What Is A Number? Numbers, Numerals, Digits And Types
The short version
- A number is an idea that tells how many, how much, or which position. It’s the amount itself, not the mark on paper.
- A numeral is the symbol you write for a number (5, five, V). A digit is one of the ten symbols 0 through 9 used to build numerals.
- The main types nest inside each other: natural numbers sit inside whole numbers, which sit inside integers, then rational numbers, then real numbers.
- Irrational numbers like π and √2 are real numbers that can’t be written as a fraction. Their decimals never end and never repeat.
- Zero is a whole number, an integer and an even number, and it’s neither positive nor negative.
What is a number? A number is an idea that tells you a quantity, a measurement or a position: how many apples, how long a board is, who came in 3rd. The number itself is the idea of that amount. The symbols we write to show it, like 7 or seven, are called numerals.
That distinction sounds fussy, but kids get tested on it, and it helps later when they meet numbers like π that you can’t write out in full. Below we cover numbers vs numerals vs digits, the main types of numbers with a chart, how to classify any number, and practice problems.
What is a number, exactly? Number vs numeral vs digit
These three words get used as if they mean the same thing. They don’t.
| Word | What it is | Example |
|---|---|---|
| Number | The amount or idea itself | The amount of fingers on one hand |
| Numeral | A symbol or word that stands for a number | 5, five, V |
| Digit | One of the ten symbols used to write numerals in base ten | 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 |
Think of it like a person and their name. The person is the number. The name, written in English or Spanish or a nickname, is the numeral. The letters in the name are the digits.
So 347 is one numeral made of three digits: 3, 4 and 7. Each digit has a value that depends on its place. In 347, the 4 is worth 40, because it’s in the tens place.
Example: In 5,382, what is the value of the 5?
The 5 is in the thousands place.
Value = 5 × 1,000 = 5,000
Types of numbers
A full answer to what is a number includes the kinds of numbers there are. Numbers come in families, and the families fit inside each other like nesting cups. Each new family was added because people needed an answer the old one couldn’t give. You can’t take 5 from 3 with whole numbers, so negatives came along. You can’t split 3 pizzas among 4 kids with integers, so fractions came along.
| Type | What it includes | Examples | Usually taught |
|---|---|---|---|
| Natural (counting) numbers | 1, 2, 3 and on forever | 1, 12, 500 | Pre-K and K |
| Whole numbers | Natural numbers plus 0 | 0, 7, 1,000 | K to 2 |
| Integers | Whole numbers and their negatives | -8, 0, 15 | Grade 6 |
| Rational numbers | Anything that can be written as a fraction a/b, with b not 0 | 3/4, -2.5, 0.333…, 6 | Grades 3 to 7 |
| Irrational numbers | Real numbers that can’t be written as a fraction | π, √2, √5 | Grade 8 |
| Real numbers | All rational and irrational numbers together | Every point on the number line | Grade 8 |
Beyond the real numbers there are imaginary and complex numbers, built on i, where i × i = -1. Most students see those in Algebra 2.
Other ways to sort numbers
- Even and odd. Even whole numbers split into two equal groups with nothing left over. 0 is even.
- Prime and composite. A prime has exactly two factors, 1 and itself, like 7 or 13. A composite has more than two, like 12. The number 1 is neither.
- Positive and negative. Positive numbers are greater than 0, negatives are less than 0, and 0 is neither.
Numbers that do different jobs
A cardinal number says how many (4 cookies). An ordinal number says position (4th in line). A nominal number is a label that doesn’t measure anything, like a jersey number or a phone number. Adding two phone numbers makes no sense, and that’s the clue it’s a label.
How to classify a number, with worked examples
Start at the top of the chart and work down, checking each family. A number usually belongs to several.
Example 1: -7
Natural? No, it’s negative.
Whole? No, it’s negative.
Integer? Yes.
Rational? Yes, it’s -7/1.
Real? Yes.
So -7 is an integer, a rational number and a real number.
Example 2: 0.25
0.25 = 25/100 = 1/4, a fraction, so it’s rational and real. It isn’t an integer because it sits between 0 and 1.
