The decimal 4.64 converts to the fraction 464/100, which simplifies to 116/25.
This means that the decimal 4.64 can be expressed as a ratio of two integers, 116 over 25. The process involves removing the decimal point by multiplying numerator and denominator by 100, then simplifying the resulting fraction to its lowest terms.
Conversion
Result in fraction:
Conversion Formula
The formula to convert a decimal to a fraction involves multiplying the decimal by a power of ten, based on the number of decimal places, then simplifying the resulting fraction. For 4.64, since there are two decimal digits, multiply by 100:
- Numerator = decimal × 10number of decimal places = 4.64 × 100 = 464
- Denominator = 10number of decimal places = 100
Resulting fraction: 464/100. Simplify by dividing both numerator and denominator by their GCD, which is 4, resulting in 116/25.
Conversion Example
- Convert 2.75 to a fraction:
- Multiply by 100 (since two decimal places): 2.75 × 100 = 275
- Write as 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 0.5 to a fraction:
- Multiply by 10: 0.5 × 10 = 5
- Write as 5/10
- GCD of 5 and 10 is 5
- Divide both by 5: 5 ÷ 5 = 1, 10 ÷ 5 = 2
- Simplified fraction: 1/2
Conversion Chart
| Decimal | Fraction |
|---|---|
| -20.4 | -102/5 |
| -19.8 | -99/5 |
| -15.2 | -76/5 |
| -10.6 | -53/5 |
| -6.0 | -3/1 |
| -1.4 | -7/5 |
| 0 | 0/1 |
| 4.64 | 116/25 |
| 10.2 | 51/5 |
| 15.6 | 78/5 |
| 20.0 | 20/1 |
| 25.4 | 127/5 |
| 29.6 | 148/5 |
This chart helps to quickly find the fraction equivalent of any decimal within the range, making conversions faster and easier to reference.
Related Conversion Questions
- How do I convert 4.64 to a mixed number?
- What is the simplest form of 4.64 as a fraction?
- Can 4.64 be written as a percentage?
- How to convert 4.64 into a ratio?
- What is the decimal equivalent of 116/25?
- How do I convert 4.64 to a percentage?
- Is 4.64 a terminating or repeating decimal?
Conversion Definitions
Decimal
A decimal is a number expressed using a decimal point to separate the whole number part from the fractional part, representing values less than one in fractional form, and is based on powers of ten.
Fraction
A fraction is a way of representing parts of a whole with two integers, numerator over denominator, showing how many parts are considered out of a total number, often simplified to its lowest terms for clarity and ease of use.
Conversion FAQs
How do I convert 4.64 to a simplified fraction?
First, multiply 4.64 by 100 to remove decimal places, obtaining 464/100. Then, find the GCD of 464 and 100, which is 4. Divide numerator and denominator by 4, resulting in 116/25. This is the simplified form.
Why is 4.64 written as 116/25 in lowest terms?
Because 116 and 25 share no common divisors other than 1, and dividing both by their GCD, 4, results in the fraction 116/25, which cannot be simplified further, making it in lowest terms.
Can I convert 4.64 to a mixed number?
Since 4.64 is not a whole number, but its fractional form is 116/25, which is an improper fraction, it can be converted to a mixed number by dividing numerator by denominator: 116 ÷ 25 = 4 with a remainder of 16, so it becomes 4 16/25.
Is 4.64 a terminating decimal?
Yes, because it has a finite number of decimal places (two), representing a terminating decimal, which can be exactly expressed as a fraction with a denominator that is a power of 10, such as 116/25.
What are the common mistakes when converting decimals to fractions?
Common errors include forgetting to simplify the fraction, not multiplying enough to clear the decimal point, or using incorrect GCD calculations, leading to fractions that are not in lowest terms or inaccurate conversions.