What is 0.0225 as a fraction?

Converting decimals to fractions can be useful in many situations. Let's go through the steps to convert a decimal 0.0225 to a fraction.

You can try other values to get more familiar with the conversion process.

Often, convert 0.02222 to a fraction or 0.023 to a fraction, depending on the task.

Understanding the decimal: “0.0225”

A decimal number consists of an integer part and a fractional part, separated by a decimal point. The integer part is on the left, and the fractional part is on the right. For example, in 0.0225, 0 is the integer part and 0225 is the fractional part.

Conversion Explanation:

1. For the numerator:
   • We start with the number 0.0225.
   • By removing the decimal point, we derive the numerator as 225.
2. For the denominator:
   • Each position after the decimal represents a division by 10.
   • Thus, having 4 positions after the decimal equates to 10000 or 10⁴.
3. Factors:
   • The factors for the numerator and the denominator are numbers that can evenly divide each of them.
   • For instance, the factors of 225 include 1, 3, 5, 9, 15, 25, 45, 75, and 225.
   • The factors of 10000 comprise 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 625, 1000, 1250, 2000, 2500, 5000, and 10000.
4. Greatest Common Divisor (GCD):
   • It's the largest number that can evenly divide both the numerator and the denominator.
   • In this instance, the GCD for 225 and 10000 is 25.

The factors of 225 are:

The factors of 10000 are:

Conversion formula (equation):

Solution:

Step-by-step solution:

• Step 1: First, write the decimal as a fraction over 1. This sets up the next steps. 0.0225 = $\frac{0.0225}{1}$
• Step 2: Decimals can have different lengths. We will align the number of digits after the decimal point. For 0.0225, we have three digits. This means multiplying the fraction by a factor of 10 for each digit. Factor = 10⁴ = 10000
• Step 3: Using this factor, multiply both the numerator and the denominator. $\frac{\mathrm{0.0225\; \times \; 10000}}{\mathrm{1\; \times \; 10000}}$ = $\frac{225}{10000}$
• Step 4: Now we need to simplify the fraction by finding common divisors. The greatest common divisor is 25. Divide both the numerator and the denominator by this common divisor. $\frac{\mathrm{225\; ÷\; 25}}{\mathrm{10000\; ÷\; 25}}$ = $\frac{9}{400}$

Answer in mixed fraction format:

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