Understanding 10.8 As A Fraction: Simplifying The Decimal Representation. In the world of mathematics, numbers can be expressed in various forms, including fractions, decimals, and percentages. Understanding these different representations is essential for performing calculations, solving equations, and making accurate comparisons. In this blog post, we will explore the number 10.8 and its conversion into a fraction. By comprehending how to express 10.8 as a fraction and simplify it, we can effectively work with this number in mathematical operations.
The Basics: What Is A Fraction?
Before we dive into converting 10.8 into a fraction, let’s briefly review what a fraction represents. A fraction is a numerical representation that expresses a part of a whole or a ratio between two quantities. It consists of a numerator and a denominator, separated by a horizontal line known as the fraction bar.
Converting 10.8 Into A Fraction
To convert a decimal into a fraction, it is crucial to understand the place value of the decimal. In the case of 10.8, the number is read as ten and eight tenths. The decimal point separates the whole number part from the fractional part.
To express 10.8 as a fraction, follow these steps:
Step 1: Let x be the given decimal (10.8).
Step 2: Since 10.8 has one decimal place, the denominator of the fraction will be 10 raised to the power of the number of decimal places, which is 10^1 = 10.
Step 3: Multiply both sides of the equation by the denominator: 10x = 108.
Step 4: Simplify the equation if possible. In this case, no further simplification is needed.
Step 5: Divide both sides of the equation by the denominator: x = 108 ÷ 10.
Step 6: Simplify the fraction (if necessary) to its lowest terms: x = 54/5.
Therefore, 10.8 as a fraction is 54/5.
Now that we have expressed 10.8 as a fraction (54/5), let’s simplify it further. Simplifying a fraction involves dividing both the numerator and the denominator by their greatest common divisor (GCD) to reduce the fraction to its simplest form.
In the case of 54/5, the GCD of 54 and 5 is 1. Since there are no common factors between the numerator and the denominator, the fraction 54/5 is already in its simplest form.
Converting 54/5 To A Mixed Number Or Decimal
While 54/5 is a fraction, it can also be represented as a mixed number or a decimal.
To convert 54/5 to a mixed number, divide the numerator (54) by the denominator (5). The quotient becomes the whole number part, and the remainder (if any) becomes the numerator of the fractional part. In this case, the division results in 10 and no remainder, which can be written as 10.
To convert 54/5 to a decimal, divide the numerator (54) by the denominator (5). The division yields 10.8. Hence, the decimal representation of 54/5 is 10.8.
Understanding different number representations is crucial in mathematics. By converting decimals to fractions, we can work with numbers in various contexts. In the case of 10.8, it can be expressed as 54/5. Remember that fractions can be simplified to their simplest form, and in this case, 54/5 is already simplified. By mastering these concepts, we enhance our mathematical skills and become more proficient in solving equations and analyzing numerical relationships.
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What Is 10.7 As A Fraction?
10.7 as a fraction is 107/10.
What Is 10.8 As A Decimal?
Remember This: 10.8 as a decimal is 0.108 and you can multiply 0.108 by a number to get 10.8 percent of that number.
What Is 10.9 In To A Fraction?
10.9 as a fraction is 109/10.
What Is 11.8 As A Fraction?
11.8 as a fraction is 59/5.
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