Scientific notation is a method used by scientists, mathematicians, and engineers to express very large or very small numbers in a simplified way. It follows the format m × 10n, where m is the coefficient (a number between 1 and 10) and n is the exponent (an integer).
How to Convert Standard Numbers to Scientific Notation
To convert a standard decimal number into scientific notation, follow these steps:
Step 1: Move the decimal point until you have a number between 1 and 10. This is your coefficient.
Step 2: Count how many places you moved the decimal point. This count is your exponent.
Step 3: If you moved the decimal to the left (because the original number was large), the exponent is positive. If you moved it to the right (original number was less than 1), the exponent is negative.
Common Examples
Speed of Light: 299,792,458 m/s becomes 2.9979 × 108 m/s.
Size of a Bacterium: 0.000002 meters becomes 2.0 × 10-6 meters.
Mass of the Earth: 5,972,000,000,000,000,000,000,000 kg becomes 5.972 × 1024 kg.
Why Use This Calculator?
Manual calculations with powers of ten can lead to easy mistakes, especially when adding or subtracting numbers with different exponents. This scientific notation calculator handles the shifting of decimal points and the normalization of the coefficient automatically, ensuring your significant figures remain accurate for physics, chemistry, or engineering homework.
function formatScientific(val) {
var parts = val.toExponential().split('e');
var coeff = parseFloat(parts[0]).toFixed(4).replace(/\.?0+$/, "");
var exp = parseInt(parts[1]);
return coeff + " × 10" + exp + "";
}
function convertToScientific() {
var input = document.getElementById("decimalInput").value;
var num = parseFloat(input);
var resultDiv = document.getElementById("sciResult");
var box = document.getElementById("sciResultBox");
if (isNaN(num)) {
resultDiv.innerHTML = "Please enter a valid number.";
box.style.display = "block";
return;
}
resultDiv.innerHTML = "Scientific: " + formatScientific(num);
box.style.display = "block";
}
function convertToDecimal() {
var coeff = parseFloat(document.getElementById("coeffInput").value);
var exp = parseInt(document.getElementById("expInput").value);
var resultDiv = document.getElementById("decResult");
var box = document.getElementById("decResultBox");
if (isNaN(coeff) || isNaN(exp)) {
resultDiv.innerHTML = "Please enter both coefficient and exponent.";
box.style.display = "block";
return;
}
var val = coeff * Math.pow(10, exp);
// Handle long decimals for display
var displayVal = (val.toString().length > 15) ? val.toPrecision(10) : val.toString();
resultDiv.innerHTML = "Standard: " + displayVal;
box.style.display = "block";
}
function calculateScientific() {
var c1 = parseFloat(document.getElementById("aCoeff").value);
var e1 = parseInt(document.getElementById("aExp").value);
var c2 = parseFloat(document.getElementById("bCoeff").value);
var e2 = parseInt(document.getElementById("bExp").value);
var op = document.getElementById("operation").value;
var resultDiv = document.getElementById("arithResult");
var box = document.getElementById("arithResultBox");
if (isNaN(c1) || isNaN(e1) || isNaN(c2) || isNaN(e2)) {
resultDiv.innerHTML = "Fill all coefficient and exponent fields.";
box.style.display = "block";
return;
}
var val1 = c1 * Math.pow(10, e1);
var val2 = c2 * Math.pow(10, e2);
var finalResult;
if (op === "add") finalResult = val1 + val2;
else if (op === "sub") finalResult = val1 – val2;
else if (op === "mul") finalResult = val1 * val2;
else if (op === "div") {
if (val2 === 0) {
resultDiv.innerHTML = "Cannot divide by zero.";
box.style.display = "block";
return;
}
finalResult = val1 / val2;
}
var displayStandard = (finalResult.toString().length > 12) ? finalResult.toExponential(4) : finalResult;
resultDiv.innerHTML = "Result: " + formatScientific(finalResult) + "Standard: " + displayStandard + "";
box.style.display = "block";
}