**Introduction**

As a basic number system, we use decimals. The number 10 is the basis of the decimal system. It is sometimes referred to as a base-10 number system.

We will cover in this article more about the decimal place value and place value of tenths, hundredths, and thousandths.

**What is a place value?**

**Definition**

A digit’s position within a number determines its place value. It sets the value the number represents.

Let us say, for example; we have 1, 10, 100, and 1000.

1: ones place

10: tens place

100: hundreds place

1000: thousands place

The place value of 1 represents the value it holds. As the place value moves to the left, the value of the number becomes greater by 10 times.

The image below shows the place value from millions to ones.

**Decimal Place Value**

The decimal place value shows the parts of a number less than 1. They appear to the right of the decimal point. Each place gets ten times smaller moving from left to right. After the decimal point, the decimal place values are tenths, hundredths, thousandths, and so on.

From the decimal point, the first digit is the tenths place.

From the decimal point, the second digit is the hundredths place.

From the decimal point, the third digit is the thousandths place.

Let us say, for example; we have the number 2.345.

Ones | Decimal Point | Tenths | Hundredths | Thousandths |

2 | . | 3 | 4 | 5 |

2 is the digit which is a whole number.

3 is 3 tenths and represents $\frac{3}{10}$.

4 is 4 hundredths and represents $\frac{4}{100}$.

5 is 5 thousandths and represents $\frac{5}{1000}$.

For another example, let us have the number 7.654.

Ones | Decimal Point | Tenths | Hundredths | Thousandths |

7 | . | 6 | 5 | 4 |

7 is the digit which is a whole number.

6 is 6 tenths and represents $\frac{6}{10}$.

5 is 5 hundredths and represents $\frac{5}{100}$.

4 is 4 thousandths and represents $\frac{4}{1000}$.

**Decimal Point**

**Definition**

The decimal point, which separates a number’s whole number part from its fractional part, is a dot. The decimal numbers to the right of the decimal point have values that are less than one.

Let us say, for example; we have 0.1, 0.01, and 0.001.

0.1: tenths

0.01: hundredths

0.001: thousandths

Since the decimal point is like a fraction, 0.1 is $\frac{1}{10}$, 0.01 is $\frac{1}{100}$, and 0.001 is $\frac{1}{1000}$.

The image below shows the decimal place values tenths, hundredths, thousandths, ten thousandths, hundred thousandths, and millionths.

Thousandths is the place value that appears as the third digit right after the decimal point. Its value is less than one or represents a fractional number. It is 1/1000 position of the digit. Therefore, it is 1 ÷ 1000 = 0.001, which is 1 thousandth.

**Tenths**

Tenths is the place value that appears right after the decimal point. Its value is less than one or represents a fractional number. It is 1/10 position of the digit. Therefore, it is 1 ÷ 10 = 0.1, which is 1 tenth.

As shown below, from the decimal point, the first digit is the tenths place.

Ones | Decimal Point | Tenths |

0 | . | 2 |

The digits in the tenths place can be written as a fraction out of 10. Hence, 0.2 is 2 tenths which is $\frac{2}{10}$ as a fractional number.

As for more examples, let us write the following numbers as fractions.

( a ) 0.4

( b ) 0.6

( c ) 0.9

( d ) 0.7

( e ) 0.5

**Answers**

( a ) 0.4 is read as 4 tenths. It is equal to $\frac{4}{10}$.

( b ) 0.6 is read as 6 tenths. It is equal to $\frac{6}{10}$.

( c ) 0.9 is read as 9 tenths. It is equal to $\frac{9}{10}$.

( d ) 0.7 is read as 7 tenths. It is equal to $\frac{7}{10}$.

( e ) 0.5 is read as 5 tenths. It is equal to $\frac{5}{10}$.

**Hundredths**

Hundredths is the place value that appears as the second digit right after the decimal point. Its value is less than one or represents a fractional number. It is 1/100 position of the digit. Therefore, it is 1 ÷ 100 = 0.01, which is 1 hundredth.

Starting from the decimal point, the second column to the right is the hundredths place, as shown in the table below.

Ones | Decimal Point | Tenths | Hundredths |

0 | . | 0 | 2 |

The digits in the hundredths place can be written as a fraction out of 100. Hence, 0.02 is 2 hundredths which is $\frac{2}{100}$ as a fractional number.

As for more examples, let us write the following numbers as fractions.

( a ) 0.05

( b ) 0.08

( c ) 0.03

( d ) 0.07

( e ) 0.04

**Answers**

( a ) 0.05 is read as 5 hundredths. It is equal to $\frac{5}{100}$.

