The decimal 4.64 converts to the fraction 116/25. This is because 4.64 equals 4 + 0.64, representing a fraction where 64 is over 100, simplifying to 16/25, and combining with 4 gives 116/25.
To convert 4.64 to a fraction, first multiply it by 100 to eliminate decimal places, obtaining 464 over 100. Then simplify by dividing numerator and denominator by their greatest common divisor, which is 16, resulting in 116/25. This process ensures an exact fractional form of the decimal number.
Conversion Result
4.64 decimal is equivalent to the fraction 116/25.
Conversion Tool
Result in fraction:
Conversion Formula
The conversion formula involves taking the decimal number, multiplying it by a power of 10 based on decimal places, then dividing by the same power of 10. Simplifying the fraction reduces it to its lowest terms.
For 4.64, multiply by 100 (since two decimal places): 4.64 × 100 = 464. Then, place over 100: 464/100. Simplify by dividing numerator and denominator by their greatest common divisor, which is 16, resulting in 29/25. But since 4.64 is exactly 116/25, dividing numerator and denominator by 4 gives 29/5, which is incorrect because the previous step shows 464/100 simplifies to 29/5. The proper step is to find the GCD of 464 and 100, which is 16, giving 29/25.
Conversion Example
- Convert 2.75 to fraction:
- Multiply by 100: 2.75 × 100 = 275
- Place over 100: 275/100
- Simplify by dividing numerator and denominator by 25: 11/4
- Convert 0.5 to fraction:
- Multiply by 10: 0.5 × 10 = 5
- Place over 10: 5/10
- Simplify by dividing numerator and denominator by 5: 1/2
- Convert 3.125:
- Multiply by 1000: 3.125 × 1000 = 3125
- Place over 1000: 3125/1000
- Simplify by dividing numerator and denominator by 125: 25/8
Conversion Chart
| Decimal | Fraction |
|---|---|
| -20.4 | -102/5 |
| -15.8 | -79/5 |
| -10.6 | -53/5 |
| -5.2 | -26/5 |
| 0 | 0/1 |
| 4.64 | 116/25 |
| 10.2 | 51/5 |
| 15.8 | 79/5 |
| 20.4 | 102/5 |
| 29.6 | 148/5 |
This chart allows you to quickly see decimal numbers and their exact fractional equivalents. To use, find your decimal in the left column and read across to see its fractional form, simplifying if necessary.
Related Conversion Questions
- How can I convert 4.64 to a mixed number instead of a fraction?
- What is the simplified form of 4.64 as a fraction?
- Can I convert 4.64 to a percentage and then to a fraction?
- How do I convert repeating decimals like 4.64 to fractions?
- What is the best way to convert decimal 4.64 to a fraction manually?
- Is 116/25 the only fraction equivalent to 4.64?
Conversion Definitions
Decimal
A decimal is a number expressed in the base-10 positional numeral system, using a decimal point to separate the whole part from the fractional part, representing parts of a whole with digits after the point.
Fraction
A fraction is a mathematical expression representing a part of a whole, written as two numbers separated by a slash, where the numerator indicates parts and the denominator indicates total parts of a division.
Conversion FAQs
How do I ensure the fraction I get from 4.64 is in lowest terms?
To reduce a fraction to its lowest terms, find the greatest common divisor (GCD) of numerator and denominator, then divide both by this number. For 116/25, since 116 and 25 share no common divisors other than 1, it’s already simplified.
What if my decimal has more than two decimal places?
For decimals with more places, multiply by 10 raised to the number of decimal digits to convert to an integer, then divide by the same power of 10. Simplify by finding the GCD to get the fraction in lowest terms.
Can I convert negative decimals to fractions using this method?
Yes, simply treat the negative sign as part of the numerator or denominator during conversion. The process remains the same, and the negative sign indicates the fraction’s direction on the number line.
Is there a difference between converting 4.64 and 4.6400?
Both represent the same value, but 4.6400 has more decimal places, which may affect the conversion process slightly. In both cases, the fraction simplifies to 116/25, as trailing zeros don’t change the value.
What tools can help me convert decimals to fractions quickly?
Online calculators, scientific calculators with fraction functions, and programming scripts can quickly convert decimals to fractions, especially for complex or repeating decimals, saving time and ensuring accuracy.
