What is 19.875 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 19.875 to a fraction.

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

Often, convert 19.8 to a fraction or 20 to a fraction, depending on the task.

Understanding the decimal: “19.875”

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 19.875, 19 is the integer part and 875 is the fractional part.

Conversion Explanation:

For the numerator:
- We start with the number 19.875.
- By removing the decimal point, we derive the numerator as 19875.
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.
Factors:
- The factors for the numerator and the denominator are numbers that can evenly divide each of them.
- For instance, the factors of 19875 include 1, 3, 5, 15, 25, 53, 75, 125, 159, 265, 375, 795, 1325, 3975, 6625, and 19875.
- The factors of 1000 comprise 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, and 1000.
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 19875 and 1000 is 125.

The factors of 19875 are:

1 3 5 15 25 53 75 125 159 265 375 795 1325 3975 6625 19875

The factors of 1000 are:

1 2 4 5 8 10 20 25 40 50 100 125 200 250 500 1000

Conversion formula (equation):

$19.875 = \frac{19.875}{1} = \frac{19.875 × 1000}{1 × 1000} = \frac{19875}{1000} = \frac{19875÷125}{1000÷125} = \frac{159}{8}$

Solution:

19.875 = $\frac{159}{8}$

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. 19.875 = $\frac{19.875}{1}$
Step 2: Decimals can have different lengths. We will align the number of digits after the decimal point. For 19.875, 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. $\frac{19.875 × 1000}{1 × 1000}$ = $\frac{19875}{1000}$
Step 4: Now we need to simplify the fraction by finding common divisors. The greatest common divisor is 125. Divide both the numerator and the denominator by this common divisor. $\frac{19875 ÷ 125}{1000 ÷ 125}$ = $\frac{159}{8}$

Answer in mixed fraction format:

19.875 =

19

7

8

What is 19.875 as a fraction?