Digit in Math: Definition, Place Value & Examples

Definitionnoun

What is a digit in math?

A digit is one of the ten symbols 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 that we use to write every number. The number 507 has three digits: 5, 0 and 7. What a digit is worth depends on its place: in 507, the 5 stands for 5 hundreds, or 500.

In Spanish: dígito
Also called: numeral, figure, number symbol
Grade level: K-5

Grade 1Grade 2Grade 3Grade 4Grade 5CCSS 2.NBT.A.1CCSS 4.NBT.A.1CCSS 4.NBT.A.2GEDTABEISEESSAT

Digit in a picture

Ten digits are enough to write any number, because a digit’s place decides what it is worth. The same 5 means 500, 50 or 5.

Formal definition and notation

In the base-ten (decimal) number system, a digit is one of the symbols 0 through 9. A whole number written with the digits d₂ d₁ d₀ has the value d₂ × 100 + d₁ × 10 + d₀: each digit is multiplied by the place value of its position, and each place is worth 10 times the place to its right. The digit by itself is its face value; the digit times its place is its value. Other bases use other digit sets, for example only 0 and 1 in base 2.

Key facts

There are exactly ten digits, 0 through 9. The number 10 is not a digit: it is a two-digit number written with the digits 1 and 0.
The same digit can have different values. In 4,444 the four 4s are worth 4,000, 400, 40 and 4.
A 0 holds a place: 507 and 57 use the same nonzero digits but are very different numbers.
One-digit whole numbers run from 0 to 9, two-digit numbers from 10 to 99, and three-digit numbers from 100 to 999.
A whole number never starts with 0 unless it is 0 itself, so the smallest four-digit number is 1,000.
Adding the digits gives a quick factor test: the digits of 126 add to 1 + 2 + 6 = 9, so 126 is divisible by both 3 and 9.

Value of a digit

value = digit × place value

digit: the symbol in that position, 0 to 9
place value: what one unit in that position is worth: 1, 10, 100, 1,000, … or 0.1, 0.01, … after the decimal point

In 6,384 the 3 is in the hundreds place, so its value is 3 × 100 = 300. In 2.65 the 6 is in the tenths place, so its value is 6 × 0.1 = 0.6.

Try it: change a digit

Interactive

Press the arrows to change a digit, or select a digit to see its value. Watch the 0 in the thousands place: it keeps the 3 in the ten thousands place.

This interactive needs JavaScript. The worked examples below show the same ideas step by step.

Digit examples, step by step

Example 1: Count the digits and name a place

Warm-up

How many digits does 40,915 have, and which digit is in the thousands place?

List the digits, ignoring the comma: 4, 0, 9, 1, 5. That is 5 digits.
Name the places from the right: ones (5), tens (1), hundreds (9), thousands (0), ten thousands (4).

Answer: 40,915 has 5 digits, and the digit in the thousands place is 0.

Example 2: A digit after the decimal point

Core

What is the value of the digit 7 in 3.472?

Name the places after the decimal point: 4 is in the tenths, 7 in the hundredths, 2 in the thousandths.
Multiply the digit by its place value: 7 × 0.01 = 0.07.

Answer: The value of the 7 is 0.07 (7 hundredths).

Example 3: Build the largest and smallest numbers

Test-style

Use each of the digits 4, 0, 8 and 2 exactly once. What are the largest and the smallest four-digit numbers you can make?

Largest: put the biggest digit in the biggest place, then go down: 8,420.
Smallest: put the smallest digit first, but a four-digit number cannot start with 0.
So start with 2, then use 0, 4, 8 in order: 2,048.

Answer: The largest is 8420 and the smallest is 2048.

Common mistakes

✗ MistakeCalling 10, 25 or 100 digits.

✓ InsteadThey are numbers written with digits: 25 is a two-digit number made of the digits 2 and 5.

Only the ten single symbols 0 to 9 are digits. Every larger number is built from them.

✗ MistakeSaying the 3 in 6,384 is worth 3.

✓ InsteadThe 3 is in the hundreds place, so it is worth 3 × 100 = 300.

A digit’s face value is just the symbol. Its value depends on the place it sits in.

✗ MistakeWriting 0248 as the smallest four-digit number made from 0, 2, 4 and 8.

✓ Instead0248 is really 248, a three-digit number. The smallest four-digit choice is 2,048.

A leading 0 adds no value, so it does not count as a digit of the number.

✗ MistakeSkipping zeros when counting digits: 3,005 has 2 digits.

✓ Instead3,005 has 4 digits: 3, 0, 0 and 5.

Zeros between or after other digits hold places, so they count.

Not to be confused with

Digitvs.Number

A number is an amount; digits are the symbols used to write it. Twenty-five is one number written with two digits, 2 and 5.

Digitvs.Place value

Place value is what a position is worth (ones, tens, hundreds). The digit is the symbol in that position. In 382, the digit 8 sits in the tens place, so it is worth 80.

Quick check: 3 questions

Question 1 of 3

Which digit is in the tens place of 8,615?

Show answer and explanation

Answer: B. Count places from the right: 5 is ones, 1 is tens, 6 is hundreds, 8 is thousands. Picking 6 or 8 counts from the left, and 5 is the ones digit.

Question 2 of 3

What is the value of the 4 in 54,210?

Show answer and explanation

Answer: C. The 4 is in the thousands place, so its value is 4 × 1000 = 4000. 4 is only its face value, and 400 and 40,000 put it one place too far right or left.

Question 3 of 3

How many digits does one million (1,000,000) have?

Show answer and explanation

Answer: D. Write it out: 1 followed by six zeros, so 7 digits. 6 counts only the zeros, 1 counts only the nonzero digit, and 10 confuses the digits with the base.

Digit: frequently asked questions

How many digits are there?

