Understanding fractions is a fundamental concept in mathematics, and being able to convert numbers between different formats, such as converting a decimal to a fraction, is a crucial skill. The number 5.635, when considered as a decimal, can be converted into a fraction using a few straightforward steps. This process involves placing the decimal part over the place value of the last digit, which, in the case of 5.635, would be the thousandths place, or 1/1000.
Conversion Process
To convert 5.635 into a fraction, we start by separating the whole number from the decimal part. The whole number part is 5, and the decimal part is 0.635. The decimal part, 0.635, can be written directly as 635⁄1000 because there are three digits after the decimal point, indicating thousandths.
Simplifying the Fraction
After converting 0.635 to 635⁄1000, the next step is to simplify this fraction if possible. To simplify a fraction, we divide both the numerator and the denominator by their greatest common divisor (GCD). In the case of 635 and 1000, we need to find the GCD of these two numbers to simplify the fraction.
| Step | Explanation |
|---|---|
| 1 | Identify the numerator and the denominator: 635 and 1000. |
| 2 | Find the greatest common divisor (GCD) of 635 and 1000. |
| 3 | Divide both the numerator and the denominator by the GCD to simplify the fraction. |
Upon examination, the GCD of 635 and 1000 is 5, as 5 is the largest number that can divide both 635 and 1000 without leaving a remainder. Dividing both 635 and 1000 by 5 gives us 127/200. Therefore, the simplified fraction of 5.635 is 5 127/200, combining the whole number part with the simplified fraction.
Practical Applications
The conversion of decimals to fractions, as seen with 5.635, has numerous practical applications. In measurement, fractions are often more intuitive for certain types of calculations, such as determining lengths or quantities of ingredients in cooking. Additionally, in financial calculations, understanding how to work with fractions can be crucial for determining percentages and interest rates accurately.
Key Points
- Converting decimals to fractions involves placing the decimal part over its place value.
- Simplifying fractions requires finding and dividing both the numerator and the denominator by their greatest common divisor.
- The practical applications of converting decimals to fractions include measurement, financial calculations, and problem-solving in various fields.
- Understanding fractions and decimals enhances mathematical fluency and problem-solving skills.
- The GCD of 635 and 1000 is 5, simplifying 635/1000 to 127/200.
In conclusion, converting 5.635 to a fraction and simplifying it to 5 127/200 demonstrates a basic yet crucial mathematical skill. This process, and the understanding of fractions in general, underpins a wide range of mathematical and real-world applications, making it an essential part of any mathematical education.
What is the first step in converting a decimal to a fraction?
+The first step is to identify the decimal part and place it over its corresponding place value, such as tenths, hundredths, or thousandths, depending on the number of digits after the decimal point.
How do you simplify a fraction?
+To simplify a fraction, you divide both the numerator and the denominator by their greatest common divisor (GCD). This reduces the fraction to its simplest form while maintaining its value.
What are some practical applications of converting decimals to fractions?
+Practical applications include measurement in construction or cooking, financial calculations for percentages and interest rates, and enhancing mathematical fluency for problem-solving in science, engineering, and finance.