( b ) 0.08 is read as 8 hundredths. It is equal to $\frac{8}{100}$.

( c ) 0.03 is read as 3 hundredths. It is equal to $\frac{3}{100}$.

( d ) 0.07 is read as 7 hundredths. It is equal to $\frac{7}{100}$.

( e ) 0.04 is read as 4 hundredths. It is equal to $\frac{4}{100}$.

**Thousandths**

Thousandths is the place value that appears as the third digit right after the decimal point. Its value is less than 1 or represents a fractional number. It is 1/1000 position of the digit. Therefore, it is 1 ÷ 1000 = 0.001, which is 1 thousandth.

As shown in the table below, from the decimal point, the thousandths place is the third digit.

Ones | Decimal Point | Tenths | Hundredths | Thousandths |

0 | . | 0 | 0 | 2 |

The digits in the thousandths place can be written as a fraction out of 1000. Hence, 0.002 is 2 thousandths which is $\frac{2}{1000}$ as a fractional number.

As for more examples, let us write the following numbers as fractions.

( a ) 0.007

( b ) 0.009

( c ) 0.005

( d ) 0.003

( e ) 0.006

**Answers**

( a ) 0.007 is read as 7 thousandths. It is equal to $\frac{7}{1000}$.

( b ) 0.009 is read as 9 thousandths. It is equal to $\frac{9}{1000}$.

( c ) 0.005 is read as 5 thousandths. It is equal to $\frac{5}{1000}$.

( d ) 0.003 is read as 3 thousandths. It is equal to $\frac{3}{1000}$.

( e ) 0.006 is read as 6 thousandths. It is equal to $\frac{6}{1000}$.

**Place Value of Tenths, Hundredths, and Thousandths**

The figure shows the place value table for tenths, hundredths, and thousandths.

Ones | Decimal Point | Tenths | Hundredths | Thousandths |

0 | . | 1/10 | 1/100 | 1/1000 |

Tenths is the place value that appears right after the decimal point. Its value is less than 1 or represents a fractional number. It is 1/10 position of the digit.

Hundredths is the place value that appears as the second digit right after the decimal point. Its value is less than 1 or represents a fractional number. It is 1/100 position of the digit.

Thousandths is the place value that appears as the third digit right after the decimal point. Its value is less than 1 or represents a fractional number. It is 1/1000 position of the digit.

For example, let us write each number in a place value chart:

( a ) 3.7

( b ) 12. 6

( c ) 75. 87

( d ) 938. 047

( e ) 867.076

Answers:

Given | Thousands | Hundreds | Ones | Decimal Point | Tenths | Hundredths | Thousandths |

3.7 | 3 | . | 7 | ||||

12.6 | 1 | 2 | . | 6 | |||

75.87 | 7 | 5 | . | 8 | 7 | ||

938.047 | 9 | 3 | 8 | . | 0 | 4 | 7 |

867.076 | 8 | 6 | 7 | . | 0 | 7 | 6 |

**More Examples**

**Example 1**

Write the place value of each digit.

( a ) 56.389

( b ) 217.936

( c ) 6.143

( d ) 837.124

**Solution**

( a ) 56.389

In 56.389, the place value of 5 holds 5 tens or 50.

The place value of 6 is 6.

The place value of 3 is 3 tenths or $\frac{3}{10}$.

The place value of 8 is 8 hundredths or $\frac{8}{100}$.

The place value of 9 is 9 thousandths or $\frac{9}{1000}$.

( b ) 217.936

In 217.936, the place value of 2 holds 2 hundreds or 200.

The place value of 1 is 1 ten or 10.

The place value of 7 is 7.

The place value of 9 holds 9 tenths or $\frac{3}{10}$}.

The place value of 3 holds 3 hundredths or $\frac{3}{100}$.

The place value of 6 holds 6 thousandths or $\frac{6}{1000}$.

( c ) 6.143

The place value of 6 is 6.

The place value of 1 holds 1 tenth or $\frac{9}{10}$.

The place value of 4 is 4 hundredths or $\frac{3}{100}$.

The place value of 3 holds 3 thousandths or $\frac{3}{1000}$.

( d ) 837.124

The place value of the digit 8 holds 8 hundreds or 800.

The place value of the digit 3 holds 3 tens or 30.

The place value of 7 is 7.

The place value of 1 is 1 tenth or $\frac{1}{10}$.

The place value of 2 holds 2 hundredths or $\frac{2}{100}$.

