Remember the place value chart of whole numbers? Complete the following exercise for a refresher.

Turning a Decimal Into Words

Have you ever wondered what goes to the right of the decimal in a place value chart? That is where the decimal numbers go! (The parts of the whole.)

Table 4.2.2 shows a place value chart for decimals:

Table 4.2.2: Place Value Chart For Decimals

Hundreds	Tens	Ones	Decimal	Tenths	Hundredths	Thousandths	Ten thousandths	Hundred thousandths
—	—	3	.	4	5	3	—	—
—	—	0	.	9	6	—	—	—

See the words to the right of the decimal point? They look different than the usual whole number words you are used to. These are all the names for the decimal places. You will see them in the next lesson.

The first number on the chart above is 3.453. We say, “Three point four five three,” or, “Three and four hundred fifty-three thousandths.”

• 3 is in the ones spot.
• 4 is in the tenths spot.
• 5 is in the hundredths spot.
• 3 is in the thousandths spot.

The second number is 0.96. We say, “Zero point nine six,” or, “Zero and ninety-six hundredths.”

• 0 is in the ones spot.
• 9 is in the tenths spot.
• 6 is in the hundredths spot.

Tenths Place

Common fractions with a denominator of 10 are written as a decimal with one place to the right of the decimal point. This is the tenths place.

We often shorten “places to the right of the decimal point” to “decimal places.” We can say that tenths have one decimal place.

• [latex]\dfrac{6}{10}[/latex] = 0.6 = six tenths
• [latex]\dfrac{3}{10}[/latex] = 0.3 three tenths

An easy way to remember this is that there’s one zero in the denominator, so there is one decimal place taken up.

Decimals with one digit to the right of the decimal point have an unwritten denominator of ten. This means that the whole thing is broken into 10 equal parts. Each part is called a tenth.

When we write decimals, we put a zero to the left of the decimal point to show there is no whole number. This zero keeps the decimal point from being “lost” or unnoticed.

For example, .2 should be written as 0.2.

Hundredths Place

Decimals with two digits to the right of the decimal point have an unwritten denominator of one hundred. This means that the whole thing is broken into 100 equal parts. Each part is called a hundredth.

Common fractions with a denominator of one hundred are written as decimals with two decimal places.

• [latex]\dfrac{23}{100}[/latex] = 0.23
• [latex]\dfrac{99}{100}[/latex] = 0.99
• [latex]\dfrac{4}{100}[/latex] = 0.04

Look at that last example. The 0 must be used after the decimal point in 0.04 to hold the tenths place. This makes it clear that the denominator is one hundred. There are two zeros in the denominator, so there must be two decimal places taken up.

This is called prefixing zeros.

Thousandths Place

Decimals with three digits to the right of the decimal point (three decimal places) have an unwritten denominator of one thousand. This means that the whole thing is broken into 1000 equal parts. Each part is one thousandth.

Look carefully at how thousandths are written. Watch for the prefixing zeros that may be needed to hold the tenth decimal place or the hundredth decimal place.

• 0.472 = four hundred seventy-two thousandths  = [latex]\dfrac{472}{1\,000}[/latex]
• 0.085 = eighty-five thousandths   = [latex]\dfrac{85}{1\,000}[/latex]
• 0.003 = three thousandths = [latex]\dfrac{3}{1\,000}[/latex]

There are three zeros in the denominator, so there must be three decimal places taken up.

Ten-Thousandths Place

Decimals with four decimal places have an unwritten denominator of ten-thousand. The whole thing is being thought of as having 10000 equal parts. Each part is one ten-thousandth.

• 0.1458 = [latex]\dfrac{1458}{10\,000}[/latex] = one thousand four hundred fifty-eight ten-thousandths
• 0.0581 = [latex]\dfrac{582}{10\,000}[/latex] = five hundred eighty-one ten-thousandths

Notice that there are four zeros in the denominator. That means there must be four decimal places taken up.

Mixed Decimals

Mixed decimals are a whole number and a decimal written together.

4.3 = [latex]4\dfrac{3}{10}[/latex] = four and three tenths

27.27 = [latex]27\dfrac{27}{100}[/latex] = twenty-seven and twenty-seven hundredths

8.104 = [latex]8\dfrac{104}{1\,000}[/latex] = eight and one hundred four thousandths

The digits to the left of the decimal point are whole numbers. The digits to the right of the decimal point are fractions. We say “and” for the decimal point.

Look at the mixed decimals from the examples above in the place value chart below (see Table 4.2.7):

Table 4.2.7: Mixed Decimal Place Value Chart

Hundreds	Tens	Ones	Decimal	Tenths	Hundredths	Thousandths	Ten Thousandths	Hundred Thousandths
—	—	4	.	3	—	—	—	—
—	2	7	.	2	7	—	—	—
—	—	8	.	1	0	4	—	—

Turning Words Into a Decimal

Step 1: Read the number. Does the word “and” show that this is a mixed decimal?

• If it does, the whole number is before the word “and.” Write the whole number with the decimal point after it.
• If there is no whole number, write a 0 with the decimal point after it.

Step 2: Decide how many decimal places you need. Look and listen for the “ths” ending. The word with “ths” is the understood denominator. It may help if you draw a little line for each decimal place that you need.

