Number foundations
Decimal Place Value Worksheets
Read, compare and explain decimals with visual examples, six printable questions and a worked answer guide. Free practice through thousandths.
Foundation practice · through thousandths · 6 questions · Free to print · Answers included
Make sense of the method
A decimal point separates whole units from parts of a unit. Each place to its right is ten times smaller than the place before it: tenths, hundredths, then thousandths.
Use this practice when a learner can calculate with decimals but is unsure why 0.7 is greater than 0.65. It is useful for foundation recovery at any age; it is not a complete grade-level assessment.
- Name the whole unit before comparing amounts.
- Line up the decimal points and label the place-value columns.
- Compare the first different place. Extra digits do not automatically mean a larger number.
- Use an expanded sum or a drawing to explain your answer.
A worked example
Which is larger: 0.7 or 0.65? Explain using hundredths.
- 0.7 = 7 tenths = 70 hundredths. Writing 0.70 does not change its value.
- Both amounts now use the same unit. Since 70 > 65, 0.70 > 0.65.
0.7 is larger: 70 hundredths > 65 hundredths.
Try the worksheet
Start with the first two questions, then build toward the final challenge. Show your method with calculations, drawings or a short explanation. These are practice questions with published answers, not a full-topic readiness check.
Build the foundation
1.In 8.406, give the value of the digits 4 and 6. Explain what the zero tells you.
Show your work on paper.Build the foundation
2.Write 3.052 as a sum of its non-zero place values, then write it in words using thousandths.
Show your work on paper.Strengthen your method
3.A whole strip is divided into ten equal parts. Write the shaded amount as a fraction and a decimal. Explain the denominator.
One whole strip Show your work on paper.Strengthen your method
4.Arrange 2.09, 2.9, 2.109 and 2.19 from least to greatest. Explain the first comparison and the last comparison.
Show your work on paper.Apply and explain
5.A learner says 0.58 is larger than 0.6 because 58 is larger than 6. Correct the explanation using a common place-value unit.
Show your work on paper.Apply and explain
6.A ribbon is 0.047 m long. Find ten times that length and one tenth of that length. Explain the new value of the digit 4 in each result.
Show your work on paper.
Worked answers
Try the questions first. Then compare the reasoning, not just the final result.
Show all six worked solutions
1. 4 tenths (0.4); 6 thousandths (0.006); zero hundredths.
- Label the places: 8 ones, 4 tenths, 0 hundredths, 6 thousandths.
- The zero keeps the 6 in the thousandths place; deleting it would change the number to 8.46.
2. 3 + 0.05 + 0.002; three and fifty-two thousandths.
- There are 3 ones, no tenths, 5 hundredths and 2 thousandths.
- Five hundredths are 50 thousandths. The fractional part is 52 thousandths.
3. 3/10 = 0.3.
- There are ten equal parts in the whole, so each part is one tenth.
- Three shaded parts represent three tenths: 3/10 or 0.3.
4. 2.09 < 2.109 < 2.19 < 2.9.
- Write equivalent forms: 2.090, 2.109, 2.190 and 2.900.
- 2.090 < 2.109 because 0 tenths < 1 tenth. 2.190 < 2.900 because 1 tenth < 9 tenths.
- Between 2.109 and 2.190, compare hundredths: 0 < 9.
5. 0.58 < 0.6 because 58 hundredths < 60 hundredths.
- The digits 58 and 6 originally refer to different units.
- Rewrite 6 tenths as 60 hundredths. Now compare 58 with 60.
6. Ten times: 0.47 m (4 tenths). One tenth: 0.0047 m (4 thousandths).
- 0.047 × 10 = 0.47: every digit's value becomes ten times as large. The 4 changes from hundredths to tenths.
- 0.047 ÷ 10 = 0.0047: every digit's value becomes one tenth as large. The 4 changes from hundredths to thousandths.
- This final question stretches beyond thousandths to ten-thousandths.
Mistakes worth catching
Comparing decimals as whole-number digit strings.
Use the same unit: 0.6 is 60 hundredths, not 6 hundredths.
Deleting zeros between the point and a non-zero digit.
Placeholder zeros matter. Only trailing zeros can be removed without changing a decimal's value.
Turn your work into a next step
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If this feels difficult
These suggested building blocks help with this lesson. Choose one to review, then return to these questions.
Skills covered
Number foundations
- Represent and compare decimal values using equal units.
- Explain the effect of multiplying or dividing a value by ten.
Choose this practice by the skills you need. Grade placement and strand names vary between school systems; one worksheet covers selected skills rather than every expectation in a topic.
Related practice
Explore a connected skill. These suggestions are not a personalized assessment of what you need next.