What is 7.8 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 7.8 to a fraction.

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

Often, convert 7.75 to a fraction or 7.8125 to a fraction, depending on the task.

Understanding the decimal: “7.8”

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 7.8, 7 is the integer part and 8 is the fractional part.

Conversion Explanation:

For the numerator:
- We start with the number 7.8.
- By removing the decimal point, we derive the numerator as 78.
For the denominator:
- Each position after the decimal represents a division by 10.
- Thus, having 1 positions after the decimal equates to 10 or 10¹.
Factors:
- The factors for the numerator and the denominator are numbers that can evenly divide each of them.
- For instance, the factors of 78 include 1, 2, 3, 6, 13, 26, 39, and 78.
- The factors of 10 comprise 1, 2, 5, and 10.
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 78 and 10 is 2.

The factors of 78 are:

1 2 3 6 13 26 39 78

The factors of 10 are:

1 2 5 10

Conversion formula (equation):

$7.8 = \frac{7.8}{1} = \frac{7.8 × 10}{1 × 10} = \frac{78}{10} = \frac{78÷2}{10÷2} = \frac{39}{5}$

Solution:

7.8 = $\frac{39}{5}$

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. 7.8 = $\frac{7.8}{1}$
Step 2: Decimals can have different lengths. We will align the number of digits after the decimal point. For 7.8, we have three digits. This means multiplying the fraction by a factor of 10 for each digit. Factor = 10¹ = 10
Step 3: Using this factor, multiply both the numerator and the denominator. $\frac{7.8 × 10}{1 × 10}$ = $\frac{78}{10}$
Step 4: Now we need to simplify the fraction by finding common divisors. The greatest common divisor is 2. Divide both the numerator and the denominator by this common divisor. $\frac{78 ÷ 2}{10 ÷ 2}$ = $\frac{39}{5}$

Answer in mixed fraction format:

7.8 =

7

4

5

What is 7.8 as a fraction?