What is 5 85/4 as a decimal?

Converting the fraction to an improper fraction

To convert $\normalsize{5}\frac{\normalsize{85}}{\normalsize{4}}$ into a decimal, we start by converting it to an improper fraction. First, multiply 5 by 4 then add the result to 85 in the numerator,

= $\frac{\left(\normalsize{5}\;\times\;\normalsize{4}\right) \;+\; \normalsize{85}}{\normalsize{4}}$

= $\frac{\normalsize{105}}{\normalsize{4}}$

Next, we will convert $\frac{\normalsize{105}}{\normalsize{4}}$ ​ to a decimal using the following methods.

Solve using Division Method

A fraction is made up of two parts: the numerator, which is the number on top, and the denominator, which is the number on the bottom. We can find the decimal equivalent by dividing the numerator 105 by the denominator 4.

105 (numerator) ÷ 4 (denominator) = 26.25

This division gives us the decimal equivalent of the fraction.

So, when you change $\frac{105}{4}$ to a decimal, your answer will be 26.25

The following animation demonstrates the Division method,

Factor of Power of 10 Method

Sometimes, dividing a number by a power of 10, like 10, 100, 1000, etc., is straightforward because you just move the decimal place to the left by the number of zeros in the power of 10. However, in this case, the denominator, 85, isn’t a power of 10.

But don't worry, we can adjust the fraction. If the denominator is a factor of a power of 10, such as 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, and so on, then we can transform the fraction into one that is easy to calculate.

To do this, we aim to make the denominator a power of 10. By multiplying the denominator by 25, denoted as (4 * 25 = 100), we achieve this. Since we multiplied the denominator by 25, we must also multiply the numerator by 25 as well:

$\frac{105 \times 25}{4 \times 25} = \frac{2625}{100} = 26.25$

In the end, your answer becomes 26.25 when you convert $\frac{105}{4}$ to a decimal.