What is 9.75 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 9.75 to a fraction.

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

Often, convert 9.73 to a fraction or 9.76 to a fraction, depending on the task.

Understanding the decimal: “9.75”

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 9.75, 9 is the integer part and 75 is the fractional part.

Conversion Explanation:

For the numerator:
- We start with the number 9.75.
- By removing the decimal point, we derive the numerator as 975.
For the denominator:
- Each position after the decimal represents a division by 10.
- Thus, having 2 positions after the decimal equates to 100 or 10².
Factors:
- The factors for the numerator and the denominator are numbers that can evenly divide each of them.
- For instance, the factors of 975 include 1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, and 975.
- The factors of 100 comprise 1, 2, 4, 5, 10, 20, 25, 50, and 100.
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 975 and 100 is 25.

The factors of 975 are:

1 3 5 13 15 25 39 65 75 195 325 975

The factors of 100 are:

1 2 4 5 10 20 25 50 100

Conversion formula (equation):

$9.75 = \frac{9.75}{1} = \frac{9.75 × 100}{1 × 100} = \frac{975}{100} = \frac{975÷25}{100÷25} = \frac{39}{4}$

Solution:

9.75 = $\frac{39}{4}$

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. 9.75 = $\frac{9.75}{1}$
Step 2: Decimals can have different lengths. We will align the number of digits after the decimal point. For 9.75, we have three digits. This means multiplying the fraction by a factor of 10 for each digit. Factor = 10² = 100
Step 3: Using this factor, multiply both the numerator and the denominator. $\frac{9.75 × 100}{1 × 100}$ = $\frac{975}{100}$
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. $\frac{975 ÷ 25}{100 ÷ 25}$ = $\frac{39}{4}$

Answer in mixed fraction format:

9.75 =

9

3

4

What is 9.75 as a fraction?