Our fraction to decimal calculator is a tool that converts fractions into their decimal equivalents using Decimal = Numerator ÷ Denominator formula.
let’s consider the fraction 3/4:
- Input: 3/4
- Output: 0.75
The calculator performs the division of the numerator by the denominator to provide the decimal result.
Fraction to Decimal Calculator
| Fraction Converted to | Decimal | Explanation |
|---|---|---|
| 1/4 | 0.25 | 1 ÷ 4 = 0.25 |
| 2/5 | 0.4 | 2 ÷ 5 = 0.4 |
| 3/8 | 0.375 | 3 ÷ 8 = 0.375 |
| 5/6 | 0.833… | 5 ÷ 6 = 0.833… (rounded to 3 decimal places) |
| 7/3 | 2.333… | 7 ÷ 3 = 2.333… (mixed number: 2 1/3) |
| 11/4 | 2.75 | 11 ÷ 4 = 2.75 (mixed number: 2 3/4) |
| 1/7 | 0.142… | 1 ÷ 7 = 0.142857… (recurring decimal) |
| 9/16 | 0.5625 | 9 ÷ 16 = 0.5625 |
| 1/10 | 0.1 | 1 ÷ 10 = 0.1 |
| 3/10 | 0.3 | 3 ÷ 10 = 0.3 |
| 7/10 | 0.7 | 7 ÷ 10 = 0.7 |
| 1/12 | 0.083… | 1 ÷ 12 = 0.083333… (repeating 3) |
| 5/12 | 0.416… | 5 ÷ 12 = 0.416666… (repeating 6) |
| 7/12 | 0.583… | 7 ÷ 12 = 0.583333… (repeating 3) |
| 11/12 | 0.916… | 11 ÷ 12 = 0.916666… (repeating 6) |
| 1/16 | 0.0625 | 1 ÷ 16 = 0.0625 |
| 3/16 | 0.1875 | 3 ÷ 16 = 0.1875 |
| 5/16 | 0.3125 | 5 ÷ 16 = 0.3125 |
| 7/16 | 0.4375 | 7 ÷ 16 = 0.4375 |
| 9/16 | 0.5625 | 9 ÷ 16 = 0.5625 |
| 11/16 | 0.6875 | 11 ÷ 16 = 0.6875 |
| 13/16 | 0.8125 | 13 ÷ 16 = 0.8125 |
| 15/16 | 0.9375 | 15 ÷ 16 = 0.9375 |
| 7/20 | 0.35 | 7 ÷ 20 = 0.35 |
| 9/20 | 0.45 | 9 ÷ 20 = 0.45 |
| 3/20 | 0.15 | 3 ÷ 20 = 0.15 |
| 1/16 | 0.0625 | 1 ÷ 16 = 0.0625 |
| 1/2 | 0.5 | 1 ÷ 2 = 0.5 |
| 5/12 | 0.416… | 5 ÷ 12 = 0.416666… (repeating 6) |
| 11000/1 | 11000 | 11000 ÷ 1 = 11000 |
These additional examples demonstrate:
- Fractions with denominators that are powers of 10 (1/10, 3/10, 7/10)
- Fractions with denominators that result in recurring decimals (1/12, 5/12, 7/12, 11/12)
- Fractions with denominators that are powers of 2 (1/16, 3/16, 5/16, …, 15/16)
- Fractions with denominators that are not powers of 2 or 10 (7/20, 9/20, 3/20)
- Unit fraction (1/2)
- Improper fraction (11000/1)
Fraction to Decimal Chart
| Fraction Change to | Decimal |
|---|---|
| 1/2 | 0.5 |
| 1/3 | 0.333… |
| 1/4 | 0.25 |
| 2/3 | 0.666… |
| 3/4 | 0.75 |
| 1/5 | 0.2 |
| 4/5 | 0.8 |
| 1/6 | 0.166… |
| 5/6 | 0.833… |
| 1/8 | 0.125 |
| 7/8 | 0.875 |
Fraction to Decimal Conversion Formula
The formula for converting a fraction to a decimal is straightforward:
Decimal = Numerator ÷ DenominatorLet’s look at some examples:
5/8 = 5 ÷ 8 = 0.625
2/3 = 2 ÷ 3 ≈ 0.666… (recurring decimal)
7/2 = 7 ÷ 2 = 3.5
How do you convert Fraction to Decimal?
To convert a fraction a/b to a decimal, you can use the following formula: Decimal = a / b and steps.
- Identify the numerator and denominator.
- Divide the numerator by the denominator.
- Round the result if necessary (for recurring decimals).
Let’s convert 5/6 to a decimal:
- Numerator = 5, Denominator = 6
- 5 ÷ 6 = 0.833333…
- Rounded to three decimal places: 0.833
For terminating decimals, the division will end with a remainder of zero. For recurring decimals, you may need to round off or use a bar notation to indicate the repeating part.
What is a decimal and a fraction?
A fraction represents a part of a whole. It consists of two parts:
- Numerator: The number above the line, representing the number of parts.
- Denominator: The number below the line, representing the total number of equal parts in the whole.
A decimal is a way of writing fractions based on powers of ten. It uses a decimal point to separate the whole number part from the fractional part.
Key Differences:
- Fractions use two numbers (numerator and denominator), while decimals use a single number with a decimal point.
- Decimals are easier for calculations, especially with calculators or computers.
- Fractions can represent exact values for certain numbers that decimals can only approximate (e.g., 1/3).
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