Place Value with Decimals
Learn to read, write and order decimal numbers up to thousandths, and understand what each digit is worth.
What Are Decimals?
Decimals are numbers that have a whole number part and a fractional part, separated by a decimal point. They help us show amounts that are between whole numbers, like $3.50 or 1.25 metres.
whole part ← 4.253 → decimal part
Place Value Chart
| Tens | Ones | . | Tenths | Hundredths | Thousandths |
|---|---|---|---|---|---|
| 10 | 1 | . | 0.1 | 0.01 | 0.001 |
| 4 | . | 2 | 5 | 3 |
In 4.253: the 4 means 4 ones, the 2 means 2 tenths, the 5 means 5 hundredths, and the 3 means 3 thousandths.
Reading and Writing Decimals
When we read a decimal number aloud, we say the whole number part first, then say "point", then read each digit after the decimal point one by one.
3.7
"Three point seven"
= 3 ones + 7 tenths
12.04
"Twelve point zero four"
= 1 ten + 2 ones + 0 tenths + 4 hundredths
0.156
"Zero point one five six"
= 1 tenth + 5 hundredths + 6 thousandths
7.500
"Seven point five zero zero" or "seven and five tenths"
= 7 ones + 5 tenths (trailing zeros don't change value)
Remember: Trailing zeros after the decimal point do not change the value of a number. 3.5 = 3.50 = 3.500
Ordering Decimals
To order decimals from smallest to largest, compare digit by digit starting from the left. Look at the ones first, then the tenths, then the hundredths.
Example: Order 3.45, 3.4 and 3.405
Step 1: Write them all to the same number of decimal places:
Step 2: Compare from left to right. All have 3 ones and 4 tenths. Look at hundredths: 5, 0, 0.
Step 3: 3.400 and 3.405 both have 0 hundredths. Compare thousandths: 0 vs 5.
Order: 3.4 < 3.405 < 3.45
Decimals on a Number Line
Decimals in Everyday Life
We use decimals all the time without even realising it!
$14.95
Prices use tenths and hundredths (cents)
9.58 seconds
Race times measured in hundredths
36.5 °C
Body temperature in tenths
Key Vocabulary
Decimal Point
The dot that separates the whole number part from the fractional part of a number.
Tenths
The first digit after the decimal point. Each tenth is worth 0.1 (one part out of 10).
Hundredths
The second digit after the decimal point. Each hundredth is worth 0.01 (one part out of 100).
Thousandths
The third digit after the decimal point. Each thousandth is worth 0.001 (one part out of 1000).
Worked Examples
What is the value of the digit 6 in 2.361?
Step 1: Identify the position of the 6. It is the second digit after the decimal point.
Step 2: The second decimal place is the hundredths place.
Answer: The 6 is worth 6 hundredths or 0.06.
Write 8 ones + 3 tenths + 0 hundredths + 7 thousandths as a decimal.
Step 1: Ones = 8, so the whole number part is 8.
Step 2: After the decimal point: 3 tenths, 0 hundredths, 7 thousandths.
Answer: 8.307
Order these from smallest to largest: 0.52, 0.502, 0.5
Step 1: Rewrite with the same number of decimal places: 0.520, 0.502, 0.500
Step 2: All have 5 tenths. Compare hundredths: 2, 0, 0.
Step 3: 0.500 and 0.502 both have 0 hundredths. Compare thousandths: 0 vs 2.
Answer: 0.5 < 0.502 < 0.52
Knowledge Check
Select the correct answer for each question.
Question 1
What is the value of the digit 8 in the number 5.089?
Question 2
Which number is the largest? 0.6, 0.59, 0.601
Question 3
How do you write "four and twenty-three thousandths" as a decimal?
Question 4
Which of these is equal to 0.70?
Question 5
Order these from smallest to largest: 2.31, 2.103, 2.3
Key Concepts Summary
- ●The decimal point separates whole numbers from fractional parts.
- ●After the decimal point: tenths (0.1), hundredths (0.01), thousandths (0.001).
- ●To compare decimals, write them with the same number of decimal places and compare from left to right.
- ●Trailing zeros after the decimal do not change the value: 0.5 = 0.50 = 0.500.
- ●Decimals are used every day in money, measurements and sport.