Problem 27 - Calculate With Confidence

Question

Change the following fractions to decimals. Carry division three decimal places as necessary. $$\frac{3}{50}$$

Step-by-Step Solution

Answer

The decimal representation of \( \frac{3}{50} \) is 0.06.

Step 1: Set up the division

We are converting \( \frac{3}{50} \) into a decimal. To do this, perform the division of 3 by 50.

Step 2: Perform the division

Place 3 inside the division bracket and 50 outside. Since 50 does not divide into 3, add a decimal and zeros to 3 to proceed with the division. Begin with 3.000.

Step 3: Divide 300 by 50

Determine how many times 50 goes into 300. 50 goes into 300 exactly 6 times (\(50 \times 6 = 300\)), so place 6 after the decimal point in the result.

Step 4: Complete the division

Since 300 minus 300 leaves a remainder of 0, the division ends here. The decimal representation is complete.

Key Concepts

Division Process

When converting fractions to decimals, the division process is the key step. It involves dividing the numerator by the denominator. In this situation, we are converting the fraction \( \frac{3}{50} \) into a decimal form. To achieve this, one must understand how division works step-by-step and be comfortable with the idea of adding decimal places.

Start by placing the numerator (3) inside the division bracket—known as the dividend—and the denominator (50) outside as the divisor. In our example, 50 cannot go into 3 because it's larger. Therefore, you introduce a decimal point and start adding zeros to 3, turning it into 3.000. Each zero allows you to bring down a digit in the quotient.

This process essentially extends your number until you can perform the division. Adding decimal places is entirely permissible in mathematics as it doesn't change the value; it just refines the division.

Decimal Representation

The goal of dividing a fraction like \( \frac{3}{50} \) is to express it as a decimal. The decimal representation is the final numerical form you get after completing the division process. In our example, once you divide 300 by 50, you are left with 6, which is placed after a decimal, creating 0.06 as the final result.

Decimal representation is important as it allows us to easily compare sizes, perform calculations, and understand numerical data. In daily life, decimals are frequently used for prices, measurements, and statistical data. Hence, understanding how to convert fractions into decimals is a vital arithmetic skill.

Mathematics Education

A solid understanding of mathematics forms the backbone of many disciplines. Learning to convert fractions into decimals through division enhances computational skills and boosts confidence in handling various numerical problems.

Emphasizing practice and repetition is crucial in mathematics education. Working with examples like \( \frac{3}{50} \) helps students relate division to real-world contexts, developing their ability to comprehend mathematical concepts deeply.

• Builds fluency in performing operations.


• Encourages critical thinking and problem-solving skills.


• Applies concepts to practical situations.

Whether for academic achievement or everyday applications, a robust foundation in mathematics enhances logical reasoning and opens doors to various opportunities.