What is 0.21875 as a fraction? Tutorial in mathshowcase.info

Converting decimals to fractions can be useful in many situations. Let's go through the steps to convert a decimal 0.21875 to a fraction.

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

Often, convert 0.218 to a fraction or 0.219 to a fraction, depending on the task.

Understanding the decimal: “0.21875”

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 0.21875, 0 is the integer part and 21875 is the fractional part.

Conversion Explanation:

For the numerator:
- We start with the number 0.21875.
- By removing the decimal point, we derive the numerator as 21875.
For the denominator:
- Each position after the decimal represents a division by 10.
- Thus, having 5 positions after the decimal equates to 100000 or 10⁵.
Factors:
- The factors for the numerator and the denominator are numbers that can evenly divide each of them.
- For instance, the factors of 21875 include 1, 5, 7, 25, 35, 125, 175, 625, 875, 3125, 4375, and 21875.
- The factors of 100000 comprise 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 125, 160, 200, 250, 400, 500, 625, 800, 1000, 1250, 2000, 2500, 3125, 4000, 5000, 6250, 10000, 12500, 20000, 25000, 50000, and 100000.
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 21875 and 100000 is 3125.

The factors of 21875 are:

1 5 7 25 35 125 175 625 875 3125 4375 21875

The factors of 100000 are:

1 2 4 5 8 10 16 20 25 32 40 50 80 100 125 160 200 250 400 500 625 800 1000 1250 2000 2500 3125 4000 5000 6250 10000 12500 20000 25000 50000 100000

Conversion formula (equation):

$0.21875 = \frac{0.21875}{1} = \frac{0.21875 × 100000}{1 × 100000} = \frac{21875}{100000} = \frac{21875÷3125}{100000÷3125} = \frac{7}{32}$

Solution:

0.21875 = $\frac{7}{32}$

What is a decimal?

A decimal is a numeral system that includes a point to separate the whole number part from the fractional part. This system makes it easy to work with numbers less than one.

What is a fraction?

A fraction is a mathematical way of showing a part of a whole. It has two parts: the numerator on top and the denominator below, which help express partial values and comparisons.

Step-by-step solution:

Step 1: First, write the decimal as a fraction over 1. This sets up the next steps. 0.21875 = $\frac{0.21875}{1}$
Step 2: Decimals can have different lengths. We will align the number of digits after the decimal point. For 0.21875, we have three digits. This means multiplying the fraction by a factor of 10 for each digit. Factor = 10⁵ = 100000
Step 3: Using this factor, multiply both the numerator and the denominator. $\frac{0.21875 × 100000}{1 × 100000}$ = $\frac{21875}{100000}$
Step 4: Now we need to simplify the fraction by finding common divisors. The greatest common divisor is 3125. Divide both the numerator and the denominator by this common divisor. $\frac{21875 ÷ 3125}{100000 ÷ 3125}$ = $\frac{7}{32}$

Answer in mixed fraction format:

0.21875 =

7

32

What is 0.21875 as a fraction?