Key takeaway: An integer is a number from the list of whole numbers, their negatives, and zero, such as −14, 0 and 23, and none of these values is a fraction or a decimal.
Grade 66.NS.C.5Numbers and Operations
Definition of Integer
An integer is a number with no fractional or decimal part that can be positive, negative or zero. The set contains the counting numbers 1, 2, 3, …, their opposites -1, -2, -3, …, and 0.
These numbers describe situations with two directions: temperatures above and below zero, elevations above and below sea level, deposits and withdrawals. On a horizontal number line they are evenly spaced, with negatives to the left of 0 and positives to the right. A number farther right is always greater. Adding, subtracting or multiplying two of them always gives another whole-number result of the same kind, but division may not.
Formula and notation
The set of integers lists in both directions without end:
\[\{\text{…}, -7, -6, -5, \text{…}, 0, \text{…}, 5, 6, 7, \text{…}\}\]
Positive ones have no sign or a plus sign; negative ones carry a minus sign. Zero is neither positive nor negative.
Key facts
- Numbers such as \(\frac{1}{2}\), \(-0.5\) and \(4.7\) do not belong to this set.
- Every integer has an opposite lying just as far from 0, across it.
- Between two of them, the one placed further right on a horizontal line is larger.
- Whole numbers are the integers that are 0 or positive.
Integer example
At dawn in Fargo the temperature was \(-14^{\circ}\text{F}\). By afternoon it rose 23 degrees. (a) What is the afternoon temperature? (b) Which of \(-14\), \(\frac{8}{4}\), \(2.6\) and 0 are integers?
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(a) Rising 23 degrees means adding: \(-14 + 23 = 9\).
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(b) \(-14\) qualifies, since it is a whole number with a minus sign. \(\frac{8}{4} = 2\) qualifies. 0 qualifies. \(2.6\) has a decimal part, so it does not.
The afternoon temperature is \(9^{\circ}\text{F}\), and the integers are \(-14\), \(\frac{8}{4}\) and 0.
Common mistake
Watch out
Cal says \(-9 > -2\), because 9 is bigger than 2.
Why it is wrong
Plotted on a line, \(-9\) sits well left of \(-2\), so it is the smaller value: \(-9 < -2\). Among negative numbers, the one closer to 0 is greater. Picture owing \$9 versus owing \$2.
Related terms and lessons
Browse the glossary: A–Z list · Grade 6 vocabulary · Numbers and Operations