The decimal 4.68 converts to the fraction 468/100, which simplifies to 117/25. This means that 4.68 is equivalent to the fraction 117/25 after reduction.
To convert 4.68 into a fraction, multiply the decimal by 100 to remove the decimal point, giving 468 over 100. Then, find the greatest common divisor (GCD) of 468 and 100, which is 4, and divide both numerator and denominator by 4. This results in 117 over 25, the simplified fraction form.
Conversion Result
4.68 is equal to the fraction 117/25 in its simplest form.
Conversion Tool
Result in fraction:
Conversion Formula
The formula to convert a decimal to a fraction involves multiplying the decimal part by a power of 10 equal to the number of decimal places, then simplifying. For example, for 4.68, multiply 4.68 by 100 to get 468, and place it over 100. Simplify the fraction by dividing numerator and denominator by their GCD.
Mathematically, if x is your decimal, then x = numerator/denominator, where numerator = x * 10^n (n is number of decimal places), and then reduce the fraction. This works because decimals are just fractions with denominators as powers of 10.
Example: 4.68 x 100 = 468, so initial fraction is 468/100. Find GCD of 468 and 100, which is 4, then divide both by 4: 468/4=117, 100/4=25. So, 4.68 = 117/25.
Conversion Example
- Convert 2.75 to a fraction:
- Multiply 2.75 by 100 to get 275
- Initial fraction: 275/100
- Find GCD of 275 and 100, which is 25
- Divide numerator and denominator by 25: 275/25 = 11, 100/25=4
- Simplified fraction: 11/4
- Convert 0.125 to a fraction:
- Multiply 0.125 by 1000 to get 125
- Initial fraction: 125/1000
- GCD of 125 and 1000 is 125
- Divide both by 125: 125/125=1, 1000/125=8
- Result: 1/8
- Convert 3.6 to a fraction:
- Multiply 3.6 by 10 to get 36
- Initial fraction: 36/10
- GCD of 36 and 10 is 2
- Divide numerator and denominator by 2: 36/2=18, 10/2=5
- Simplified fraction: 18/5
Conversion Chart
| Decimal | Fraction |
|---|---|
| -20.3 | -203/10 |
| -19.7 | -197/10 |
| -15.5 | -31/2 |
| -10.2 | -51/5 |
| -5.8 | -29/5 |
| 0 | 0/1 |
| 4.68 | 117/25 |
| 10.5 | 21/2 |
| 15.2 | 76/5 |
| 20.7 | 207/10 |
| 25.4 | 127/5 |
| 29.7 | 297/10 |
This chart shows decimal values alongside their fractional equivalents for quick reference. To use, find your decimal in the first column and read across to see the simplified fraction, which helps in understanding the precise value.
Related Conversion Questions
- How can I convert 4.68 to a mixed number?
- What is the simplified fraction for 4.68?
- Can 4.68 be expressed as a fraction with denominator 50?
- How do I convert decimal 4.68 into a fraction step-by-step?
- What is the decimal form of the fraction 117/25?
- How to convert 4.68 to a fraction in lowest terms?
- Is 4.68 a terminating decimal or a repeating decimal?
Conversion Definitions
Decimal
A decimal is a number expressed using a base-10 system, including a decimal point to separate whole numbers from fractional parts, allowing precise representation of values, especially those that are not whole numbers.
Fraction
A fraction is a way to represent a part of a whole, written as numerator over denominator, indicating how many parts of a certain size are being considered, and can be simplified to lowest terms for clarity and ease of use.
Conversion FAQs
How do I convert 4.68 to a simplified fraction manually?
Multiply 4.68 by 100 to eliminate the decimal, resulting in 468/100. Find the GCD of 468 and 100, which is 4. Divide both numerator and denominator by 4, giving 117/25. This is the simplified form of 4.68 as a fraction.
Can I convert 4.68 to a fraction without multiplying?
Multiplying by 100 is the easiest way, but technically, you can use continued fractions or approximation methods. However, multiplying by 100 and reducing is the simplest and most accurate method for terminating decimals like 4.68.
Why does 4.68 convert to 117/25 instead of 468/100?
Because 468/100 can be simplified by dividing numerator and denominator by their GCD, which is 4, resulting in 117/25. Simplification makes the fraction easier to work with and reflects the same value in a more concise form.
Is 4.68 a rational or irrational number?
4.68 is a rational number because it can be expressed as a fraction, specifically 117/25, which means it has a finite decimal representation and can be written as a ratio of two integers.
