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# Decimal Place Value

Just like whole numbers (or integers), decimal numbers also have **place value** and a corresponding **number word**. The place value of decimal numbers also allows you to know the number word of a decimal number. In other words, the number word of a decimal comes from its place value.

Let's look at the decimal number **4.25** which we can also write as **four and twenty five hundredths**. This number has both whole and a fractional parts. **The "and" represents the decimal point**. It is made up of:

**4 ones (4 x 1)**

**2 tenths (2 x 0.1)**

**5 hundredths (5 x 0.01)**

For this you may want to refer to the place value chart below:

First, let's look at some decimal numbers and see how they are expressed in words.

**Example 1)**

**0.4**is made up of

**4 tenths (4 x 0.1)**

The **number word **for 0.4 is **four tenths** and is the same as its **place value**.That is because the digit **4** is in the **tenths** place.

Remember, when dealing with decimals with the place value of tenths like 0.4 there are equivalent decimals to 0.4 such as to 0.40 (forty hundredths) and 0.400 (four thousandths), etc.

**Example 2)**

**0.65**is made up of

**6 tenths (6 x 0.1)**

**5 hundredths (5 x 0.01)**

The **number word** for 0.65 is **sixty-five hundredths** and is the same as its place value.

That is because the number 65 is to the right of the decimal point, indicating the decimal in the **hundredths** place.

**Example 3)**

**0.875**is made up of

**8 tenths (8 x 0.1)**

**7 hundredths (7 x .01)**

5 thousandths (5 x 0.001)

5 thousandths (5 x 0.001)

The **number word** for 0.875 is **eight hundred seventy-five thousandths**.That is because the number 875 is to the right of the decimal point,indicating the decimal in the **thousandths** place.

**Example 4)**

**2 ones (2 x 1)**

**8 tenths (8 x 0.1)**

1 hundredths (1 x 0.01)

1 hundredths (1 x 0.01)

The **number word** for 2.81 is **two and eighty-one hundredths**.That is because there are 2 whole parts and 81 fractional parts. The "and" represents the decimal point.

**Example 5)**

**34.24**is made up of

**3 tens (3 x 10)**

**4 ones (4 x 1)**

2 tenths (2 x 0.1)

4 hundredths(4 x 0.01)

2 tenths (2 x 0.1)

4 hundredths(4 x 0.01)

The **number word** for 34.24 is **thirty-four and twenty four hundredths**.That is because there are 34 whole parts and 24 fractional parts. The "and" represents the decimal point.

**Example 6)**

**168.973**is made up of

**1 hundred (1 x 100)**

6 tens (6 x 10) 8 ones (8 x 1)

9 tenths (9 x 0.1) 7 hundredths (7 x 0.01)

6 tens (6 x 10) 8 ones (8 x 1)

9 tenths (9 x 0.1) 7 hundredths (7 x 0.01)

**3 thousandths (3 x 0.001)**

The **number word** for 168.973 is **one hundred sixty-eight and nine hundred seventy-three thousandths**.That is because there are 168 whole parts and 973 fractional parts. The "and" represents the decimal point.

Now let's look at number words and understand how they are expressed as decimals. Examine the chart below to see how the number word is expressed as a decimal:

As you can see, the number word simply expresses each decimal as its place value.

Notice how the word **"and"** is only used when there are both whole numbers and fractional parts. The word **"and"** shows there is a fractional part: it represents the decimal point.

Let's practice identifying the place value of decimal numbers and their number words.

Look at how many digits are to the right of the decimal. There is only one digit to the right of the decimal. The 6 is the only digit to the right, so the decimal is in the **tenths** place. Write the number 6 as a word (six) and then the word tenths.

Answer: six tenths

Look at how many digits are to the right of the decimal. There are two digits to the right of the decimal. Two digits (7 and 5) are to the right of the decimal, making the decimal in the **hundredths** place. Write the number 75 as a word (seventy-five) and then the word hundredths.

Answer: seventy-five hundredths

Look at how many digits are to the right of the decimal. There are three digits to the right of the decimal. Three digits (3, 1 and 6) to the right of the decimal make the decimal in the **thousandths** place. Write the number 316 as a word (three hundred sixteen) and then the word thousandths.

Answer: three hundred sixteen thousandths

Look at how many digits are to the left and right of the decimal. There is one digit to the left and two digits to the right of the decimal. The digit 5 is to the left indicating it has 5 **ones**. Two digits (1 and 6) to the right of the decimal make the fractional portion in the **hundredths** place. Write the number 5 as a word (five), then write the word **and** which represents the decimal point. To the right of the decimal point, write the number word for 16 (sixteen) and the word hundredths.

Answer: five and sixteen hundredths

Look at how many digits are to the left and right of the decimal. There are two digits to the left and three digits to the right of the decimal. The digits 2 and 1 is to the left indicating it has 2 **tens** and 1 **ones**, or the number 21. Three digits (7, 4 and 5) to the right of the decimal make the fractional portion in the **thousandths** place. Write the number 21 as a word (twenty-one), then write the word **and** which represents the decimal point. To the right of the decimal point, write the number word for 745 (seven hundred forty-five) the word thousandths.

Answer: twenty-one and seven hundred forty-five thousandths

Look at how many digits are to the left and right of the decimal. There are three digits to the left and one digit to the right of the decimal. Three digits (6, 0 and 9) to the left represent the whole number 609. The one digit to the right (4) of the decimal make the fractional portion in the **tenths** place. Write the number 609 as a word (six hundred nine), then write the word **and** which represents the decimal point. To the right of the decimal point, write the number word for 4 (four) and the word tenths.

Answer: twenty-one and seven hundred forty-five thousandths

Since the place value is tenths, just write the word two as the number 2 to the right of a decimal point. There is no whole number (or integer), so place a zero to the left of the decimal point.

Answer: 0.2

Since the place value is hundredths, just write the word twenty-seven as the number 27 to the right of a decimal point. There is no whole number (or integer), so place a zero to the left of the decimal point.

Answer: 0.27

Since the place value is thousandths, just write the word three hundred fifteen as the number 315 to the right of a decimal point. There is no whole number (or integer), so place a zero to the left of the decimal point.

Answer: 0.315

This number word uses "and" and has both whole numbers and fractional parts. Write the word six as the number 6 then a decimal point to represent the "and". Next, the place value of decimal is tenths, so just write the word two as the number 2 to the right of a decimal point.

Answer: 6.2

This number word uses "and" and has both whole numbers and fractional parts. Write the word fourteen as the number 14 then a decimal point to represent the "and". Next, the place value of decimal is hundredths, so just write the word fifty-two as the number 52 to the right of a decimal point.

Answer: 14.52

## Decimal Place Value

- Decimal numbers have
**place value**and a corresponding**number word**. Knowing the place value of decimal numbers also allows you to also know the number word of a decimal number. - The
**number word**of a decimal corresponds to its**place value**. - 0.4 is a decimal number with a place value of
**tenth**, so the number word for 0.4 is four tenths. - 0.56 is a decimal number with a place value of a
**hundredth**, so the number word for 0.56 is fifty-six hundredths. - 0.178 is a decimal number with a place value of a
**thousandth**, so the number word for 0.178 is one hundred seventy-eight thousandths. - The word
**"and"**is only used when there are both whole numbers and fractional parts. The word**"and"**represents the decimal point.