the exponent (n) is positive, move the decimal point n places to the right. Add zeros as placeholders if necessary.
If the exponent (n) is negative, move the decimal point |n| places to the left. Add zeros as placeholders if necessary.
Example: Convert 3.14 × 105 to standard form:
Coefficient is 3.14.
Exponent is +5.
Move the decimal point 5 places to the right: 314000.
So, 3.14 × 105 = 314,000.
Example: Convert 9.8 × 10-4 to standard form:
Coefficient is 9.8.
Exponent is -4.
Move the decimal point 4 places to the left: 0.00098.
So, 9.8 × 10-4 = 0.00098.
Why Use Scientific Notation?
Scientific notation simplifies the representation of extremely large or small numbers, making them easier to read, write, and comprehend. It also streamlines calculations involving such numbers, reducing the risk of errors with misplaced decimal points or incorrect counts of zeros.
This calculator helps you quickly convert between standard and scientific notation, useful for:
Reading scientific papers or data.
Inputting values into scientific software.
Understanding large astronomical distances or tiny atomic sizes.
Performing complex mathematical operations.
function convertNotation() {
var numberInput = document.getElementById("numberInput").value;
var notationType = document.getElementById("notationType").value;
var resultDiv = document.getElementById("result");
resultDiv.style.backgroundColor = "var(–success-green)"; // Reset color
if (numberInput.trim() === "") {
resultDiv.textContent = "Please enter a number.";
resultDiv.style.backgroundColor = "#ffc107"; // Warning yellow
return;
}
var parsedNumber;
try {
// Attempt to parse the input robustly.
// This handles standard decimal numbers and numbers already in scientific notation (like '1.23e+4').
parsedNumber = parseFloat(numberInput);
// If the input was like '1.23e4' and parseFloat gives a valid number, it's good.
// If input was 'abc', parseFloat returns NaN.
if (isNaN(parsedNumber)) {
throw new Error("Invalid number format.");
}
// Additional check for explicit scientific notation format if parseFloat missed it (rare but possible)
if (numberInput.includes('e') || numberInput.includes('E')) {
var parts = numberInput.toLowerCase().split('e');
if (parts.length === 2 && parts[1].match(/^[-+]?\d+$/)) {
// It looks like scientific notation, and parseFloat already handled it.
} else {
throw new Error("Invalid scientific notation format.");
}
}
} catch (e) {
resultDiv.textContent = "Invalid input. Please enter a valid number.";
resultDiv.style.backgroundColor = "#dc3545"; // Error red
return;
}
var formattedResult;
if (notationType === "scientific") {
if (parsedNumber === 0) {
formattedResult = "0.0e+0"; // Standard representation for zero
} else {
formattedResult = parsedNumber.toExponential();
}
resultDiv.textContent = formattedResult;
} else if (notationType === "standard") {
// toLocaleString() is good for general formatting and handling large/small numbers gracefully.
// The default precision might need adjustment for very specific cases, but it's generally robust.
// For scientific notation to standard, we can also use Number.prototype.toFixed() if we want more control,
// but toLocaleString() handles large numbers without scientific notation display by default.
formattedResult = parsedNumber.toLocaleString();
resultDiv.textContent = formattedResult;
}
}