Decimals are a way of representing numbers that are between whole numbers. They use a decimal point to separate the whole number part from the fractional part. Whether you are managing finances, performing scientific measurements, or baking, understanding how to calculate decimals accurately is a fundamental skill.
How to Perform Decimal Operations
1. Adding Decimals
The golden rule for adding decimals is to align the decimal points. If the numbers have a different number of digits after the decimal, you can add trailing zeros as placeholders.
Example: 12.5 + 3.75
Align: 12.50 + 03.75 = 16.25
2. Subtracting Decimals
Similar to addition, you must line up the decimal points. Be careful when subtracting a longer decimal from a shorter one; always use zeros to keep your columns straight.
Example: 10.8 – 4.25
Align: 10.80 – 04.25 = 6.55
3. Multiplying Decimals
When multiplying, you do not need to align the decimal points. Multiply the numbers as if they were whole numbers, then count the total number of decimal places in both factors. Move the decimal point in your answer that many places to the left.
Example: 0.5 × 0.03
5 × 3 = 15. Total decimal places: 1 (in 0.5) + 2 (in 0.03) = 3.
Result: 0.015
4. Dividing Decimals
To divide by a decimal, move the decimal point in the divisor to the right until it is a whole number. Move the decimal point in the dividend the same number of places. Then divide as usual.
Decimal Conversion Table
Fraction
Decimal
Percentage
1/2
0.5
50%
1/4
0.25
25%
3/4
0.75
75%
1/10
0.1
10%
1/5
0.2
20%
Common Practical Examples
Example 1 (Shopping): If a shirt costs 19.99 and you buy 3 of them, you multiply: 19.99 × 3 = 59.97.
Example 2 (Fuel Efficiency): If you drive 150.5 miles on 5.2 gallons of gas, you divide to find miles per gallon: 150.5 ÷ 5.2 ≈ 28.94 MPG.
function calculateDecimals() {
var valA = document.getElementById("valA").value;
var valB = document.getElementById("valB").value;
var op = document.getElementById("operation").value;
var resultDisplay = document.getElementById("decimal-result");
var resultArea = document.getElementById("decimal-result-area");
if (valA === "" || valB === "") {
alert("Please enter both numbers.");
return;
}
var numA = parseFloat(valA);
var numB = parseFloat(valB);
var result = 0;
if (isNaN(numA) || isNaN(numB)) {
alert("Please enter valid numerical values.");
return;
}
switch (op) {
case "add":
result = numA + numB;
break;
case "subtract":
result = numA – numB;
break;
case "multiply":
result = numA * numB;
break;
case "divide":
if (numB === 0) {
alert("Cannot divide by zero.");
return;
}
result = numA / numB;
break;
default:
result = 0;
}
// Fix floating point precision issues (e.g. 0.1 + 0.2)
// We round to a high precision and then strip trailing zeros
var formattedResult = parseFloat(result.toFixed(10));
resultDisplay.innerHTML = formattedResult;
resultArea.style.display = "block";
}