Chapter 2 – Decimals and Fractions
OBJECTIVES
- Read, write, and round decimal numbers.
- Identify the types of fractions and perform computations with them.
- Determine the least common denominator (LCD).
- Solve problems involving fractions and decimal numbers.
- Determine the relationship between fractions and decimal numbers.
- Perform arithmetic operations combined with fractions and decimal numbers.
CHAPTER OUTLINE
2.1 Decimal Numbers
2.2 Arithmetic Operations with Decimal Numbers
2.3 Fractions
2.4 Arithmetic Operations with Fractions
2.5 Converting Between Fractions and Decimal Numbers and Combined Order of Operations
2 Review Exercises
2 Self-Test Exercises
2 Case Study – Lightning Wholesale
Introduction
In the previous chapter, we learned about whole numbers and how to perform basic arithmetic operations with whole numbers. However, measurements and calculations of quantities, values, amounts, etc., cannot always be represented by whole numbers. Most of these involve portions of whole numbers, represented by fractions and decimal numbers.
Fractions and decimal numbers express values that are a portion of a whole number. Fractions are widely used throughout mathematics, including measurement, probability, and data applications. Decimal numbers are a special type of fraction that express numbers as a portion of powers of 10 (10, 100, 1,000, etc.).
Fractions and decimal numbers have different benefits. Fractions can be more precise than decimal numbers; for example, it is impossible to exactly represent the fraction [latex]\displaystyle{\frac{1}{3}}[/latex] as a decimal number.
However, reading, writing, and performing arithmetic operations with decimal numbers is easier than with fractions. In addition, it is easier to determine the magnitude of numbers when they are expressed as decimal numbers rather than as fractions. For example, it is easier to recognize that the decimal number 7.75, as opposed to its fractional form [latex]\displaystyle{\frac{31}{4}}[/latex], lies between the whole numbers 7 and 8.
Unless otherwise indicated, this chapter is an adaptation of the eTextbook Foundations of Mathematics (3rd ed.) by Thambyrajah Kugathasan, published by Vretta-Lyryx Inc., with permission. Adaptations include supplementing existing material and reordering chapters.
