Understanding decimals as fractions is an important concept in math. 0.95 represents a decimal value that can be simplified and expressed as a fraction in simplest form. This allows us to see 0.95 in relation to 1 whole unit. Converting 0.95 to a fraction and simplifying it helps develop a deeper understanding of fractions and decimal values.
Understanding 0.95 as a Fraction
To start, 0.95 represents a decimal number with a value of 95/100. This is because the digit 9 is in the tenth place and the digit 5 is in the hundredth place. The easiest way to convert 0.95 to a fraction is to simply express it as 95/100.
However, this fraction is not in its simplest form. To simplify, we look for the greatest common factor (GCF) between 95 and 100. The GCF of 95 and 100 is 5.
When we divide both the numerator and denominator of a fraction by the GCF, we arrive at an equivalent fraction in simplest form.
Dividing 95 and 100 by the GCF of 5 gives us:
95/100 = 19/20
Therefore, 0.95 simplified as a fraction in simplest form is 19/20.
To summarize the process:
- Express the decimal as a fraction with the appropriate denominator. For 0.95, the fraction is 95/100.
- Find the GCF between the numerator and denominator. For 95/100, the GCF is 5.
- Divide both the numerator and denominator by the GCF. 95/5 = 19 and 100/5 = 20.
- The resulting fraction is the simplest form. For 0.95, the simplified fraction is 19/20.
Understanding how to simplify fractions is an important skill. Let’s look at some key steps and concepts:
Identifying the Greatest Common Factor
The key to simplifying fractions is identifying the GCF between the numerator and denominator. The GCF is the largest number that divides both the numerator and denominator.
To find the GCF:
- Break down the numerator and denominator into prime factors.
- The GCF will be the product of the common prime factors between the numerator and denominator.
For example, to simplify 36/60:
- Prime factors of 36 = 2 x 2 x 3 x 3
- Prime factors of 60 = 2 x 2 x 3 x 5
- The GCF is 2 x 2 x 3 = 12
Dividing the Numerator and Denominator
Once we’ve identified the GCF, we divide both the numerator and denominator by that number:
For the fraction 36/60:
- GCF is 12
- Divide the numerator by 12: 36/12 = 3
- Divide the denominator by 12: 60/12 = 5
- The simplified fraction is 3/5
Simplifying fractions helps reduce them tothe lowest terms. This makes the values easier to work with in calculations and comparisons. Understanding how to convert decimal values like 0.95 to fractions and simplify them is an important math skill.