7.0: A Guide to Understanding Decimals

Introduction

Decimals are a way of representing fractions that are less than one. They are written using a decimal point (.) to separate the whole number part from the fractional part. For example, the decimal 0.5 represents the fraction 1/2.

Decimals are used in a wide variety of applications, including:

• Mathematics
• Science
• Engineering
• Finance
• Everyday life

Converting Decimals to Fractions

Step 1: Write the decimal as a fraction.

The numerator of the fraction is the number to the right of the decimal point. The denominator of the fraction is a power of 10, where the exponent is the number of digits to the right of the decimal point.

For example, to convert the decimal 0.5 to a fraction, we write:

Numerator = 5
Denominator = 10^1 = 10

Therefore, 0.5 is equivalent to the fraction 5/10.

Step 2: Simplify the fraction.

The fraction 5/10 can be simplified by dividing both the numerator and denominator by 5:

5/10 = (5 ÷ 5) / (10 ÷ 5) = 1/2

Therefore, 0.5 is equivalent to the fraction 1/2.

Converting Fractions to Decimals

Step 1: Divide the numerator by the denominator.

To convert a fraction to a decimal, we divide the numerator by the denominator. The quotient is the decimal representation of the fraction.

For example, to convert the fraction 1/2 to a decimal, we divide 1 by 2:

1 ÷ 2 = 0.5

Therefore, 1/2 is equivalent to the decimal 0.5.

Step 2: Add a decimal point to the quotient.

If the quotient is a whole number, we add a decimal point to the quotient and then add zeros to the end of the decimal.

For example, to convert the fraction 1 to a decimal, we divide 1 by 1:

1 ÷ 1 = 1.0

Therefore, 1 is equivalent to the decimal 1.0.

Applications of Decimals

Decimals are used in a wide variety of applications, including:

• Mathematics: Decimals are used to represent fractions, solve equations, and perform calculations.
• Science: Decimals are used to measure distances, temperatures, and other physical quantities.
• Engineering: Decimals are used to design and build bridges, buildings, and other structures.
• Finance: Decimals are used to represent interest rates, stock prices, and other financial data.
• Everyday life: Decimals are used to measure time, weights, and distances.

Why Decimals Matter

Decimals are important because they provide a convenient way to represent fractions. Decimals are also used in a wide variety of applications, from mathematics to science to everyday life.

Benefits of Using Decimals

There are many benefits to using decimals, including:

• Easy to use: Decimals are easy to understand and use.
• Precise: Decimals can be used to represent fractions very precisely.
• Versatile: Decimals can be used in a wide variety of applications.

Pros and Cons of Decimals

Pros:

• Easy to use
• Precise
• Versatile

Cons:

• Can be difficult to understand for some people
• Can be difficult to convert between decimals and fractions

How to Use Decimals

Decimals are easy to use. To use decimals, you simply need to be able to read and write numbers.

Step 1: Read a decimal.

To read a decimal, simply read the whole number part, followed by the decimal point, followed by the fractional part.

For example, the decimal 0.5 is read as "zero point five".

Step 2: Write a decimal.

To write a decimal, simply write the whole number part, followed by the decimal point, followed by the fractional part.

For example, the decimal 0.5 is written as "0.5".

Stories and What We Learn

Story 1:

A scientist is measuring the temperature of a reaction. The scientist measures the temperature to be 27.5 degrees Celsius.

What we learn: Decimals are used to measure temperatures very precisely.

Story 2:

An engineer is designing a bridge. The engineer needs to know the length of the bridge to the nearest tenth of a foot. The engineer measures the length of the bridge to be 100.5 feet.

What we learn: Decimals are used to measure distances very precisely.

Story 3:

A cashier is calculating the total cost of a customer's groceries. The customer's groceries cost $12.50.

What we learn: Decimals are used to represent prices very precisely.

How to Step-by-Step Approach

Step 1: Understand the concept of decimals.

Decimals are a way of representing fractions that are less than one. They are written using a decimal point (.) to separate the whole number part from the fractional part.

Step 2: Convert decimals to fractions.

To convert a decimal to a fraction, we write the decimal as a fraction with the numerator being the number to the right of the decimal point and the denominator being a power of 10.

Step 3: Convert fractions to decimals.

To convert a fraction to a decimal, we divide the numerator by the denominator. The quotient is the decimal representation of the fraction.

Step 4: Use decimals in everyday life.

Decimals are used in a wide variety of everyday applications, such as measuring time, weights, and distances.

Tables

Table 1: Examples of Decimals

Table 2: Applications of Decimals

Table 3: Pros and Cons of Decimals