Number basics
Place Value
Place value is the value a digit has because of where it sits in a number. In 555, the same digit is worth 500, 50 and 5. Each place is worth ten times the place to its right. This guide has place value charts for whole numbers up to billions and for decimal places down to thousandths and beyond, plus expanded form, comparing and rounding by place, and the mistakes people make.
What place value means
Our number system uses only ten digits, 0 through 9. It can still write any number because a digit’s position multiplies its worth. Moving one place to the left makes a digit worth 10 times as much; moving one place to the right makes it worth one tenth as much.
This is called a base-ten (decimal) system, because ten of one place make one of the next place up: ten ones make a ten, ten tens make a hundred, ten hundreds make a thousand. The same rule runs the other way past the decimal point: ten hundredths make a tenth, and ten tenths make a one.
Place value applies to every whole number and every decimal. It also explains where a decimal sits on a number line: 2.7 is 2 ones and 7 tenths, so it lies seven tenths of the way from 2 to 3.
Zero is what makes the system work. In 4,082, the 0 says “no hundreds” and holds the 4 in the thousands place. Without it, 4,082 would collapse to 482.
You can watch place value at work on any online four function calculator: multiply 37 by 10 and each digit moves one place to the left, giving 370.
Place value chart for whole numbers
Whole-number places are grouped in threes, called periods: ones, thousands, millions, billions. Each period has a hundreds, tens and ones place of its own. In the US, commas separate the periods.
| Period | Place | Value | Digit in 3,482,915,067 | Worth |
|---|---|---|---|---|
| Billions | Billions | 1,000,000,000 | 3 | 3,000,000,000 |
| Millions | Hundred millions | 100,000,000 | 4 | 400,000,000 |
| Millions | Ten millions | 10,000,000 | 8 | 80,000,000 |
| Millions | Millions | 1,000,000 | 2 | 2,000,000 |
| Thousands | Hundred thousands | 100,000 | 9 | 900,000 |
| Thousands | Ten thousands | 10,000 | 1 | 10,000 |
| Thousands | Thousands | 1,000 | 5 | 5,000 |
| Ones | Hundreds | 100 | 0 | 0 |
| Ones | Tens | 10 | 6 | 60 |
| Ones | Ones | 1 | 7 | 7 |
To read a long number, read each period as a three-digit number and then say the period name: “three billion, four hundred eighty-two million, nine hundred fifteen thousand, sixty-seven.” The ones period is read without a name.
A million has 6 zeros (1,000,000) and a billion has 9 (1,000,000,000) in US usage. Beyond that come trillions, with 12 zeros. For numbers too long to handle comfortably, scientific notation writes them as a power of ten, and the big number calculator does exact arithmetic on them.
Decimal place value
Decimal place value continues the same pattern to the right of the decimal point. Each place is one tenth of the place to its left, and the place names end in -ths.
| Place | As a fraction | As a decimal | Digit in 4,036.275 | Worth |
|---|---|---|---|---|
| Thousands | 1,000 | 1,000 | 4 | 4,000 |
| Hundreds | 100 | 100 | 0 | 0 |
| Tens | 10 | 10 | 3 | 30 |
| Ones | 1 | 1 | 6 | 6 |
| decimal point | ||||
| Tenths | 1/10 | 0.1 | 2 | 0.2 |
| Hundredths | 1/100 | 0.01 | 7 | 0.07 |
| Thousandths | 1/1,000 | 0.001 | 5 | 0.005 |
| Ten-thousandths | 1/10,000 | 0.0001 | — | — |
Notice the pattern is symmetric around the ones place, not around the decimal point. Tens mirror tenths, hundreds mirror hundredths, thousands mirror thousandths. There is no “oneths” place — the first place after the point is tenths.
The fraction column explains how decimals convert to fractions. 0.275 is 275 thousandths, or 275/1000, which simplifies to 11/40. The decimal to fraction calculator does that for any decimal. Money uses two decimal places: in $8.43, the 4 is 4 dimes (tenths of a dollar) and the 3 is 3 cents (hundredths).
Standard, expanded and word form
The same number can be written three ways, and moving between them is the most common place value exercise.
- Standard form: 4,036.275
- Expanded form: each digit times its place value, added up.
- Word form: four thousand thirty-six and two hundred seventy-five thousandths.
Expanded form can also be written with fractions (2 × 1/10 + 7 × 1/100 + 5 × 1/1,000) or powers of ten (4 × 10³ + 3 × 10¹ + 6 × 10⁰ + 2 × 10⁻¹ …). Zero digits can be left out of the sum, as in the second line, because they add nothing.
Reading decimals aloud
Say the whole-number part, say “and” for the decimal point, then read the decimal digits as one number and name the last place. 0.36 is “thirty-six hundredths”; 12.5 is “twelve and five tenths”; 0.008 is “eight thousandths”. Use “and” only for the decimal point: 305 is “three hundred five”, not “three hundred and five”, in careful US usage.
Place, value and face value
Three words get mixed up. For the digit 7 in 274,615.38:
- Its place is the ten-thousands place.
