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Introduction to the Properties of Real Numbers
Introduction to the Properties of Real Numbers — from OpenStax Prealgebra 2e.
Introduction to the Properties of Real Numbers
A quilt is formed by sewing many different pieces of fabric together. The pieces can vary in color, size, and shape. The combinations of different kinds of pieces provide for an endless possibility of patterns. Much like the pieces of fabric, mathematicians distinguish among different types of numbers. The kinds of numbers in an expression provide for an endless possibility of outcomes. We have already described counting numbers, whole numbers, and integers. In this chapter, we will learn about other types of numbers and their properties.
Symbols used here
Both signs at once: x = 3 ± 2 means 5 and 1.
The two sides are different.
Inequalities that allow equality; < and > exclude it.
Equal to the precision shown, not exactly.
The non-negative number whose square (n-th power) is x.
What is left after dividing a by n.
Per hundred: 15% = 15/100.
a for every b; a divided by b.
Questions people ask
Why does the order of operations matter?
Because 2 + 3 × 4 would otherwise be two different numbers. The convention (brackets, exponents, multiplication and division, addition and subtraction) exists so every reader gets the same value from the same expression.
How do I check an arithmetic answer?
Estimate first (round every number and compute roughly), then compare. If the estimate and the exact answer disagree by more than a little, one of them is wrong. The solver shows every operation, so you can find which line went astray.
Why are fractions harder than decimals?
They are not harder, they are more exact: 1/3 is a precise number, 0.333 is an approximation. Fractions need a common denominator to add, which is the one extra step people trip on.
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Parts of this page are adapted from OpenStax Prealgebra 2e (CC BY-NC-SA 4.0). Condensed and re-explained here; errors are ours.