Converting a Mixed Number With a Denominator of 2, 4, or 5 to a Decimal

Definition

A mixed number is a whole number and a proper fraction combined. So, a mixed number consists of two parts, the whole number part and the fractional part. For example, in mixed number 225225 , the whole number part is 2 and the fractional part is 2525.

In this lesson, we convert given mixed number with a denominator of 2, 4 or 5 into a decimal.

Rules to convert a mixed number with a denominator of 2, 4 or 5 into a decimal.

• At first, we convert a mixed number with a denominator of 2, 4 or 5 into a fraction using the algorithm method.
• Then, we write its equivalent fraction such that the denominator is a power of ten.
• We then shift the decimal that many places to the left as there are zeros after 1 in the denominator.

Example 1

Convert 212212 into a decimal.

Solution

Step 1:

At first, we convert the mixed number into a fraction using the algorithm

212=(2×2+1)2=52212=(2×2+1)2=52

Step 2:

Then we write an equivalent fraction of 5/2 with a denominator 10.

52=(5×5)2×5=251052=(5×5)2×5=2510

Step 3:

Shifting the decimal one place to the left we get

2510=25.010=2.52510=25.010=2.5

Step 4:

So, 212=2.5212=2.5Example 2

Convert 334334 into a decimal.

Solution

Step 1:

At first, we convert the mixed number into a fraction using the algorithm

334=(3×4+3)4=154334=(3×4+3)4=154

Step 2:

Then we write an equivalent fraction of 15/4 with a denominator 100.

154=(15×25)(4×25)=375100154=(15×25)(4×25)=375100

Step 3:

Shifting the decimal two places to the left we get

375100=375.0100=3.75375100=375.0100=3.75

Step 4:

So, 334=3.75334=3.75