Chapter Notes: Decimals in Word Form
Decimals are numbers that include parts smaller than one whole. You have seen decimals in money, like $3.50, and in measurements, like 2.75 inches. Just as we can write whole numbers in word form, we can also write decimals in word form. Learning to read and write decimals using words helps you understand what each digit in a decimal means and how to communicate these numbers clearly.
Understanding Place Value in Decimals
Before we write decimals in word form, we need to understand the place value of each digit in a decimal number. A decimal point is the dot that separates the whole number part from the part that is less than one. The digits to the left of the decimal point show whole numbers. The digits to the right of the decimal point show parts of a whole.
Here are the place values you need to know:
| Place Value (Left of Decimal) | Place Value (Right of Decimal) |
|---|---|
| Thousands | Tenths |
| Hundreds | Hundredths |
| Tens | Thousandths |
| Ones |
The first place to the right of the decimal point is called the tenths place. This is because each unit is divided into 10 equal parts. The second place to the right is called the hundredths place because each unit is divided into 100 equal parts. The third place is the thousandths place, where each unit is divided into 1,000 equal parts.
Think of money to help you remember: One dime is one-tenth of a dollar (0.1), and one penny is one-hundredth of a dollar (0.01).
Reading Decimals
When you read a decimal aloud, you follow these steps:
- Read the whole number part (the digits to the left of the decimal point).
- Say the word "and" for the decimal point.
- Read the digits to the right of the decimal point as if they were a whole number.
- Say the place value name of the last digit on the right.
The word "and" is very important because it tells you exactly where the decimal point is located.
Example: Read the decimal 3.7
How do you read this decimal in word form?
Solution:
Step 1: Read the whole number part = 3 is "three"
Step 2: Say "and" for the decimal point
Step 3: Read the digit to the right = 7 is "seven"
Step 4: The 7 is in the tenths place, so say "tenths" = three and seven tenths
The decimal 3.7 is read as three and seven tenths.
Example: Read the decimal 0.45
How do you read this decimal in word form?
Solution:
Step 1: Read the whole number part = 0 is "zero"
Step 2: Say "and" for the decimal point
Step 3: Read the digits to the right = 45 is "forty-five"
Step 4: The last digit (5) is in the hundredths place, so say "hundredths" = zero and forty-five hundredths
The decimal 0.45 is read as zero and forty-five hundredths or simply forty-five hundredths.
When the whole number part is zero, you can choose to say "zero and" or just start with the decimal part. Both ways are correct.
Writing Decimals in Word Form
Writing decimals in word form means using words instead of digits. You follow the same pattern as reading decimals. Let's practice with different types of decimals.
Decimals with Tenths
When a decimal has only one digit after the decimal point, that digit is in the tenths place.
Example: Write 5.2 in word form.
What is 5.2 written in words?
Solution:
The whole number part is 5 = "five"
The decimal point is read as "and"
The digit 2 is in the tenths place = "two tenths"
Combine all parts = five and two tenths
The decimal 5.2 written in word form is five and two tenths.
Decimals with Hundredths
When a decimal has two digits after the decimal point, the last digit is in the hundredths place. You read both digits together as one number, then say "hundredths."
Example: Write 12.68 in word form.
What is 12.68 written in words?
Solution:
The whole number part is 12 = "twelve"
The decimal point is read as "and"
The digits 68 after the decimal = "sixty-eight"
The last digit is in the hundredths place = "hundredths"
Combine all parts = twelve and sixty-eight hundredths
The decimal 12.68 written in word form is twelve and sixty-eight hundredths.
Decimals with Thousandths
When a decimal has three digits after the decimal point, the last digit is in the thousandths place. Read all three digits as one number, then say "thousandths."
Example: Write 0.375 in word form.
What is 0.375 written in words?
Solution:
The whole number part is 0 = we can skip saying "zero and"
The digits 375 after the decimal = "three hundred seventy-five"
The last digit is in the thousandths place = "thousandths"
Combine the parts = three hundred seventy-five thousandths
The decimal 0.375 written in word form is three hundred seventy-five thousandths.
Special Cases and Important Rules
Zeros in the Decimal Part
Sometimes zeros appear in the decimal part of a number. You must include these zeros when reading the number because they affect the place value.
Example: Write 4.06 in word form.
What is 4.06 written in words?
Solution:
The whole number part is 4 = "four"
The decimal point is read as "and"
The digits after the decimal are 06 = "six" (we read it as 06, not just 6)
The last digit is in the hundredths place = "hundredths"
Combine all parts = four and six hundredths
The decimal 4.06 written in word form is four and six hundredths.
