Exploring 0.6875 as a Fraction: Examples, Solutions, and FAQs
- Author: Noreen Niazi
- Last Updated on: December 19, 2023
Because they represent a portion or division of a whole, fractions are a crucial component of mathematics. They are utilized in many facets of daily life, including percentage calculations and cookery instructions. In this article, we will examine the fractional representation of a particular decimal, 0.6875. We’ll give multiple illustrations, thorough solutions, and responses to frequently asked problems about this mathematical idea.
Understanding 0.6875 as a Decimal
Let’s first examine what 0.6875 signifies as a decimal before converting it to a fraction. The decimal point is followed by the figures 6, 8, 7, 5, and the phrase “six hundred eighty-seven and five thousandths” to represent the number 0.6875. You must express this decimal in a way that demonstrates its fractional equivalent in order to convert it to a fraction.
Expressing 0.6875 as a Fraction
You can do the following operations to convert a decimal to a fraction:
Find the place value of the digit that comes after the decimal point. It is in the thousandths place in this instance.
With the same value as the decimal number, represent the decimal as a fraction. Depending on the place value of the last digit, the denominator will be a power of 10.
If required, simplify the fraction.
Let’s apply these procedures to find 0.6875 as a Fraction.
Example 1: Converting 0.6875 as a Fraction
The final digit is in the thousandths place, so please indicate the place value.
Put the decimal in fraction form:
$$0.6875 = \frac{6875}{10000}$$
If you can, make the fraction simpler. Both the numerator and the denominator in this situation are divisible by 125:
$$\frac{6875} {125} =55$$
$$\frac{10000}{125} = 80$$
The simple fraction is as follows:
$$\frac{55}{80}$$
Now that we have successfully reduced 0.6875 as a Fraction, 55/80, we can go on.
Example 2: Simplifying the Fraction
It’s crucial to remember that fractions can frequently be made even simpler. By determining the greatest common divisor (GCD) of the numerator and denominator, which is 5 in the previous example, 55/80 can be made simpler:
$$\frac{\frac{55}{5}} {\frac{80}{5}} = \frac{11}{16}$$
$$\frac{55}{80}$$ is therefore reduced to $$\frac{11}{16}$$. This is the fraction that represents $$0.6875$$ in its most basic form.
Example 3: Converting to a Mixed Number
In some cases, you may prefer to express the fraction as a mixed number. To do this, you divide the numerator by the denominator to find the whole number part and the remainder becomes the numerator of the fractional part. Here’s how you can convert 11/16 to a mixed number:
- Divide the numerator (11) by the denominator (16):
- $$\frac{11} {16} = 0$$ with a remainder of 11
- Write the whole number part (0) and the remainder (11) as the numerator of the fractional part over the denominator:
- $$0\frac{11}{16}$$
So, $$\frac{11}{16}$$ as a mixed number is $$0 \frac{11}{16}$$.
So 0.6875 as a Fraction is equal to $$\frac{11}{16}$$..
Read more about decimal and fractions
Converting Mixed Numbers to Improper Fractions: A Step-by-Step Guide
6. FAQs About Percentages
Let’s address some common questions related to fractions and the conversion of decimals to fractions.
Q1: Why is it important to convert decimals to fractions?
A1: The ability to represent decimal values as rational numbers makes the conversion of decimals to fractions crucial. In mathematical computations, fractions are frequently simpler to use and offer a clearer grasp of the relationship between various quantities.
Q2: Are there decimals that cannot be exactly expressed as fractions?
A2: Certain decimals cannot be precisely translated into fractions. For instance, it is impossible to precisely represent (pi) as a fraction since its decimal expansion has an infinite and non-repeating pattern. Irrational numbers are what these decimals are known as.
Q3: How can I convert other decimals into fractions?
A3: Use the procedures outlined before in this article to turn other decimals into fractions. Determine the place value, represent the decimal as a fraction, and, if necessary, simplify it. For every decimal, follow these instructions.
Q4: Can fractions be simplified further than the examples shown here?
A4: Yes, fractions may frequently be made even simpler by determining their greatest common divisor (GCD). In mathematics, breaking down fractions into their simplest forms is an effective technique.
Q5: What is the significance of mixed numbers?
A5: Mixed numbers come in handy when you need to represent a value as both a whole number and a fraction in the actual world. For instance, you might need to measure ingredients in recipes using mixed amounts.
Q6: Are there shortcuts or tricks for converting decimals to fractions?
A6: The method described in this blog is applicable to all decimals, even though there are some shortcuts for simple decimals. Finding the place value and writing the decimal as a fraction over the right power of 10 are the critical steps.
Conclusion
Percentage comprehension is a fundamental mathematical skill that is essential to everyday life. Remembering that percentages are fractions of 100 will help you solve problems involving percentages, such as “What percentage is 15 of 60?” You can quickly compute percentages and use this information in a variety of situations by using the percentage formula.