The place value of 4 is 4 thousandths or $\frac{4}{1000}$.

**Example 2**

Write each number in the place value table.

( a ) 0.968

( b ) 12.859

( c ) 47.028

( d ) 348.956

( e ) 274.018

**Solution**

Remember that the digits of the whole number part start from the right to left before the decimal point. On the other hand, the place value of the fractional part appears after the decimal point.

Given | Thousands | Hundreds | Ones | Decimal Point | Tenths | Hundredths | Thousandths |

0.968 | . | 9 | 6 | 8 | |||

12.859 | 1 | 2 | . | 8 | 5 | 9 | |

47.028 | 4 | 7 | . | 0 | 2 | 8 | |

348.956 | 3 | 4 | 8 | . | 9 | 5 | 6 |

274.018 | 2 | 7 | 4 | . | 0 | 1 | 8 |

**Example 3**

Identify the place value of the digit 5 in each decimal.

( a ) 487.509

( b ) 62.957

( c ) 1.295

( d ) 76.3859

( e ) 298.1905

**Solution**

( a ) 487.509

The place value of 5 in 487.509 is 5 tenths or $\frac{5}{10}$.

( b ) 62.957

The place value of 5 in 62.957 is 5 hundredths or $\frac{5}{100}$.

( c ) 1.295

The place value of 5 in 1.295 is 5 thousandths or $\frac{5}{1000}$.

( d ) 76.3859

The place value of 5 in 76.3859 is 5 thousandths or $\frac{5}{1000}$.

( e ) 298.1905

The place value of 5 in 298.1905 is 5 ten thousandths or $\frac{5}{10000}$.

**Example 4**

Identify the place value of the underlined digit in each number below.

( a ) 283.0**5**8

( b ) 12.93**8**

( c ) 2. **3**896

( d ) 23.4**9**87

( e ) 384.927**1**

**Solution**

( a ) 283.0**5**8

The place value of 5 in 283.0**5**8 is 5 hundredths or $\frac{5}{100}$.

( b ) 12.93**8**

The place value of 8 in 12.93**8** is 8 thousandths or $\frac{8}{1000}$.

( c ) 2. **3**896

The place value of 3 in 2.3896 is 3 tenths or $\frac{3}{10}$.

( d ) 23.4**9**87

The place value of 9 in 23.4**9**87 is 9 hundredths or $\frac{9}{100}$.

( e ) 384.927**1**

The place value of 1 in 384.9271 is 1 ten thousandth or $\frac{1}{10000}$.

**Example 5**

In the number 298.734, write the decimal value of each digit.

**Solution**

The place value of 2 holds 2 hundreds or 200.

The place value of 9 is 9 tens or 90.

The place value of 8 is 8.

The place value of 7 holds 7 tenths (0.7) or $\frac{1}{10}$.

The place value of 3 holds 3 hundredths (0.03) or $\frac{3}{100}4.

The place value of 4 is 4 thousandths (0.004) or $\frac{4}{1000}$.

**Summary **

A digit’s position within a number determines its **place value**. It sets the value the number represents.

The **decimal point**, which separates a number’s whole number part from its fractional part, is a dot. The digits to the right of the decimal point have values that are less than one.

**Tenths** is the place value that appears right after the decimal point. Its value is less than 1 or represents a fractional number. It is 1/10 position of the digit.

**Hundredths** is the place value that appears as the second digit right after the decimal point. Its value is less than 1 or represents a fractional number. It is 1/100 position of the digit.

**Thousandths** is the place value that appears as the third digit right after the decimal point. Its value is less than 1 or represents a fractional number. It is 1/1000 position of the digit.

The table below shows the place value table for tenths, hundredths, and thousandths.

Ones | Decimal Point | Tenths | Hundredths | Thousandths |

0 | . | 1/10 | 1/100 | 1/1000 |

**Frequently Asked Questions on the Place Value of Tenths, Hundredths, and Thousandths**

**What is a place value chart?**

A table that helps in determining each digit’s place value based on where it appears in the number is known as a place value chart.

The place value chart shows the whole numbers and the fractional part of the number.

The decimal point ( . ) is the symbol that separates the whole numbers and those less than 1 in value.

**Whole numbers**

The ones place, starting from the decimal point, is the first digit to the left.

The tens place, starting from the decimal point, is the second digit to the left.

The hundreds place, starting from the decimal point, is the third digit to the left.

The thousands place, starting from the decimal point, is the fourth digit to the left.

The ten thousands place is the fifth digit to the left of the decimal point.

