GRADE 6 · MATHEMATICS

Understanding Decimals and Place Value

Decimals help us describe parts of a whole using place value. Learn how to read, write, compare, order and round decimal numbers with clear examples and practical activities.

Learning time: approximately 25–30 minutes · Beginner level

What You Will Learn

Understand tenths, hundredths and thousandths.
Read and write decimal numbers in words and digits.
Use place value to compare and order decimals.
Round decimals to the nearest whole number, tenth or hundredth.
Connect simple decimals with fractions.

1. What Is a Decimal?

A decimal is a way to write a number that includes a whole part and a fractional part. The decimal point separates these parts.

In 24.638:

Tens	Ones	Decimal point	Tenths	Hundredths	Thousandths
2	4	.	6	3	8

24 is the whole-number part. 638 thousandths is the fractional part.

2. Decimal Place Values

Each place to the right of the decimal point is ten times smaller than the place before it.

Place	Value	Fraction form
Ones	1	1
Tenths	0.1	1/10
Hundredths	0.01	1/100
Thousandths	0.001	1/1000

Example: In 5.274, the digit 2 means 2 tenths (0.2), the digit 7 means 7 hundredths (0.07), and the digit 4 means 4 thousandths (0.004).

3. Read and Write Decimals

Read the whole-number part first. Then read the digits after the decimal point as a number followed by the place value of the final digit.

0.4 = four tenths.
0.35 = thirty-five hundredths.
2.08 = two and eight hundredths.
6.125 = six and one hundred twenty-five thousandths.

Zero matters: In 2.08, the zero shows there are no tenths. It is not the same as 2.8.

4. Compare Decimals

Line up the decimal points. Compare digits from left to right, starting with the greatest place value. You can add zeros to the end of a decimal without changing its value.

Worked example: Compare 3.5 and 3.47

Write both numbers with the same number of decimal places: 3.50 and 3.47.
Ones are equal: 3 and 3.
Tenths are equal: 5 and 5.
Compare hundredths: 0 is less than 7.

Therefore, 3.5 is greater than 3.47.

Remember: 3.5 = 3.50. Adding a zero at the end of a decimal does not change its value.

5. Order Decimals

To arrange decimals, write them with the same number of decimal places if helpful, then compare from left to right.

Worked example: Order 0.8, 0.65 and 0.705 from least to greatest

Write them to three decimal places: 0.800, 0.650 and 0.705.
Compare the tenths: 6 is smallest, then 7, then 8.
The order is 0.65, 0.705, 0.8.

6. Round Decimals

To round a number, look at the digit immediately to the right of the place you are rounding to:

If that digit is 0, 1, 2, 3 or 4, keep the rounding digit the same.
If that digit is 5, 6, 7, 8 or 9, increase the rounding digit by 1.
Remove the digits after the rounding place, unless they are needed to show a specified number of decimal places.

Worked example: Round 6.274

Round to	Look at	Answer
Nearest whole number	Tenths digit is 2	6
Nearest tenth	Hundredths digit is 7	6.3
Nearest hundredth	Thousandths digit is 4	6.27

Careful: The rounding digit is not always the digit you inspect. Look one place to its right.

7. Decimals and Fractions

Decimals and fractions can describe the same value.

Decimal	Fraction	Read as
0.5	5/10 = 1/2	Five tenths
0.25	25/100 = 1/4	Twenty-five hundredths
0.75	75/100 = 3/4	Seventy-five hundredths
0.2	2/10 = 1/5	Two tenths

8. Common Mistakes to Avoid

Thinking more decimal digits means a larger number: 0.8 is greater than 0.75, even though 0.75 has more digits.

Ignoring place value: In 4.06, the 6 is in the hundredths place, not the tenths place.

Removing important zeros: 2.08 is different from 2.8. A zero between the decimal point and another digit changes place value.

Rounding using the wrong digit: Always inspect the digit immediately to the right of the target place.

9. Practice Exercises

Try these before revealing the answers.

What is the value of 7 in 3.472?
Write 0.06 in words.
Which is greater: 0.9 or 0.85?
Order 0.4, 0.35 and 0.405 from least to greatest.
Round 8.67 to the nearest whole number.
Round 5.284 to the nearest tenth.
Write 0.75 as a fraction in simplest form.

Show practice answers and explanations

7 hundredths, or 0.07.
Six hundredths.
0.9 is greater because 0.90 is greater than 0.85.
0.35, 0.4, 0.405. Write them as 0.350, 0.400 and 0.405.
9, because the tenths digit is 6.
5.3, because the hundredths digit is 8.
75/100 = 3/4.

11. Free Printable Worksheet

Print this worksheet or save it as a PDF for extra practice.

Learnora — Grade 6 Mathematics

Understanding Decimals Worksheet

Name: __________________________ Date: _______________

Instructions: Show your working where needed.

In 8.532, what is the value of the digit 5?
Write 0.09 in words.
Write 4.07 in words.
Use >, < or =: 0.6 ___ 0.58.
Order 0.25, 0.5 and 0.45 from least to greatest.
Round 9.76 to the nearest whole number.
Round 3.846 to the nearest hundredth.
Write 0.5 as a fraction in simplest form.

Keep practising — you are making progress!

Learnora — Learn Better. Practice Smarter.

Teacher / Parent Answer Key

5 tenths, or 0.5.
Nine hundredths.
Four and seven hundredths.
0.6 > 0.58.
0.25, 0.45, 0.5.
10.
3.85.
5/10 = 1/2.

12. Lesson Summary

The decimal point separates the whole-number part from the fractional part.
Digits after the decimal point represent tenths, hundredths, thousandths and smaller place values.
Compare decimals from left to right, lining up decimal points when helpful.
Zeros at the end of a decimal do not change its value.
To round, inspect the digit immediately to the right of the target place.

Next learning goal: Practise adding and subtracting decimals using place-value alignment.

Educational note: This is a curriculum-neutral Grade 6 lesson. Teachers and parents can adapt examples and practice to their local curriculum.