Place Value in Math: Definition, Chart & Examples

Definitionnoun phrase

What is place value in math?

Place 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.

In Spanish: valor posicional
Also called: digit value, positional value
Grade level: K-5

Grade 3Grade 4Grade 5Grade 6CCSS 4.NBT.A.1CCSS 5.NBT.A.1GED

Place Value in a picture

The same digit is worth more the further left it sits. In 275.38 the 7 is worth 70 because it is in the tens place; the digits’ values add up to the number.

Formal definition and notation

In the base-ten system, a digit d that sits k places to the left of the ones place has the value d × 10^k, and a digit k places to the right of the decimal point has the value d × 110^k. A number equals the sum of the values of its digits, which is its expanded form: 6,275.38 = 6,000 + 200 + 70 + 5 + 0.3 + 0.08. A digit in one place represents 10 times what it represents in the place to its right and 110 of what it represents in the place to its left.

Symbol	Read it as	Meaning
4 × 1000 + 6 × 1	four times one thousand plus six times one	expanded form of 4,006: each digit times its place
10³	ten cubed	1,000, the value of the thousands place
0.01	one hundredth	the value of the hundredths place, 1100

Key facts

Moving one place left multiplies by 10; moving one place right divides by 10. So 700 is 10 times 70.
Zero holds a place: in 305 the 0 shows there are no tens, which keeps the 3 in the hundreds place. Without it you get 35.
Commas split whole numbers into groups of three places (ones, thousands, millions), as in 4,250,000.
Right of the decimal point the places are tenths, hundredths and thousandths. There is no oneths place: in 3.14 the 1 is in the tenths place.
Place value is behind rounding, comparing numbers and lining up digits in column addition.

Value of a digit

value = digit × place value

digit: one of the symbols 0 to 9
place value: 1, 10, 100, 1,000, … to the left of the decimal point; 0.1, 0.01, … to the right

In 8,914 the 9 is in the hundreds place, so its value is 9 × 100 = 900. The same digit is worth 9,000 in 9,814 and 0.9 in 81.94.

Try it: change a digit

Interactive

Use the up and down buttons to change any digit, or select a digit to see its value. Watch the number and its expanded form update.

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

Place Value examples, step by step

Example 1: Value of a digit

Warm-up

What is the value of the 7 in 47,120?

Name the places from the right: 0 ones, 2 tens, 1 hundred, 7 thousands, 4 ten thousands.
The 7 is in the thousands place.
Value: 7 × 1000 = 7000.

Answer: The 7 is worth 7,000.

Example 2: Digits after the decimal point

Core

In 52.684, what is the value of the 6 and of the 8?

After the decimal point the places are tenths, hundredths, thousandths.
The 6 is in the tenths place: 6 × 110 = 0.6.
The 8 is in the hundredths place: 8 × 1100 = 0.08.

Answer: The 6 is worth 0.6 (six tenths) and the 8 is worth 0.08 (eight hundredths).

Example 3: From expanded form, with missing places

Test-style

Write 5 × 10,000 + 3 × 100 + 2 × 1 + 9 × 110 in standard form.

Make one column for each place from ten thousands down to tenths.
Fill in: 5 ten thousands, 0 thousands, 3 hundreds, 0 tens, 2 ones, 9 tenths.
The thousands and tens places are empty, so they get zeros.
Read the digits in order: 50,302.9.

Answer: The number is 50,302.9.

Common mistakes

✗ MistakeIn 70, the digit 7 is worth 7.

✓ InsteadThe 7 is in the tens place, so it is worth 7 × 10 = 70.

A digit and its value are not always the same. In 70, the digit 7 has value 70.

✗ MistakeFour thousand six is written 46.

✓ Instead4,006: 4 thousands, 0 hundreds, 0 tens, 6 ones.

Every place between the first digit and the last needs a digit, so empty places get 0.

✗ Mistake0.125 is greater than 0.5, because 125 is greater than 5.

✓ InsteadCompare tenths first: 0.125 has 1 tenth and 0.5 has 5 tenths, so 0.5 is greater.

Line the numbers up by place value. More digits after the decimal point does not mean a bigger number.

Not to be confused with

Place Valuevs.Digit

A digit is one of the ten symbols 0 to 9. Place value is what that digit is worth where it sits: the digit 4 has value 400 in 3,415.

Place Valuevs.Decimal

A decimal is a number written with a decimal point, like 2.75. Place value is the rule that gives each of its digits a value: the 7 is 7 tenths.

Place Valuevs.Expanded form

Expanded form writes a number as the sum of its digits’ values: 352 = 300 + 50 + 2. It uses place value; it is not a different idea.

