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convert-fractions-to-decimals-and-vice-versa-accurately

🚀 Fractions and decimals are two ways of representing numbers that are not whole. A fraction consists of a numerator (the top part) and a denominator (the bottom part), while a decimal uses a point to separate the whole number from the fractional part. Understanding how to convert between fractions and decimals is essential in mathematics, as it allows us to work with numbers in different forms depending on the context. This concept is particularly useful in measurements, money, and various calculations.

Theory Explanation

Understanding Fractions

A fraction represents a part of a whole. The numerator indicates how many parts we have, while the denominator shows how many equal parts the whole is divided into. For example, in the fraction 3/4, 3 is the numerator and 4 is the denominator, meaning we have 3 out of 4 equal parts.

\[ \frac{3}{4} \]
Understanding Decimals

A decimal is another way to represent fractions, especially those with denominators of 10, 100, 1000, etc. For example, the fraction 1/10 can be written as 0.1 in decimal form. The position of the digits after the decimal point indicates the value of each digit based on powers of ten.

\[ 0.1 \]
Converting Fractions to Decimals

To convert a fraction to a decimal, divide the numerator by the denominator. For example, to convert 1/4 to a decimal, you would calculate 1 ÷ 4, which equals 0.25.

\[ \frac{1}{4} = 1 \div 4 = 0.25 \]
Converting Decimals to Fractions

To convert a decimal to a fraction, write the decimal as a fraction with a denominator of 1, and then multiply the numerator and denominator by 10 for each digit after the decimal point. For example, to convert 0.75 to a fraction, write it as 75/100 and simplify it to 3/4.

\[ 0.75 = \frac{75}{100} = \frac{3}{4} \]

Key Points

  • 🎯 Fractions consist of a numerator and a denominator.
  • 🎯 Decimals represent fractions using a point to separate whole numbers from parts.
  • 🎯 To convert a fraction to a decimal, divide the numerator by the denominator.
  • 🎯 To convert a decimal to a fraction, express it over a power of ten and simplify.
  • 🎯 Understanding both forms helps in various mathematical applications.

Examples:💡

Convert the fraction 2/5 to a decimal.

Solution:

Step 1: Divide the numerator (2) by the denominator (5).

\[ 2 \div 5 = 0.4 \]

Step 2: The decimal equivalent of 2/5 is 0.4.

Convert the decimal 0.6 to a fraction.

Solution:

Step 1: Write 0.6 as 6/10 because there is one digit after the decimal point.

\[ 0.6 = \frac{6}{10} \]

Step 2: Simplify the fraction by dividing both the numerator and denominator by 2.

\[ \frac{6 \div 2}{10 \div 2} = \frac{3}{5} \]

Common Mistakes

  • Mistake: Confusing the numerator and denominator when converting fractions to decimals.

    Correction: Always remember that the numerator is the number of parts you have, and the denominator is the total number of equal parts.

  • Mistake: Not simplifying the fraction after converting a decimal to a fraction.

    Correction: Always check if the fraction can be simplified by finding the greatest common divisor.

  • Mistake: Forgetting to place the decimal point correctly when converting fractions to decimals.

    Correction: Use long division carefully to ensure the decimal point is placed correctly in the result.

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