What Does .486 As A Fraction Mean?
Understanding Decimal Notation
In mathematics, decimal notation is a way to represent numbers that lie between two whole numbers. Decimals are often used to express values that are not exact whole numbers but fall within a certain range. A decimal number consists of two main parts: the whole number part and the decimal part. For instance, in the number 3.14, the whole number part is 3, and the decimal part is 0.14.
Converting Decimals to Fractions
Decimal numbers can also be expressed as fractions. To convert a decimal to a fraction, one needs to consider the place value of each digit in the decimal part. For example, let’s examine the decimal .486.
Understanding the Decimal Place Value
The number .486 can be broken down into three place values: the tenths, the hundredths, and the thousandths. The digit 4 is in the tenths place, the digit 8 is in the hundredths place, and the digit 6 is in the thousandths place. By recognizing these place values, we can convert .486 into a fraction.
Converting .486 to a Fraction
To convert decimal .486 to a fraction, we need to consider the place values mentioned earlier. The digit 4 is in the tenths place, which means it should be divided by 10. The digit 8 is in the hundredths place, so it should be divided by 100, and the digit 6 in the thousandths place should be divided by 1000.
Now, we can write the fraction as follows:
.486 = 4/10 + 8/100 + 6/1000
Simplifying the Fraction
To simplify the fraction, we can start by finding the lowest common denominator (LCD) of the three fractions. In this case, the LCD is 1000. By multiplying the numerator and denominator of each fraction by the appropriate values, we can express the decimal .486 as a simplified fraction:
4/10 + 8/100 + 6/1000 = 400/1000 + 80/1000 + 6/1000
Adding the fractions together, we have:
400/1000 + 80/1000 + 6/1000 = (400 + 80 + 6)/1000 = 486/1000
Further Simplification
To simplify the fraction 486/1000 further, we can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 2. By dividing both 486 and 1000 by 2, we get:
486 ÷ 2 / 1000 ÷ 2 = 243/500
Therefore, the decimal .486 can be expressed as the simplified fraction 243/500.
Conclusion
In conclusion, when we see the decimal .486, we know that it can be converted into the fraction 243/500. Understanding decimal notation and its corresponding fraction representation is essential in various mathematical and real-life applications. Converting decimals to fractions allows for more precise and flexible representation of values, making it easier to perform calculations and comparisons.
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