The decimal 4.64 as a fraction is approximately 116/25.
To convert 4.64 into a fraction, we recognize it as 4.64 = 464/100, then simplify by dividing numerator and denominator by their greatest common divisor, which is 4, resulting in 116/25. This process makes it easier to work with the number in fractional form, especially for calculations or comparisons.
Conversion of 4.64 Decimal to Fraction
Result in fraction:
Conversion Formula
The conversion from decimal to fraction is based on expressing the decimal as a ratio of two integers. The formula involves multiplying the decimal number by a power of 10 equal to the number of decimal places, then simplifying the resulting fraction by dividing numerator and denominator by their GCD. For example, 4.64 multiplied by 100 gives 464, which over 100, then simplified to 116/25, represents the decimal precisely.
Conversion Example
- Convert 2.75 to a fraction:
- Step 1: Write as 2.75 = 275/100
- Step 2: Find GCD of 275 and 100, which is 25
- Step 3: Divide numerator and denominator by 25: 275/25 = 11, 100/25 = 4
- Result: 11/4
- Convert 0.125 to a fraction:
- Step 1: 0.125 = 125/1000
- Step 2: GCD of 125 and 1000 is 125
- Step 3: Divide numerator and denominator by 125: 125/125 = 1, 1000/125 = 8
- Result: 1/8
Conversion Chart
| Decimal | Fraction |
|---|---|
| -20.4 | -102/5 |
| -19.8 | -99/5 |
| -15.6 | -78/5 |
| -10.2 | -51/5 |
| -5.4 | -27/5 |
| 0 | 0 |
| 4.64 | 116/25 |
| 10.2 | 51/5 |
| 15.6 | 78/5 |
| 20.4 | 102/5 |
| 29.6 | 148/5 |
This chart helps to quickly find decimal values and their fractional equivalents, aiding in quick conversions or comparisons across a range of numbers. You can scan down the list to see how different decimals translate into fractions.
Related Conversion Questions
- How do I convert 4.64 to a simplified fraction?
- What is the fractional form of 4.64 with the least common denominator?
- Can 4.64 be expressed as a mixed number or improper fraction?
- What are the steps to convert 4.64 decimal to a fraction manually?
- Is 116/25 the only fraction representation for 4.64?
- How accurate is the fraction 116/25 for 4.64?
Conversion Definitions
A decimal is a number expressed using a decimal point to separate the whole part from the fractional part, representing parts of a whole based on powers of ten. A fraction is a ratio of two integers, indicating how many parts of a whole are being considered, often simplified for clarity.
Conversion FAQs
Can I convert 4.64 into a mixed number?
Since 4.64 is greater than 1, it can be expressed as a mixed number like 4 16/25, where 4 is the whole number, and 16/25 is the fractional part after converting 0.64 into a fraction.
Why do some decimals have repeating fractions?
Decimals with repeating patterns, like 0.333…, can be expressed as fractions because the repeating part can be modeled with a geometric series, allowing a precise fractional representation that captures the repeating nature accurately.
What is the importance of simplifying fractions after conversion?
Simplifying fractions reduces the numerator and denominator to their smallest whole numbers, making the fraction easier to interpret, compare, and use in calculations, avoiding unnecessary complexity or misinterpretation of the value.
How do I convert a decimal to a fraction if it has many decimal places?
Multiply the decimal by a power of ten corresponding to the number of decimal places, then simplify the resulting fraction by dividing numerator and denominator by their GCD. For long decimals, this process can be automated or done with calculator assistance.
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