Quick check: 3 questions

Question 1 of 3

What is the value of the 9 in 29,156?

Show answer and explanation

Answer: C. From the right: 6 ones, 5 tens, 1 hundred, 9 thousands. So the 9 is worth 9,000. Choice A gives only the digit, and B and D put it one place too far right or left.

Question 2 of 3

Which digit is in the hundredths place of 85.736?

Show answer and explanation

Answer: B. After the decimal point come tenths (7), hundredths (3) and thousandths (6), so the answer is 3. Choice A is the tenths digit, C the thousandths digit and D the ones digit.

Question 3 of 3

The 4 in 640 is how many times the value of the 4 in 64?

Show answer and explanation

Answer: A. In 640 the 4 is worth 40; in 64 it is worth 4. 40 ÷ 4 = 10: one place to the left is 10 times as much. Choice B is two places, and D compares them the wrong way round.

Place Value: frequently asked questions

What are the place values in order?

From right to left for whole numbers: ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions, and so on, each 10 times the one before. After the decimal point, from left to right: tenths, hundredths, thousandths, ten-thousandths, each 110 of the one before. The ones place sits just left of the decimal point.

Why is place value important?

It lets just ten digits, 0 to 9, write any number. The position of a digit tells its size, so 507 and 750 use the same digits but mean different amounts. Place value is also what makes column addition, regrouping, rounding, comparing decimals and multiplying by 10 work.

What is the difference between face value and place value?

Face value is the digit itself; place value (the value of the digit) depends on where it sits. In 4,825 the 8 has face value 8 and is in the hundreds place, so its value is 800. The face value of a digit never changes, but its value changes every time it moves one place.

Practice and tools

Effortless Math practicePractice on Effortless Math Rounding CalculatorRound to any place value Scientific Notation ConverterPlace value with powers of 10

Sources

Updated November 2026·Reviewed by the Effortless Math team·Standards: CCSS 4.NBT.A.1, CCSS 5.NBT.A.1

Cite this entry

Effortless Math Team. “Place Value.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/place-value/

Flashcard

TermPlace Valuewhere a digit sits

DefinitionA digit’s value depends on its position. In 482 the 8 is in the tens place, so it is worth 80.

Study the full deck

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

Decimal 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 6NumberA 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 2Expanded 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 4HundredthsHundredths 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 6Whole 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 5TenthsTenths 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 5RoundingRounding 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 5AdditionAddition is the operation that puts amounts together to find the total. The numbers you add are called addends, the answer is the sum, and the sign is the plus sign, +. For example, 7 + 5 = 12. On a number line, adding a positive number means moving to the right.Operations · Kindergarten, Grade 1, Grade 2Standard FormStandard form of a number is the usual way of writing it with digits, such as 4,306, with each digit in its place-value position. It is the short form you get from expanded form (4,000 + 300 + 6) or from word form (four thousand, three hundred six). Zeros hold any empty places.Number System · Grade 2, Grade 3, Grade 4DigitA 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.Number System · Grade 1, Grade 2, Grade 3DecimalA 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 6RegroupingRegrouping is trading 10 of one place value for 1 of the next larger place, or 1 for 10 of the next smaller place, so that column addition or subtraction works. In 47 + 38, the 15 ones become 1 ten and 5 ones; in 52 − 27, 1 ten becomes 10 ones. It is also called carrying and borrowing.Operations · Grade 1, Grade 2, Grade 3EstimateAn estimate is an answer that is close to the exact one, and to estimate is to find an answer that is close enough, usually by rounding or using friendly numbers. For example, 49 × 21 is about 50 × 20 = 1000. Estimation helps you check whether an exact answer is reasonable.Problem Solving · Grade 3, Grade 4, Grade 5Scientific 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 1ExponentAn exponent tells how many times to use a base as a factor. It is the small raised number to the upper right of the base: in 5³, the base is 5 and the exponent is 3, so 5³ = 5 × 5 × 5 = 125. Any nonzero number with an exponent of 0 equals 1.Algebra · Grade 6, Grade 7, Grade 8

Place Value

What is place value in math?

Place Value in a picture

Formal definition and notation

Key facts

Value of a digit

Try it: change a digit

Place Value examples, step by step

Example 1: Value of a digit

Example 2: Digits after the decimal point

Example 3: From expanded form, with missing places

Common mistakes

Not to be confused with

Quick check: 3 questions

Place Value: frequently asked questions

What are the place values in order?

Why is place value important?

What is the difference between face value and place value?

Related terms

Practice and tools

Sources

Flashcard

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