.calculator-container {
font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
background-color: #f9f9f9;
padding: 20px;
border-radius: 8px;
box-shadow: 0 2px 10px rgba(0, 0, 0, 0.1);
max-width: 600px;
margin: 20px auto;
color: #333;
}
.calculator-container h2 {
text-align: center;
color: #0056b3;
margin-bottom: 25px;
font-size: 1.8em;
}
.calculator-section {
background-color: #ffffff;
border: 1px solid #e0e0e0;
border-radius: 6px;
padding: 18px;
margin-bottom: 20px;
box-shadow: 0 1px 5px rgba(0, 0, 0, 0.05);
}
.calculator-section h3 {
color: #0056b3;
margin-top: 0;
margin-bottom: 15px;
font-size: 1.4em;
border-bottom: 1px solid #eee;
padding-bottom: 10px;
}
.calculator-section label {
display: block;
margin-bottom: 8px;
font-weight: bold;
color: #555;
}
.calculator-section input[type="text"],
.calculator-section select {
width: calc(100% – 22px);
padding: 10px;
margin-bottom: 15px;
border: 1px solid #ccc;
border-radius: 4px;
font-size: 1em;
box-sizing: border-box;
}
.calculator-section button {
background-color: #007bff;
color: white;
padding: 12px 20px;
border: none;
border-radius: 4px;
cursor: pointer;
font-size: 1.1em;
width: 100%;
display: block;
margin-top: 10px;
transition: background-color 0.2s ease;
}
.calculator-section button:hover {
background-color: #0056b3;
}
.calculator-section .result {
margin-top: 20px;
padding: 12px;
background-color: #e9f7ef;
border: 1px solid #d4edda;
border-radius: 4px;
font-size: 1.1em;
color: #155724;
font-weight: bold;
text-align: center;
word-wrap: break-word;
}
.calculator-section .result.error {
background-color: #f8d7da;
border-color: #f5c6cb;
color: #721c24;
}
function formatToStandardFormDisplay(num) {
if (isNaN(num)) {
return "Invalid Number";
}
if (num === 0) {
return "0 × 10^0";
}
var exponential = num.toExponential(); // e.g., "1.234567e+6″
var parts = exponential.split('e');
var mantissa = parseFloat(parts[0]);
var exponent = parseInt(parts[1], 10);
// Adjust mantissa to be between 1 and 10 (or -1 and -10)
// toExponential() already does this, but we might need to ensure precision for display
var formattedMantissa = mantissa.toFixed(6).replace(/\.?0+$/, "); // Remove trailing zeros
return formattedMantissa + " × 10^" + exponent;
}
function convertToStandardForm() {
var numberToConvertStr = document.getElementById("numberToConvert").value;
var numberToConvert = parseFloat(numberToConvertStr);
var resultDiv = document.getElementById("standardFormResult");
if (isNaN(numberToConvert)) {
resultDiv.innerHTML = "Please enter a valid number.";
resultDiv.className = "result error";
return;
}
resultDiv.innerHTML = "Standard Form: " + formatToStandardFormDisplay(numberToConvert);
resultDiv.className = "result";
}
function convertFromStandardForm() {
var standardFormInputStr = document.getElementById("standardFormInput").value;
var regularNumberResultDiv = document.getElementById("regularNumberResult");
// parseFloat can handle scientific notation directly
var regularNumber = parseFloat(standardFormInputStr);
if (isNaN(regularNumber)) {
regularNumberResultDiv.innerHTML = "Please enter a valid standard form number (e.g., 1.23e5).";
regularNumberResultDiv.className = "result error";
return;
}
regularNumberResultDiv.innerHTML = "Regular Number: " + regularNumber.toLocaleString('en-US', { maximumFractionDigits: 20 });
regularNumberResultDiv.className = "result";
}
function performStandardFormOperation() {
var firstNumStr = document.getElementById("firstStandardFormNumber").value;
var secondNumStr = document.getElementById("secondStandardFormNumber").value;
var operation = document.getElementById("operationSelect").value;
var operationResultDiv = document.getElementById("operationResult");
var num1 = parseFloat(firstNumStr);
var num2 = parseFloat(secondNumStr);
if (isNaN(num1) || isNaN(num2)) {
operationResultDiv.innerHTML = "Please enter valid numbers in standard form for both inputs.";
operationResultDiv.className = "result error";
return;
}
var result;
var error = false;
switch (operation) {
case "add":
result = num1 + num2;
break;
case "subtract":
result = num1 – num2;
break;
case "multiply":
result = num1 * num2;
break;
case "divide":
if (num2 === 0) {
operationResultDiv.innerHTML = "Error: Division by zero is not allowed.";
operationResultDiv.className = "result error";
error = true;
} else {
result = num1 / num2;
}
break;
default:
operationResultDiv.innerHTML = "Invalid operation selected.";
operationResultDiv.className = "result error";
error = true;
break;
}
if (!error) {
operationResultDiv.innerHTML = "Result in Standard Form: " + formatToStandardFormDisplay(result);
operationResultDiv.className = "result";
}
}
Understanding Standard Form on a Calculator
Standard form, also known as scientific notation, is a way of writing very large or very small numbers concisely. It's particularly useful in scientific and engineering fields where numbers can span many orders of magnitude. On a calculator, standard form is often displayed using an 'E' or 'e' to represent "times ten to the power of."
What is Standard Form?
A number in standard form is expressed as:
a × 10^b
Where:
a (the mantissa or significand) is a number greater than or equal to 1 and less than 10 (1 ≤ |a| < 10).b (the exponent) is an integer.
For example:
- The speed of light, approximately 299,792,458 meters per second, is written as
2.99792458 × 10^8 m/s in standard form.
- The mass of an electron, approximately 0.00000000000000000000000000000091093837 kg, is written as
9.1093837 × 10^-31 kg.
How Calculators Display Standard Form
Most calculators use an 'E' or 'e' to denote "times 10 to the power of." So, 2.99792458 × 10^8 might appear as 2.99792458E+08 or 2.99792458e8. Similarly, 9.1093837 × 10^-31 would be shown as 9.1093837E-31.
Using the Standard Form Calculator
1. Convert to Standard Form
This section allows you to take a regular number and convert it into its scientific notation equivalent. This is helpful when you have a very long number and want to see its compact standard form representation.
Example: If you enter 1234567.89, the calculator will output 1.234568 × 10^6.
2. Convert from Standard Form
If you encounter a number in scientific notation (e.g., from a scientific paper or another calculator) and want to see its full decimal representation, use this feature. Simply type the number using 'e' notation (e.g., 1.23e5).
Example: Entering 1.23456789e+6 will give you 1,234,567.89.
3. Perform Operations on Standard Form Numbers
This is where the power of standard form truly shines. You can perform addition, subtraction, multiplication, and division on numbers already in scientific notation. The calculator will handle the conversion to and from standard form internally to give you an accurate result, also presented in standard form.
Example:
- Addition: If you add Avogadro's number (
6.022e23) to a small number like 1.602e-19, the result will be approximately 6.022000 × 10^23.
- Multiplication: Multiplying
3e5 by 2e-2 (which is 300,000 * 0.02) will yield 6.000000 × 10^3 (or 6000).
- Division: Dividing
6.022e23 by 1.602e-19 will give approximately 3.759051 × 10^42.
This calculator simplifies complex calculations involving extremely large or small numbers, making it an indispensable tool for students, scientists, and anyone working with scientific data.