What is 3.14 as a Fraction?

The fraction equivalent of 3.14 is \(\frac{157}{50}\)

Step-by-Step Solution

Step 1: Identify the decimal number

We want to convert the decimal 3.14 to a fraction.

Step 2: Write as a fraction with 1 as the denominator

First, we write 3.14 as a fraction with 1 as the denominator:

\(3.14 = \frac{3.14}{1}\)

Step 3: Count the decimal places

The decimal 3.14 has 2 decimal places.

Step 4: Multiply to remove the decimal point

We multiply both the numerator and denominator by 10² to remove the decimal point:

\(\frac{3.14}{1} \times \frac{100}{100} = \frac{314}{100}\)

Step 5: Simplify the fraction

We need to simplify this fraction by dividing both numbers by their greatest common divisor (GCD).

The GCD of 314 and 100 is 2.

\(\frac{314}{100} = \frac{314 \div 2}{100 \div 2} = \frac{157}{50}\)

Step 6: Convert to a mixed number (optional)

Since the numerator is larger than the denominator, we can convert this to a mixed number:

\(\frac{157}{50} = 3\frac{7}{50}\)

Final Answer

The decimal 3.14 as a fraction is \(\frac{157}{50}\) or as a mixed number: \(3\frac{7}{50}\)

Try Another Conversion

Understanding Decimal to Fraction Conversion

What are Decimals?

Decimals are a way of writing numbers that aren't whole numbers. They use a decimal point to separate the whole number part from the fractional part. For example, in 3.14, the whole number part is 3 and the decimal part is 0.14.

Converting Decimals to Fractions

To convert a decimal to a fraction:

Write the decimal number as a fraction with 1 as the denominator
Multiply both the numerator and denominator by a power of 10 to remove the decimal point
Simplify the fraction if possible

Did You Know?

Every terminating decimal can be written as a fraction where the denominator is a power of 10 or a number that only contains the prime factors 2 and 5.