What is 0.415 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 0.415 to a fraction.

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

Often, convert 0.413 to a fraction or 0.416 to a fraction, depending on the task.

Understanding the decimal: “0.415”

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 0.415, 0 is the integer part and 415 is the fractional part.

Conversion Explanation:

For the numerator:
- We start with the number 0.415.
- By removing the decimal point, we derive the numerator as 415.
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 415 include 1, 5, 83, and 415.
- 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 415 and 1000 is 5.

The factors of 415 are:

1 5 83 415

The factors of 1000 are:

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

Conversion formula (equation):

$0.415 = \frac{0.415}{1} = \frac{0.415 × 1000}{1 × 1000} = \frac{415}{1000} = \frac{415÷5}{1000÷5} = \frac{83}{200}$

Solution:

0.415 = $\frac{83}{200}$

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. 0.415 = $\frac{0.415}{1}$
Step 2: Decimals can have different lengths. We will align the number of digits after the decimal point. For 0.415, 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. $\frac{0.415 × 1000}{1 × 1000}$ = $\frac{415}{1000}$
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. $\frac{415 ÷ 5}{1000 ÷ 5}$ = $\frac{83}{200}$

Answer in mixed fraction format:

0.415 =

83

200

What is 0.415 as a fraction?