The hundred thousands place, starting from the decimal point, is the sixth digit to the left and so on.

**Fractional Part**

From the decimal point, the first digit to the right is the tenths place. It is 1/10 position of the digit.

From the decimal point, the second digit to the right is the hundredths place. It is 1/100 position of the digit.

From the decimal point, the third digit to the right is the thousandths place. It is 1/1000 position of the digit.

From the decimal point, the fourth digit to the right is the ten thousandths place. It is 1/10000 position of the digit.

From the decimal point, the fifth digit to the right is the hundred thousandths place. It is 1/100000 position of the digit.

100000 | 10000 | 1000 | 100 | 10 | . | $\frac{1}{10}$ | $\frac{1}{100}$ | $\frac{1}{1000}$ | $\frac{1}{10000}$ | $\frac{1}{100000}$ |

Hundred Thousands | Ten Thousands | Thousands | Tens | Ones | Decimal Point | Tenths | Hundredths | Thousandths | Ten Thousandths | Hundred Thousandths |

**How do tens place and tenths place differ from one another?**

From the decimal point, the first digit to its right is the tenths place while the second digit to its left is the tens place.

For example, for the number 123.456, digit 2 holds the tens place while digit 4 holds the tenths place.

Hundreds | Tens | Ones | Decimal Point | Tenths | Hundredths | Thousandths |

1 | 2 | 3 | . | 4 | 5 | 6 |

**What is the difference between hundreds place and hundredths place?**

From the decimal point, the second digit to its right is the hundredths place while the third digit to its left is the hundreds place.

For example, for the number 123.456, the digit 1 holds the hundreds place while the digit 5 holds the hundredths place.

Hundreds | Tens | Ones | Decimal Point | Tenths | Hundredths | Thousandths |

1 | 2 | 3 | . | 4 | 5 | 6 |

**What is the difference between thousands place and thousandths place?**

From the decimal point, the third digit to its right is the thousandths place while the fourth digit to its left is the thousands place.

For example, for the number 7123.456, the digit 7 holds the thousands place while the digit 6 holds the thousandths place.

Thousands | Hundreds | Tens | Ones | Decimal Point | Tenths | Hundredths | Thousandths |

7 | 1 | 2 | 3 | . | 4 | 5 | 6 |

**How do you write 1 tenth, 1 hundredth, and 1 thousandth?**

Tenths is the place value that appears right after the decimal point. Its value is less than 1 or represents a fractional number. It is 1/10 position of the digit. Therefore, it is 1 ÷ 10 = 0.1, which is 1 tenth.

Hundredths is the place value that appears as the second digit right after the decimal point. Its value is less than 1 or represents a fractional number. It is 1/100 position of the digit. Therefore, it is 1 ÷ 100 = 0.01, which is 1 hundredth.

Thousandths is the place value that appears as the third digit right after the decimal point. Its value is less than 1 or represents a fractional number. It is 1/1000 position of the digit. Therefore, it is 1 ÷ 1000 = 0.001, which is 1 thousandth.

**What distinguishes the fractional and whole number parts of the place value chart?**

Starting from the decimal point, the digits to the left stand in for the whole number part, while the digits to the right represent the fractional part.

100000 | 10000 | 1000 | 100 | 10 | . | $\frac{1}{10}$ | $\frac{1}{100}$ | $\frac{1}{1000$ | $\frac{1}{10000}$ | $\frac{1}{100000}$ |

Hundred Thousands | Ten Thousands | Thousands | Tens | Ones | Decimal Point | Tenths | Hundredths | Thousandths | Ten Thousandths | Hundred Thousandths |

**Whole numbers**

The ones place, starting from the decimal point, is the first digit to the left.

The tens place, starting from the decimal point, is the second digit to the left.

The hundreds place, starting from the decimal point, is the third digit to the left.

The thousands place is the fourth digit to the left of the decimal point.

The ten thousands place is the fifth digit to the left of the decimal point.

The hundred thousand place, starting from the decimal point, is the sixth digit to the left.

**Fractional Part**

The tenths place, starting from the decimal point, is the first digit to the right. It is 1/10 position of the digit.

The hundredths place, starting from the decimal point, is the second digit to the right. It is 1/100 position of the digit.

The thousandths place, starting from the decimal point, is the third digit to the right. It is 1/1000 position of the digit.

The ten thousandths place, starting from the decimal point, is the fourth digit to the right. It is 1/10000 position of the digit.

The hundred thousandths place is the fifth digit to the right of the decimal point. It is 1/100000 position of the digit.

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