.46 Rounded To A Fraction In Simplest Form Explained
Table of Contents :
To express the decimal 0.46 as a fraction in simplest form, we follow a systematic process that ensures clarity and comprehension. Understanding how to convert decimals to fractions is a valuable skill that can be applied in various mathematical contexts. Let's delve into the process step by step.
Understanding the Decimal
A decimal is a way of expressing a number that is not whole. In our case, 0.46 indicates a value that is less than 1. It can also be read as "46 hundredths" because the decimal extends to the hundredths place.
Writing the Decimal as a Fraction
To convert the decimal to a fraction, we can express 0.46 as follows:
[ 0.46 = \frac{46}{100} ]
Breaking Down the Conversion
Here's a more detailed look at how we arrived at this fraction:
- Identify the Decimal Place: The last digit (6) is in the hundredths place.
- Set Up the Fraction: Write the number without the decimal (46) over a power of ten corresponding to the decimal place (100).
This gives us the fraction:
[ \frac{46}{100} ]
Simplifying the Fraction
Now that we have our fraction, the next step is to simplify it. Simplification involves reducing the fraction to its lowest terms. To do this, we need to find the greatest common divisor (GCD) of the numerator and denominator.
Finding the GCD
- The factors of 46 are: 1, 2, 23, 46.
- The factors of 100 are: 1, 2, 4, 5, 10, 20, 25, 50, 100.
The largest common factor is 2.
Dividing by the GCD
Now, we divide both the numerator and denominator by their GCD:
[ \frac{46 \div 2}{100 \div 2} = \frac{23}{50} ]
Thus, 0.46 expressed as a fraction in simplest form is:
[ \frac{23}{50} ]
Summary of the Steps
To recap, here are the steps taken to convert 0.46 to a fraction in simplest form:
- Write the decimal as a fraction: (\frac{46}{100}).
- Find the GCD of the numerator and denominator (which is 2).
- Divide the numerator and denominator by the GCD: (\frac{46 \div 2}{100 \div 2} = \frac{23}{50}).
Conclusion
Understanding how to convert decimals to fractions is essential in mathematics. Through clear steps, we see that 0.46 simplifies neatly to (\frac{23}{50}). This process can be applied to any decimal, enhancing your mathematical skills and confidence in working with fractions. By practicing these conversions, you'll find that turning decimals into fractions becomes second nature. 😊