Grade 4 · Fractions & Decimals · MAT-04-FD-010
Understand Decimal Notation for Tenths
Represent and solve understand decimal notation for tenths problems using accurate mathematical models, notation, and reasoning.
Learning objectives
What you should be able to do
- Represent and solve understand decimal notation for tenths problems using accurate mathematical models, notation, and reasoning.
- Explain why a strategy for understand decimal notation for tenths works and verify the result with an independent check.
Prerequisite check
Make sure the foundation is ready.
The new lesson builds directly on this prior concept, so the prerequisite should be usable rather than merely familiar.
Learn
Build the idea from meaning, not memorization.
Meaning and structure
Understand Decimal Notation for Tenths extends base-ten place value to positions right of the decimal point. Tenths, hundredths, and thousandths are powers-of-ten units, so digit position—not visual length—determines value.
Represent the idea
The Math Box uses base ten blocks as the primary representation. Translate the situation into numbers or geometry first, identify what stays fixed, then change one quantity at a time and observe which relationships remain invariant.
Reason, calculate, and verify
A convincing solution names the quantities, shows the mathematical relationship, computes accurately, and includes a reasonableness check rather than relying on an unsupported answer.
Math Box · Interactive lesson
Touch the math. Change it. See what stays true.
Use the interactive model before and after the worked examples. Change the inputs, make a prediction, then use the model to test whether your reasoning holds.
Decimal Place-Value Lab
Change one place at a time and watch how its value contributes to the complete decimal.
- Build one example of understand decimal notation for tenths in the Math Box.
- Change one input and predict the effect before moving the control.
- Explain which mathematical relationship stayed invariant after the change.
Worked examples
Twenty different ways to see the concept work.
Write 1/10 as a decimal.
1/10 = 0.1The tenths place records how many tenths are present; ten tenths can be regrouped as one whole.
Write 2/10 as a decimal.
2/10 = 0.2The tenths place records how many tenths are present; ten tenths can be regrouped as one whole.
Write 3/10 as a decimal.
3/10 = 0.3The tenths place records how many tenths are present; ten tenths can be regrouped as one whole.
Write 4/10 as a decimal.
4/10 = 0.4The tenths place records how many tenths are present; ten tenths can be regrouped as one whole.
Write 5/10 as a decimal.
5/10 = 0.5The tenths place records how many tenths are present; ten tenths can be regrouped as one whole.
Write 6/10 as a decimal.
6/10 = 0.6The tenths place records how many tenths are present; ten tenths can be regrouped as one whole.
Write 7/10 as a decimal.
7/10 = 0.7The tenths place records how many tenths are present; ten tenths can be regrouped as one whole.
Write 8/10 as a decimal.
8/10 = 0.8The tenths place records how many tenths are present; ten tenths can be regrouped as one whole.
Write 9/10 as a decimal.
9/10 = 0.9The tenths place records how many tenths are present; ten tenths can be regrouped as one whole.
Write 11/10 as a decimal.
11/10 = 1.1The tenths place records how many tenths are present; ten tenths can be regrouped as one whole.
Write 12/10 as a decimal.
12/10 = 1.2The tenths place records how many tenths are present; ten tenths can be regrouped as one whole.
Write 13/10 as a decimal.
13/10 = 1.3The tenths place records how many tenths are present; ten tenths can be regrouped as one whole.
Write 14/10 as a decimal.
14/10 = 1.4The tenths place records how many tenths are present; ten tenths can be regrouped as one whole.
Write 15/10 as a decimal.
15/10 = 1.5The tenths place records how many tenths are present; ten tenths can be regrouped as one whole.
Write 16/10 as a decimal.
16/10 = 1.6The tenths place records how many tenths are present; ten tenths can be regrouped as one whole.
Write 17/10 as a decimal.
17/10 = 1.7The tenths place records how many tenths are present; ten tenths can be regrouped as one whole.
Write 18/10 as a decimal.
18/10 = 1.8The tenths place records how many tenths are present; ten tenths can be regrouped as one whole.
Write 19/10 as a decimal.
19/10 = 1.9The tenths place records how many tenths are present; ten tenths can be regrouped as one whole.
Write 21/10 as a decimal.
21/10 = 2.1The tenths place records how many tenths are present; ten tenths can be regrouped as one whole.
Write 22/10 as a decimal.
22/10 = 2.2The tenths place records how many tenths are present; ten tenths can be regrouped as one whole.
Practice
Guided practice with hints
01Write 23/10 as a decimal.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 23/10 = 2.3
02Write 24/10 as a decimal.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 24/10 = 2.4
03Write 25/10 as a decimal.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 25/10 = 2.5
04Write 26/10 as a decimal.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 26/10 = 2.6
05Write 27/10 as a decimal.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 27/10 = 2.7
06Write 28/10 as a decimal.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 28/10 = 2.8
Practice
Independent practice
01Write 29/10 as a decimal.
Answer: 29/10 = 2.9
02Write 31/10 as a decimal.
Answer: 31/10 = 3.1
03Write 32/10 as a decimal.
Answer: 32/10 = 3.2
04Write 33/10 as a decimal.
Answer: 33/10 = 3.3
05Write 34/10 as a decimal.
Answer: 34/10 = 3.4
06Write 35/10 as a decimal.
Answer: 35/10 = 3.5
07Write 36/10 as a decimal.
Answer: 36/10 = 3.6
08Write 37/10 as a decimal.
Answer: 37/10 = 3.7
Common mistakes
Learn to catch the error, not just the answer.
Compare corresponding place values; trailing zeros do not change a decimal's value.
Align place values vertically before combining digits.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Scale recipes, measurements, money, and data while preserving the meaning of the unit.
- Compare quantities that are not whole numbers in science, construction, shopping, and measurement.
Challenge problems
Write 38/10 as a decimal.
38/10 = 3.8
Write 39/10 as a decimal.
39/10 = 3.9
Write 41/10 as a decimal.
41/10 = 4.1
Write 42/10 as a decimal.
42/10 = 4.2
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Grade 4 Math Strategy Sprint
Solve and explain understand decimal notation for tenths problems accurately, then check each result with a second method.
Practice
Mastery check
01Write 43/10 as a decimal.
Answer: 43/10 = 4.3
02Write 44/10 as a decimal.
Answer: 44/10 = 4.4
03Write 45/10 as a decimal.
Answer: 45/10 = 4.5
04Write 46/10 as a decimal.
Answer: 46/10 = 4.6
05Write 47/10 as a decimal.
Answer: 47/10 = 4.7
06Write 48/10 as a decimal.
Answer: 48/10 = 4.8
07Write 49/10 as a decimal.
Answer: 49/10 = 4.9
08Write 51/10 as a decimal.
Answer: 51/10 = 5.1
Terminology
Words to know
- decimal point
- The symbol separating whole-number places from fractional base-ten places.
- tenth
- One of ten equal parts of a whole.
- hundredth
- One of one hundred equal parts of a whole.
- place value
- The value a digit has because of its position in a numeral.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Mathematics Framework (2023)
Grade-level instructional guidance, mathematical practices, and coherent progression.Common Core State Standards for Mathematics — Grades 4–5
Grade-level expectations for operations, number and fraction work, measurement, data, and geometry.Principles to Actions: Ensuring Mathematical Success for All
Evidence-based emphasis on reasoning, representations, discourse, and conceptual understanding.