Example 3: √16
√16 = 4, because 4 × 4 = 16.
4 is natural, whole, an integer, rational and real. Always simplify first.
Example 4: √5
2 × 2 = 4 and 3 × 3 = 9, so √5 is between 2 and 3. No fraction squares to exactly 5, and its decimal (2.2360679…) never ends or repeats. It’s irrational and real.
Example 5: 0.121212…
A decimal that repeats forever is rational. This one equals 12/99, which simplifies to 4/33. Check: 4 ÷ 33 = 0.121212…
Common mistakes kids make with numbers
- Mixing up digit and number. A kid asked “how many digits are in 405” should say 3, not 405.
- Thinking a long decimal must be irrational. 0.333… goes on forever, but it repeats, so it’s the rational number 1/3.
- Calling 1 prime. It has only one factor, so it’s neither prime nor composite.
- Saying 0 is positive, or saying 0 is odd. Zero is neither positive nor negative, and it’s even.
- Forgetting that whole numbers are also integers. 6 is a whole number and an integer and a rational number. The families overlap.
- Not simplifying square roots first. √49 looks irrational but it’s just 7.
Practice problems
- How many digits are in 40,061?
- What is the value of the 7 in 3,742?
- List every family that -12 belongs to.
- Is 2/3 an integer? What families does it belong to?
- Is 0 a whole number? Is it even?
- Classify √49 and √50.
- Is 0.4444… rational or irrational? If rational, write it as a fraction.
- Sort 51, 53 and 1 into prime, composite or neither.
Answers
- 5 digits: 4, 0, 0, 6 and 1.
- The 7 is in the hundreds place, so its value is 700.
- Integer, rational and real. It’s not natural or whole because it’s negative.
- No, it’s between 0 and 1. It’s rational and real.
- Yes to both.
- √49 = 7, so it’s natural, whole, an integer, rational and real. √50 is about 7.07 and isn’t a perfect square, so it’s irrational and real.
- Rational. 0.4444… = 4/9.
- 51 is composite, because 3 × 17 = 51. 53 is prime. 1 is neither.
If your kid is shaky on what a number is
Few kids will ever need to answer “what is a number?” on a test in those exact words. A kid who can’t explain the difference between a digit and a number isn’t in trouble. A kid who can’t say what the 4 in 347 is worth might be. Place value sits under nearly everything in elementary math, from regrouping in subtraction to lining up decimals, and gaps there tend to show up later as “careless” mistakes.
The other common snag is fractions as numbers. Many kids treat 3/4 as two numbers stacked up rather than one amount that has its own spot on the number line. That single idea causes a lot of the trouble we describe in why algebra struggles usually trace back to fractions. To see where place value and fractions should land by grade, check math skills by grade level. If you’re seeing a pattern of misses, these signs your child is behind are a good gut check.
Frequently asked questions
What is a number, in simple terms?
A number is an idea used to count, measure or label. It tells you how many, how much, or which one.
Is 0 a number?
Yes. Zero is a whole number, an integer, a rational number and a real number. Whether it counts as a natural number depends on the textbook; most U.S. elementary books start natural numbers at 1.
What is the difference between a number and a digit?
A digit is one of the ten symbols 0 through 9. A number is the amount, which you write with one or more digits. The number 58 is written with the digits 5 and 8.
Is infinity a number?
Not a real number. Infinity describes something that goes on without end, and you can’t place it on the number line. Higher math does treat some kinds of infinity as numbers, but not in K-12 arithmetic.
What are the main types of numbers?
Natural, whole, integers, rational, irrational and real numbers. Later, students add imaginary and complex numbers.
Find the actual gap
When number sense is shaky, homework in every unit feels harder than it should. Math Anon begins with a short adaptive assessment that checks place value, fractions, negatives and the rest of the foundation, then sends you a written report of which skills are missing.
After that, your kid works on exactly those skills for about 20 minutes a day, and you’ll see a progress report every week. It’s $49 for the assessment, credited in full toward the first month. Start the assessment or read about pricing.