- Its value is
7 × 10,000 = 70,000. - Its face value is just 7, the digit itself.
| Digit in 274,615.38 | Place | Value |
|---|---|---|
| 2 | Hundred thousands | 200,000 |
| 7 | Ten thousands | 70,000 |
| 4 | Thousands | 4,000 |
| 6 | Hundreds | 600 |
| 1 | Tens | 10 |
| 5 | Ones | 5 |
| 3 | Tenths | 0.3 |
| 8 | Hundredths | 0.08 |
Add the value column and you get the number back: 274,615.38. That check works on any number and catches a misread place quickly.
Multiplying and dividing by 10, 100 and 1,000
Because each place is ten times the next, multiplying by 10 moves every digit one place to the left, and dividing by 10 moves every digit one place to the right. In practice that looks like the decimal point moving, by one place for each zero.
This shift is the first step of dividing decimals, where you move the point in both numbers until the divisor is whole, and it is the basis of converting a percent to a decimal: 37.5% is 37.5 ÷ 100 = 0.375.
Place value is also behind carrying and borrowing. When a column adds to 10 or more, you carry because ten of that place make one of the next. In long division, each step works on one place at a time, which is why you bring down one digit at a time.
Comparing and rounding by place value
Comparing decimals
Line the numbers up by the decimal point and compare place by place from the left. The first place where the digits differ decides it. More digits does not mean bigger.
Adding zeros on the right of a decimal does not change its value, which is why 0.5 and 0.500 are equal. That is what makes the lining-up step safe.
Rounding to a place
To round, find the place you are rounding to and look at the digit one place to its right. If it is 5 or more, round up; if it is 4 or less, keep the digit.
The rounding calculator shows every rounding place at once, rounding to decimal places covers the cents and hundredths cases in detail, and significant figures rules explains the related idea of counting meaningful digits rather than places.
Common mistakes
- Tens vs tenths. Tens are to the left of the ones place; tenths are to the right of the decimal point. In 30.3 the first 3 is worth 30 and the second is worth 0.3.
- Looking for a “oneths” place. It does not exist. The first decimal place is tenths.
- Thinking longer decimals are bigger. 0.405 is less than 0.45. Compare place by place, not by length.
- Dropping placeholder zeros. 5.06 is not 5.6. The 0 holds the tenths place empty so the 6 stays in the hundredths.
- Saying “and” inside whole numbers. In careful US usage “and” marks the decimal point, so “two hundred and five” can be misheard as 200.5.
- Miscounting zeros in big numbers. Use the periods: a million is 1 followed by two periods of zeros (6 zeros), a billion by three (9 zeros).
Frequently asked questions
What is place value?
Place value is the worth of a digit based on its position in a number. Each place is worth 10 times the place to its right: ones, tens, hundreds, thousands and so on, and tenths, hundredths and thousandths after the decimal point. In 352, the 3 is worth 300 because it is in the hundreds place.
What is the place value of 7 in 4,732?
The 7 in 4,732 is in the hundreds place, so its value is 7 × 100 = 700. Reading from the right, 2 is in the ones place, 3 in the tens place, 7 in the hundreds place and 4 in the thousands place, giving 4,000 + 700 + 30 + 2.
What is the value of the digit 5 in 0.356?
The 5 in 0.356 is in the hundredths place, so its value is 5 × 0.01 = 0.05, or 5/100. The 3 is in the tenths place (0.3) and the 6 is in the thousandths place (0.006). Together, 0.3 + 0.05 + 0.006 = 0.356.
What is decimal place value?
Decimal place value is the value of digits to the right of the decimal point. The first place is tenths (0.1), then hundredths (0.01), thousandths (0.001) and ten-thousandths (0.0001). Each place is one tenth of the place to its left, following the same base-ten pattern as whole numbers.
What comes after the thousandths place?
After thousandths comes the ten-thousandths place (0.0001), then hundred-thousandths (0.00001) and millionths (0.000001). The names mirror the whole-number places with “-ths” added, and each place is one tenth the size of the place before it.
Is 0.5 the same as 0.50?
Yes. 0.5 and 0.50 are equal: five tenths and fifty hundredths are the same amount, since 5/10 = 50/100. Zeros added to the right end of a decimal do not change its value. They can show precision in measurements, and they help when lining up decimals to compare them.
What is the hundredths place?
The hundredths place is the second digit to the right of the decimal point. A digit there is worth that many hundredths: in 6.48, the 8 is worth 8/100 = 0.08. In money, the hundredths place holds the cents, so rounding to the nearest cent means rounding to the hundredths place.
How many zeros are in a million?
A million has six zeros: 1,000,000. That is two full periods of three zeros after the 1. A thousand has three zeros, a billion has nine (1,000,000,000) and a trillion has twelve in US usage. Each period name is 1,000 times the one before it.
Calculators for this
Every one of these shows the working, so you can check the method as well as the answer.
More guides
https://fourfunctioncalculator.com/place-value/