• Tenths need one decimal place.
• Hundredths need two decimal places.
• Thousandths need three decimal places.
• Ten-thousandths need four decimal places.

Step 3: Write the decimal so the last digit is on the last little line, and fill any remaining lines with zeros.

Reading & Writing Money

Dollars

We write money with a dollar sign, a whole number, and a decimal with two decimal places.

$1.00 = 1 dollar

What do we call [latex]\dfrac{1}{100}[/latex] of a dollar? Right! One cent.

• $2.33 = two dollars and thirty-three cents
• $427.05 = four hundred twenty-seven dollars and five cents
• $0.62 = sixty-two cents
• $0.03 = three cents

• centurion — commander of a hundred soldiers
• century — a hundred years
• centennial — a hundredth anniversary
• centigrade — having a hundred degrees
• cent — one hundredth of a dollar
• centimetre — one-hundredth of a metre
• centipede — wormlike creatures with a hundred legs

$14.75 = [latex]\$14\dfrac{75}{100}[/latex]

$12.25 = [latex]\$12\dfrac{25}{100}[/latex]

Cents

We have another way of writing money. We often write money that is less than one dollar using a cent sign which is a c for cent with a line through it ¢.

• $0.05 = 5¢
• $0.33 = 33¢
• $0.10 = 10¢
• $0.25 = 25¢
• $0.99 = 99¢
• $1.08 = 108¢

It is incorrect to use both a dollar sign and a cent sign.  Instead of $4.53¢, do $4.53 or 453¢.

It is incorrect to use a cent sign with a decimal point. Instead of 4.53¢, do $4.53 or 453¢.

4.2: Practice Questions

1. Write as decimals.
   1. [latex]\dfrac{3}{10}[/latex]
   2. [latex]\dfrac{24}{1\,000}[/latex]
   3. [latex]\dfrac{36}{1\,000}[/latex]
   4. [latex]\dfrac{206}{10\,000}[/latex]
   5. [latex]3\dfrac{123}{1\,000}[/latex]
   6. [latex]\dfrac{2}{100}[/latex]
   7. [latex]6\dfrac{3}{10}[/latex]
   8. [latex]4\dfrac{11}{1\,000}[/latex]
   9. [latex]6\dfrac{250}{1\,000}[/latex]
   10. [latex]9\dfrac{47}{10\,000}[/latex]

    

2. Change these decimals to common fractions.
   1. 0.5
   2. 0.04
   3. 0.37
   4. 0.010
   5. 3.0918
   6. 3.025
   7. 0.164
   8. 2.1498

    

3. Write as common fractions and as decimals.
   1. one hundredth
   2. forty-seven hundredths
   3. two hundred seventy-one thousandths
   4. forty-one thousandths
   5. one hundred twenty ten-thousandths
   6. four and four tenths
   7. two hundred sixty and fourteen ten-thousandths
   8. seven and two hundred eleven thousandths
   9. forty and six hundredths
   10. five dollars and sixty-three cents

    

4. Write the amount of money with numerals, using a $ sign.
   1. five dollars and sixty cents
   2. seventy-two cents
   3. fifty-six cents
   4. six cents
   5. one hundred twenty-four cents

4.2: Practice Answers

1. Write as decimals.
   1. 0.3
   2. 0.24
   3. 0.036
   4. 0.0206
   5. 3.123
   6. 0.02
   7. 6.3
   8. 4.011
   9. 6.250
   10. 9.0047

    

2. Change these decimals to common fractions.
   1. [latex]\dfrac{5}{10}[/latex]
   2. [latex]\dfrac{4}{100}[/latex]
   3. [latex]\dfrac{37}{100}[/latex]
   4. [latex]\dfrac{10}{1\,000}[/latex]
   5. [latex]3\dfrac{918}{10\,000}[/latex]
   6. [latex]3\dfrac{25}{1\,000}[/latex]
   7. [latex]\dfrac{164}{1\,000}[/latex]
   8. [latex]2\dfrac{1498}{10\,000}[/latex]

    

3. Write as common fractions and as decimals.
   1. [latex]\dfrac{1}{100}\text{ and }0.01[/latex]
   2. [latex]\dfrac{47}{100}\text{ and }0.47[/latex]
   3. [latex]\dfrac{271}{1\,000}\text{ and }0.271[/latex]
   4. [latex]\dfrac{41}{1\,000}\text{ and }0.041[/latex]
   5. [latex]\dfrac{120}{10\,000}\text{ and }0.0120[/latex]
   6. [latex]4\dfrac{4}{10}\text{ and }4.4[/latex]
   7. [latex]260\dfrac{14}{10\,000}\text{ and }260.0014[/latex]
   8. [latex]7\dfrac{211}{1\,000}\text{ and }7.211[/latex]
   9. [latex]40\dfrac{6}{100}\text{ and }40.06[/latex]
   10. [latex]\$5\dfrac{63}{100}\text{ and }\$5.63[/latex]

    

4. Write the amount of money with numerals, using a $ sign.
   1. $5.60
   2. $0.72
   3. $0.56
   4. $0.06
   5. $1.24

Attribution

This chapter has been adapted from Topic B: Reading & Writing Decimals in Adult Literacy Fundamental Mathematics: Book 4 – 2nd Edition (BCcampus) by Katherine Arendt, Mercedes de la Nuez, and Lix Girard (2023), which is under a CC BY 4.0 license.