Notice that 4.06 is different from 4.6. The number 4.06 is "four and six hundredths," while 4.6 is "four and six tenths." The zero is important because it shows that the 6 is in the hundredths place, not the tenths place.
Whole Numbers as Decimals
Sometimes you see a decimal that ends in zero, like 8.0. This is the same as the whole number 8. You can write it as "eight" or "eight and zero tenths." Usually, we just write "eight."
Money Amounts
Money amounts are a special type of decimal that you use every day. Dollars and cents use the hundredths place because there are 100 cents in one dollar.
Example: Write $7.35 in word form.
How do you write this money amount in words?
Solution:
The whole number part is 7 = "seven"
For money, we say "dollars" instead of just the number
The decimal point separates dollars from cents
The digits 35 represent cents = "thirty-five cents"
Combine the parts = seven dollars and thirty-five cents
The amount $7.35 written in word form is seven dollars and thirty-five cents.
Converting Word Form to Decimal Form
You also need to be able to go the other direction-from words to digits. When you see a decimal written in word form, you can write it as a number by following these steps:
- Write the whole number part before the decimal point.
- Put a decimal point where you see the word "and."
- Write the decimal part after the decimal point.
- Make sure the last digit is in the correct place value (tenths, hundredths, or thousandths).
Example: Write "nine and four tenths" in decimal form.
What is the decimal number?
Solution:
The whole number part is "nine" = 9
The word "and" tells us where to put the decimal point
The decimal part is "four tenths" = 4 in the tenths place
Write the number = 9.4
The decimal form of "nine and four tenths" is 9.4.
Example: Write "twenty-three and fifty-six hundredths" in decimal form.
What is the decimal number?
Solution:
The whole number part is "twenty-three" = 23
The word "and" tells us where to put the decimal point
The decimal part is "fifty-six hundredths" = 56 in the hundredths place
Write the number = 23.56
The decimal form of "twenty-three and fifty-six hundredths" is 23.56.
Example: Write "one hundred forty-two thousandths" in decimal form.
What is the decimal number?
Solution:
There is no whole number part mentioned, so the whole number is 0
The decimal part is "one hundred forty-two thousandths" = 142
The word "thousandths" means three decimal places
Write the number = 0.142
The decimal form of "one hundred forty-two thousandths" is 0.142.
Common Mistakes to Avoid
Here are some mistakes students often make when working with decimals in word form:
- Forgetting the word "and": The word "and" always represents the decimal point. Don't use "and" anywhere else in the number. For example, 205.3 is "two hundred five and three tenths," not "two hundred and five and three tenths."
- Using the wrong place value name: Make sure you count the decimal places correctly. The number 0.5 is "five tenths," not "five hundredths." The number 0.50 is also "five tenths" or "fifty hundredths."
- Forgetting zeros: If you see "eight hundredths," you must write 0.08, not 0.8. The zero in the tenths place is important.
- Mixing up the whole number and decimal parts: Everything before "and" is the whole number. Everything after "and" is the decimal part.
Practice with Real-World Situations
Decimals in word form appear in many everyday situations. You might see them on a thermometer, in a recipe, or when measuring distances.
Example: A recipe calls for two and five tenths cups of flour.
Write this amount as a decimal.What decimal represents this measurement?
Solution:
The whole number part is "two" = 2
The word "and" shows where the decimal point goes
The decimal part is "five tenths" = 5 in the tenths place
Write the decimal = 2.5
The recipe needs 2.5 cups of flour.
Example: The temperature outside is sixty-eight and seven tenths degrees Fahrenheit.
Write this temperature as a decimal.What is the temperature in decimal form?
Solution:
The whole number part is "sixty-eight" = 68
The word "and" shows where the decimal point goes
The decimal part is "seven tenths" = 7 in the tenths place
Write the decimal = 68.7
The temperature is 68.7 degrees Fahrenheit.
Review and Summary
Writing decimals in word form is an important skill that helps you understand place value and communicate about numbers clearly. Remember these key points:
- The decimal point is always read as "and."
- The digits to the right of the decimal point are read as a whole number, followed by the place value name of the last digit.
- The place values to the right of the decimal point are tenths, hundredths, and thousandths.
- When converting from word form to decimal form, look for the word "and" to place the decimal point correctly.
- Count the decimal places carefully to make sure each digit is in the right position.
Whether you are reading a price tag, measuring ingredients, or recording a race time, knowing how to read and write decimals in word form will help you understand and use these numbers correctly in your daily life.
