Question

Write the following fractions as decimals: (a) \(\frac{3}{5}\) (b) \(\frac{3}{10}\) (d) \(\frac{3}{40}\) (e) \(\frac{3}{100}\)

Short answer

Question: Convert the following fractions to decimals: a) \(\frac{3}{5}\) b) \(\frac{3}{10}\) c) \(\frac{3}{40}\) d) \(\frac{3}{100}\) Answer: a) \(\frac{3}{5} = 0.6\) b) \(\frac{3}{10} = 0.3\) c) \(\frac{3}{40} = 0.075\) d) \(\frac{3}{100} = 0.03\)

Step-by-step solution

(a) Convert \(\frac{3}{5}\) to decimal

To convert \(\frac{3}{5}\) to decimal, divide 3 by 5: \(3 \div 5 = 0.6\) So, \(\frac{3}{5}\) in decimal form is \(0.6\).

(b) Convert \(\frac{3}{10}\) to decimal

To convert \(\frac{3}{10}\) to decimal, divide 3 by 10: \(3 \div 10 = 0.3\) So, \(\frac{3}{10}\) in decimal form is \(0.3\).

(d) Convert \(\frac{3}{40}\) to decimal

To convert \(\frac{3}{40}\) to decimal, divide 3 by 40: \(3 \div 40 = 0.075\) So, \(\frac{3}{40}\) in decimal form is \(0.075\).

(e) Convert \(\frac{3}{100}\) to decimal

To convert \(\frac{3}{100}\) to decimal, divide 3 by 100: \(3 \div 100 = 0.03\) So, \(\frac{3}{100}\) in decimal form is \(0.03\).

Key concepts

Decimal Conversion

Understanding decimal conversion is essential to grasping more complex mathematical concepts. It is the process of changing a fraction, which has a numerator and a denominator, into a decimal number, which has digits to the right of a decimal point. To convert a fraction to a decimal, divide the numerator (the top number of the fraction) by the denominator (the bottom number).

For example, in the exercise \(\frac{3}{5}\) is converted by dividing 3 by 5 to get 0.6. This method works because decimals are essentially another way to represent fractions; they denote parts of a whole when that whole is divided into parts that are powers of ten. Learning to comfortably convert between these forms can vastly improve a student's flexibility with numbers and deepen their understanding of base-ten numeration.

Arithmetic Operations

Arithmetic operations, including addition, subtraction, multiplication, and division, are the building blocks of mathematics. When converting fractions to decimals, division plays a crucial role. It is the action of dividing one quantity by another to find out how many times the divisor is contained within the dividend.

In the context of our exercise, the act of dividing the numerator by the denominator to convert a fraction to a decimal is an application of arithmetic operations. For instance, to find the decimal form of \(\frac{3}{40}\), we perform the division 3 ÷ 40, which equals 0.075. Arithmetic operations are the tools that allow us to navigate between different representations of numbers, reinforcing the versatility and utility of mathematical concepts in problem-solving situations.

Fractions

A fraction represents a part of a whole or, more generally, any number of equal parts. In the given problems, fractions like \(\frac{3}{5}\), \(\frac{3}{10}\), and \(\frac{3}{100}\) demonstrate this concept. Each fraction consists of a numerator and a denominator, indicating how many parts we have out of a total number of equal parts. Fractions are another way of expressing division, and learning to work with them is critical to success in mathematics.

With fractions, students learn about the relationships and proportions between numbers, which leads to a deeper comprehension of concepts such as decimals and percentages. Grasping the concept of fractions is essential for converting them into decimals, as being comfortable with fractions allows students to understand why the division process yields the correct decimal representation.

Mathematics Education

Mathematics education aims to equip students with the knowledge and skills to use mathematics confidently in their daily lives. This includes understanding fundamental concepts such as fractions, decimals, and the arithmetic operations that connect them. A well-rounded mathematics education forms the foundation for critical thinking and problem-solving abilities.

Carefully structured exercises like converting fractions to decimals not only reinforce arithmetic skills but also encourage students to grasp the interconnectedness of mathematical concepts. Step-by-step solutions can greatly enhance a student's learning experience by breaking down complex problems into manageable parts, making the content more accessible, and fostering the student's ability to tackle their homework and further mathematical challenges independently.