number — Definition, Formula & Examples
A number is a value that represents a quantity, an amount, or a position. Numbers let you count things (1, 2, 3…), measure sizes (3.5 meters), show parts of a whole (½), and even describe values less than zero (−4).
A number is an abstract mathematical object used for counting, measuring, ordering, and labeling. Numbers belong to various sets organized by inclusion: the natural numbers (0, 1, 2, 3, …), the integers (…, −2, −1, 0, 1, 2, …), the rational numbers (any number expressible as a fraction of two integers), and the real numbers (all points on the continuous number line). Each larger set contains every member of the smaller sets within it.
How It Works
You already use numbers every day — when you read a clock, check a price, or keep score in a game. The type of number you need depends on the situation. If you are counting objects, whole numbers like 0, 1, 2, 3 do the job. When you need to split something into equal parts, fractions like ¾ or decimals like 0.75 step in. If a value goes below zero — such as a temperature of −10° — you use a negative number. You can picture all these types arranged on a number line, where every point corresponds to exactly one number and numbers increase as you move to the right.
Worked Example
Problem: Place the numbers 3, −1, ½, and 0 in order from least to greatest.
Step 1: Identify each number's type. 3 is a whole number, −1 is a negative integer, ½ is a fraction between 0 and 1, and 0 is neither positive nor negative.
Step 2: Find the smallest. Negative numbers are less than zero, so −1 is the smallest value in the list.
Step 3: Compare the remaining numbers. Zero comes next, then ½ (which equals 0.5), and finally 3.
Step 4: Write the full order from least to greatest.
Answer: From least to greatest: −1, 0, ½, 3.
Another Example
This example shows how negative numbers appear in real life and how to find the distance between a negative and a positive number on the number line.
Problem: A thermometer reads −5 °C in the morning and 8 °C in the afternoon. How many degrees did the temperature rise?
Step 1: Write down the two numbers: morning temperature is −5 and afternoon temperature is 8.
Step 2: To find how much the temperature rose, subtract the starting value from the ending value.
Step 3: Subtracting a negative is the same as adding its positive form.
Answer: The temperature rose 13 degrees.
Visualization
Why It Matters
Understanding what a number is and how different types relate to each other is the foundation for every math course from arithmetic through algebra, geometry, and statistics. Careers in science, engineering, finance, and computer programming all depend on fluency with numbers. Even everyday tasks — budgeting, cooking, reading data — rely on choosing the right type of number for the situation.
Common Mistakes
Mistake: Confusing a number with a digit
Correction: A digit is a single symbol (0–9). A number can contain multiple digits and represents a value. The number 83 uses two digits but is one number.
Mistake: Thinking zero is not a real number
Correction: Zero is a whole number, an integer, a rational number, and a real number. It is the additive identity — adding 0 to any number gives that same number.
Mistake: Believing negative numbers are not 'real' numbers
Correction: Negative numbers are fully valid members of the integers and the real numbers. They appear on the left side of the number line and represent values below zero, such as temperatures or debts.
Check Your Understanding
Is −7 a whole number, an integer, or both?
Hint: Whole numbers start at 0 and go up.
Answer: −7 is an integer but not a whole number. Whole numbers are 0, 1, 2, 3, … (no negatives).
Put these numbers in order from least to greatest: 4, −3, 0.5, −0.5, 2.
Hint: Negative numbers with a larger absolute value are further left on the number line.
Answer: −3, −0.5, 0.5, 2, 4
How many digits does the number 1,024 have?
Hint: Count each individual symbol in the number.
Answer: 4 digits: 1, 0, 2, and 4.