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When it comes to understanding fractions, many people find themselves puzzled by decimals. One such decimal that often raises questions is .625. In this article, we will delve into the world of fractions and explore how to express .625 as a fraction. We will also discuss the concept of simplifying fractions and provide valuable insights to help you grasp this topic with ease.
Understanding Decimals and Fractions
Before we dive into the specifics of .625 as a fraction, let’s first establish a clear understanding of decimals and fractions.
A decimal is a way of representing numbers that are not whole. It consists of a decimal point followed by digits that can extend infinitely to the right. Decimals are often used to express parts of a whole or to represent values between whole numbers.
On the other hand, a fraction represents a part of a whole or a ratio between two numbers. It consists of a numerator (the number above the line) and a denominator (the number below the line). Fractions can be proper (where the numerator is smaller than the denominator), improper (where the numerator is greater than or equal to the denominator), or mixed (a whole number combined with a proper fraction).
Expressing .625 as a Fraction
Now that we have a solid foundation, let’s explore how to express .625 as a fraction. To do this, we need to convert the decimal into a fraction form.
To convert a decimal to a fraction, we can follow these steps:
- Identify the place value of the last digit in the decimal. In this case, the last digit is 5, which is in the thousandths place.
- Write the decimal as a fraction with the decimal place value as the denominator. In this case, we have .625 as 625/1000.
- Simplify the fraction, if possible, by dividing both the numerator and denominator by their greatest common divisor. In this case, the greatest common divisor of 625 and 1000 is 125. Dividing both numbers by 125 gives us 5/8.
Therefore, .625 can be expressed as the fraction 5/8.
Simplifying Fractions
Now that we have successfully expressed .625 as a fraction, let’s explore the concept of simplifying fractions. Simplifying a fraction means expressing it in its simplest form by dividing both the numerator and denominator by their greatest common divisor.
To simplify a fraction, follow these steps:
- Find the greatest common divisor (GCD) of the numerator and denominator.
- Divide both the numerator and denominator by their GCD.
- If the GCD is 1, the fraction is already in its simplest form.
Let’s take the fraction 5/8 as an example:
- The GCD of 5 and 8 is 1.
- Dividing both 5 and 8 by 1 gives us the same fraction, 5/8.
Since the GCD is 1, we can conclude that 5/8 is already in its simplest form.
Examples of .625 as a Fraction
To further solidify our understanding, let’s explore a few more examples of expressing .625 as a fraction:
- .625 = 625/1000 = 5/8
- .6250 = 6250/10000 = 5/8
- .0625 = 625/10000 = 1/16
- .00625 = 625/100000 = 1/160
As you can see, regardless of the number of decimal places, .625 can always be expressed as the fraction 5/8. This demonstrates the consistency and predictability of converting decimals to fractions.
Q&A
1. Can .625 be expressed as a mixed number?
No, .625 cannot be expressed as a mixed number because it is already a proper fraction. Mixed numbers consist of a whole number combined with a proper fraction.
2. How can I check if a fraction is simplified?
To check if a fraction is simplified, find the greatest common divisor (GCD) of the numerator and denominator. If the GCD is 1, the fraction is already in its simplest form.
3. Can .625 be expressed as a percentage?
Yes, .625 can be expressed as a percentage by multiplying it by 100. Therefore, .625 is equal to 62.5%.
4. Is .625 a terminating or repeating decimal?
.625 is a terminating decimal because it ends after the third decimal place. Terminating decimals have a finite number of digits after the decimal point.
5. How can I convert a fraction to a decimal?
To convert a fraction to a decimal, divide the numerator by the denominator. For example, to convert 5/8 to a decimal, divide 5 by 8, which equals 0.625.
Summary
In conclusion, understanding and expressing .625 as a fraction is a straightforward process. By following the steps outlined in this article, you can convert .625 into the fraction 5/8. Additionally, we explored the concept of simplifying fractions and learned that 5/8 is already in its simplest form. Remember, decimals can always be converted to fractions, providing a clear and concise representation of their value. By mastering this skill, you will enhance your mathematical abilities and gain a deeper understanding of numbers.
