What is 117.775 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 117.775 to a fraction.

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

Often, convert 117 to a fraction or 118 to a fraction, depending on the task.

Understanding the decimal: “117.775”

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 117.775, 117 is the integer part and 775 is the fractional part.

Conversion Explanation:

For the numerator:
- We start with the number 117.775.
- By removing the decimal point, we derive the numerator as 117775.
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 117775 include 1, 5, 7, 25, 35, 175, 673, 3365, 4711, 16825, 23555, and 117775.
- 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 117775 and 1000 is 25.

The factors of 117775 are:

1 5 7 25 35 175 673 3365 4711 16825 23555 117775

The factors of 1000 are:

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

Conversion formula (equation):

$117.775 = \frac{117.775}{1} = \frac{117.775 × 1000}{1 × 1000} = \frac{117775}{1000} = \frac{117775÷25}{1000÷25} = \frac{4711}{40}$

Solution:

117.775 = $\frac{4711}{40}$

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. 117.775 = $\frac{117.775}{1}$
Step 2: Decimals can have different lengths. We will align the number of digits after the decimal point. For 117.775, 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. $\frac{117.775 × 1000}{1 × 1000}$ = $\frac{117775}{1000}$
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. $\frac{117775 ÷ 25}{1000 ÷ 25}$ = $\frac{4711}{40}$

Answer in mixed fraction format:

117.775 =

117

31

40

What is 117.775 as a fraction?