What is 40.5 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 40.5 to a fraction.

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

Often, convert 40.25 to a fraction or 41 to a fraction, depending on the task.

Understanding the decimal: “40.5”

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 40.5, 40 is the integer part and 5 is the fractional part.

Conversion Explanation:

For the numerator:
- We start with the number 40.5.
- By removing the decimal point, we derive the numerator as 405.
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 405 include 1, 3, 5, 9, 15, 27, 45, 81, 135, and 405.
- 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 405 and 10 is 5.

The factors of 405 are:

1 3 5 9 15 27 45 81 135 405

The factors of 10 are:

1 2 5 10

Conversion formula (equation):

$40.5 = \frac{40.5}{1} = \frac{40.5 × 10}{1 × 10} = \frac{405}{10} = \frac{405÷5}{10÷5} = \frac{81}{2}$

Solution:

40.5 = $\frac{81}{2}$

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. 40.5 = $\frac{40.5}{1}$
Step 2: Decimals can have different lengths. We will align the number of digits after the decimal point. For 40.5, 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. $\frac{40.5 × 10}{1 × 10}$ = $\frac{405}{10}$
Step 4: Now we need to simplify the fraction by finding common divisors. The greatest common divisor is 5. Divide both the numerator and the denominator by this common divisor. $\frac{405 ÷ 5}{10 ÷ 5}$ = $\frac{81}{2}$

Answer in mixed fraction format:

40.5 =

40

1

2

What is 40.5 as a fraction?