Answer: 0.4 can be written in a fraction as 4/10 or 2/5.
Understanding Decimals and Fractions
Decimals and fractions are two ways of representing numbers that are not whole. Decimals use a base-10 system, while fractions represent a part of a whole using a numerator and a denominator. Converting between these two forms is a fundamental math skill.
Step-by-Step Conversion of 0.4 to a Fraction
Step 1: Understanding the Decimal
The decimal 0.4 can be read as “four-tenths.” This gives us a clue on how to represent it as a fraction.
Step 2: Writing as a Fraction
Since 0.4 is four-tenths, we can write it directly as: 410\frac{4}{10}104
Step 3: Simplifying the Fraction
To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 4 and 10 is 2. We divide both the numerator and the denominator by their GCD:
4÷210÷2=25\frac{4 \div 2}{10 \div 2} = \frac{2}{5}10÷24÷2=52
So, 0.4 as a fraction in its simplest form is: 25\frac{2}{5}52
Verifying the Conversion
Converting the Fraction Back to a Decimal
To verify our conversion, we can convert the fraction 25\frac{2}{5}52 back to a decimal by performing the division: 2÷5=0.42 \div 5 = 0.42÷5=0.4
This confirms that our fraction 25\frac{2}{5}52 is correct.
Practical Examples
Example 1: Using 0.4 in a Real-World Context
If you have 0.4 of a pizza, you essentially have 2/5 of the pizza. This fraction can help you divide the pizza among friends or family more easily.
Example 2: Applying the Fraction in Measurements
In recipes, you might need to use 0.4 of a cup of an ingredient. Converting this to a fraction (25\frac{2}{5}52) can make it simpler to measure using standard fraction-based measuring cups.
Conclusion
Converting 0.4 to a fraction is straightforward. By understanding that 0.4 is the same as four-tenths and simplifying, we find that the fraction is 25\frac{2}{5}52. This conversion is useful in various real-life applications, from cooking to dividing quantities.
FAQs
1. What is 0.4 as a fraction?
0.4 as a fraction is 25\frac{2}{5}52.
2. How do you convert 0.4 to a fraction?
To convert 0.4 to a fraction, write it as 410\frac{4}{10}104 and then simplify it to 25\frac{2}{5}52.
3. Why is 0.4 written as 25\frac{2}{5}52 in simplest form?
0.4 is written as 25\frac{2}{5}52 in simplest form because both the numerator (4) and the denominator (10) can be divided by their greatest common divisor, which is 2.
4. Can 0.4 be represented as a different fraction?
0.4 can be represented as 410\frac{4}{10}104, but 25\frac{2}{5}52 is its simplest form. Other equivalent fractions can be found by multiplying the numerator and the denominator by the same number (e.g., 410\frac{4}{10}104, 820\frac{8}{20}208).
5. How is understanding fractions useful in real life?
Understanding fractions is useful for measuring ingredients in cooking, dividing quantities, understanding proportions, and in various fields like science, engineering, and finance.
