What is 0.845 as a fraction?

Converting decimals to fractions can be useful in many situations. Let's go through the steps to convert a decimal 0.845 to a fraction.

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

Often, convert 0.84375 to a fraction or 0.85 to a fraction, depending on the task.

Understanding the decimal: “0.845”

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 0.845, 0 is the integer part and 845 is the fractional part.

Conversion Explanation:

1. For the numerator:
   • We start with the number 0.845.
   • By removing the decimal point, we derive the numerator as 845.
2. For the denominator:
   • Each position after the decimal represents a division by 10.
   • Thus, having 3 positions after the decimal equates to 1000 or 10³.
3. Factors:
   • The factors for the numerator and the denominator are numbers that can evenly divide each of them.
   • For instance, the factors of 845 include 1, 5, 13, 65, 169, and 845.
   • The factors of 1000 comprise 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, and 1000.
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 845 and 1000 is 5.

The factors of 845 are:

The factors of 1000 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. 0.845 = $\frac{0.845}{1}$
• Step 2: Decimals can have different lengths. We will align the number of digits after the decimal point. For 0.845, we have three digits. This means multiplying the fraction by a factor of 10 for each digit. Factor = 10³ = 1000
• Step 3: Using this factor, multiply both the numerator and the denominator. $\frac{\mathrm{0.845\; \times \; 1000}}{\mathrm{1\; \times \; 1000}}$ = $\frac{845}{1000}$
• Step 4: Now we need to simplify the fraction by finding common divisors. The greatest common divisor is 5. Divide both the numerator and the denominator by this common divisor. $\frac{\mathrm{845\; ÷\; 5}}{\mathrm{1000\; ÷\; 5}}$ = $\frac{169}{200}$

Answer in mixed fraction format:

Related conversions:

• What is 0.6785 as a fraction?
• What is 0.687 as a fraction?
• What is 0.835 as a fraction?
• What is 0.85 as a fraction?
• What is 0.885 as a fraction?
• What is 0.906 as a fraction?