There are ten digits in our number system: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. That is why it is called base ten. With place value, these ten symbols are enough to write any whole number or decimal, however large or small, so no new symbol is ever needed for 10, 11 or 1,000.

Is 0 a digit?

Yes. Zero is one of the ten digits, and it does an important job as a placeholder. In 405 the 0 shows there are no tens, which keeps the 4 in the hundreds place. Without it you would write 45, a much smaller number. A 0 at the very start of a whole number, as in 045, adds nothing.

What is the difference between a digit and a number?

A digit is a single symbol from 0 to 9. A number is an amount, and it can be written with one digit or many. The number 7 is written with one digit, while 7,000 is written with four digits. So every digit names a one-digit number, but most numbers need several digits.

Practice and tools

Rounding CalculatorRound to a chosen digit and place Significant Figures CalculatorCount which digits are significant Binary, Decimal and Hexadecimal ConverterSee the same number written with the digits of other bases

Sources

Updated November 2026·Reviewed by the Effortless Math team·Standards: CCSS 2.NBT.A.1, CCSS 4.NBT.A.1, CCSS 4.NBT.A.2

Cite this entry

Effortless Math Team. “Digit.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/digit/

Flashcard

TermDigit0, 1, 2, 3, 4, 5, 6, 7, 8, 9

DefinitionOne of the ten symbols used to write numbers. 507 has three digits; its 5 is worth 500 because of its place.

Study the full deck

Browse all terms in the Math Dictionary · More number system terms · Random term

NumberA number is an amount or value used to count, measure, order and compare. We write numbers with digits (7), words (seven) or other symbols, but the number itself is the amount: 7 dots, the word seven and the numeral 7 all show the same number. Numbers include whole numbers, fractions, decimals and negatives.Number System · Kindergarten, Grade 1, Grade 2Whole NumberA whole number is 0 or a positive counting number: 0, 1, 2, 3, and so on. Whole numbers do not include fractions, decimals, or negative numbers, so 12 is a whole number but 8.5, 34 and −3 are not. Every whole number is also an integer.Number System · Grade 3, Grade 4, Grade 5Place ValuePlace value is the value of a digit based on its position in a number. In 3,507 the 5 is worth 500, because it sits in the hundreds place. Each place is worth 10 times the place to its right: ones, tens, hundreds, thousands, and after the decimal point, tenths and hundredths.Number System · Grade 3, Grade 4, Grade 5FactorA factor is a number or expression that divides another number or expression evenly, with no remainder. Factors multiply together to make a product: 4 × 6 = 24, so 4 and 6 are factors of 24. Every whole number greater than 1 has at least two factors, 1 and itself.Number System · Grade 4, Grade 5, Grade 6Decimal PointA decimal point is the dot that separates the whole-number part of a number from its fractional part. Digits to its left are ones, tens and hundreds; digits to its right are tenths, hundredths and thousandths. In 46.25 the point sits between 6 ones and 2 tenths, and you read it aloud as “and”.Number System · Grade 4, Grade 5, Grade 6TenthsTenths are the parts you get when one whole is split into 10 equal parts; each part is one tenth, written 110 or 0.1. The tenths place is the first digit to the right of the decimal point, so in 4.7 the 7 means 7 tenths, or 0.7.Number System · Grade 3, Grade 4, Grade 5HundredthsHundredths are the parts you get when one whole is split into 100 equal parts; one hundredth is 1100 or 0.01. The hundredths place is the second digit to the right of the decimal point, so in 3.47 the 7 means 7 hundredths. One cent is one hundredth of a dollar.Number System · Grade 4, Grade 5, Grade 6DecimalA decimal is a number written with a decimal point to show parts of a whole. Decimals use place value to represent tenths, hundredths, thousandths and more: in 3.14, the 1 means 1 tenth and the 4 means 4 hundredths. So 0.75 = 75100, and 0.5 is one half.Number System · Grade 4, Grade 5, Grade 6RoundingRounding replaces a number with a nearby number that is easier to use, to a chosen place value. Look at the digit immediately to the right of that place: 5 or more rounds up, 4 or less rounds down. So 47 rounds to 50 to the nearest ten, and 3.68 rounds to 3.7 to the nearest tenth.Number System · Grade 3, Grade 4, Grade 5Expanded FormExpanded form is a way of writing a number as the sum of the values of its digits. Each digit is multiplied by its place value, so 4072 = 4000 + 70 + 2, or 4 × 1000 + 7 × 10 + 2 × 1. It shows what every digit is worth. Zeros add nothing, so they are usually left out.Number System · Grade 2, Grade 3, Grade 4Scientific NotationScientific notation writes a number as a value from 1 to less than 10 times a power of 10, such as 5.4 × 10³ for 5,400. The exponent records how far the decimal point moved: positive for large numbers and negative for numbers between 0 and 1, as in 0.0062 = 6.2 × 10⁻³.Number System · Grade 8, Algebra 1ZeroZero (0) is the number that represents none or no quantity. It is neither positive nor negative and sits in the middle of the number line, between the negative and positive numbers. Adding zero to a number does not change it, as in 9 + 0 = 9, so zero is called the additive identity.Number System · Grade 3, Grade 4, Grade 5

Digit

What is a digit in math?

Digit in a picture

Formal definition and notation

Key facts

Value of a digit

Try it: change a digit

Digit examples, step by step

Example 1: Count the digits and name a place

Example 2: A digit after the decimal point

Example 3: Build the largest and smallest numbers

Common mistakes

Not to be confused with

Quick check: 3 questions

Digit: frequently asked questions

How many digits are there?

Is 0 a digit?

What is the difference between a digit and a number?

Related terms

Practice and tools

Sources

Flashcard

Login

Login and use all of our services.

Register

Register Fast!

Choose your next math review topic