Decimal Calculator: Rounding & Conversions

This comprehensive tool helps you manipulate decimal numbers by performing essential functions: **rounding**, **conversion to fraction**, and **conversion to percentage**. Enter your number and select your rounding preference below.

Understanding Decimals and the Rounding Rule

A decimal number is used to represent a non-whole number, where the digits to the right of the decimal point represent fractions with denominators of 10, 100, 1000, and so on (tenths, hundredths, thousandths).

The Standard Rounding Rule (Half-Up)

The universal rule for rounding is often called "round half up." To round a number to a specific decimal place:

1. Identify the Target Digit: This is the last digit you want to keep.
2. Look Right: Look at the digit immediately to its right (the next digit).
3. Apply the Rule:
   • If the next digit is $\mathbf{5}$ or greater, increase the target digit by one (round up).
   • If the next digit is $\mathbf{4}$ or less, keep the target digit as it is (round down or 'floor').

Example: Round 4.736 to the nearest hundredth (2 decimal places). The target digit is 3. The next digit is 6. Since 6 is $\geq 5$, you round the 3 up to 4. The result is 4.74.

Decimal Conversions

Decimal to Percentage

Converting a decimal to a percentage is straightforward: you multiply the decimal by 100 and add the percent symbol (%). This is mathematically equivalent to moving the decimal point two places to the right.

Example: $0.25 = 0.25 \times 100 = 25\%$

Decimal to Fraction

To convert a decimal to a fraction, the key is to determine the place value of the last digit. This determines the denominator (e.g., tenths = 10, hundredths = 100, thousandths = 1000).

1. Write the non-whole number part as the numerator.
2. Write the corresponding power of ten as the denominator.
3. Simplify the fraction using the Greatest Common Divisor (GCD).

Example: $0.125$. The last digit (5) is in the thousandths place. So, $\frac{125}{1000}$. Dividing both by the GCD (125) gives $\frac{1}{8}$.

Frequently Asked Questions (FAQ)