Grade 5 · Number & Operations in Base Ten · MAT-05-NBT-004
Round Decimals to Any Place
Represent and solve round decimals to any place problems using accurate mathematical models, notation, and reasoning.
Learning objectives
What you should be able to do
- Represent and solve round decimals to any place problems using accurate mathematical models, notation, and reasoning.
- Explain why a strategy for round decimals to any place 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
Round Decimals to Any Place 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 number line 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.
Number Line Explorer
Move along the number line.
4 is one less. 5 and 6 is one more.
- Build one example of round decimals to any place 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.
Round 1.237 to the nearest tenth.
1.237 → 1.2The hundredths digit determines whether the tenths digit stays the same or increases by one.
Round 1.350 to the nearest tenth.
1.350 → 1.4The hundredths digit determines whether the tenths digit stays the same or increases by one.
Round 1.463 to the nearest tenth.
1.463 → 1.5The hundredths digit determines whether the tenths digit stays the same or increases by one.
Round 1.576 to the nearest tenth.
1.576 → 1.6The hundredths digit determines whether the tenths digit stays the same or increases by one.
Round 1.689 to the nearest tenth.
1.689 → 1.7The hundredths digit determines whether the tenths digit stays the same or increases by one.
Round 1.802 to the nearest tenth.
1.802 → 1.8The hundredths digit determines whether the tenths digit stays the same or increases by one.
Round 1.915 to the nearest tenth.
1.915 → 1.9The hundredths digit determines whether the tenths digit stays the same or increases by one.
Round 2.028 to the nearest tenth.
2.028 → 2.0The hundredths digit determines whether the tenths digit stays the same or increases by one.
Round 2.141 to the nearest tenth.
2.141 → 2.1The hundredths digit determines whether the tenths digit stays the same or increases by one.
Round 2.254 to the nearest tenth.
2.254 → 2.3The hundredths digit determines whether the tenths digit stays the same or increases by one.
Round 2.367 to the nearest tenth.
2.367 → 2.4The hundredths digit determines whether the tenths digit stays the same or increases by one.
Round 2.480 to the nearest tenth.
2.480 → 2.5The hundredths digit determines whether the tenths digit stays the same or increases by one.
Round 2.593 to the nearest tenth.
2.593 → 2.6The hundredths digit determines whether the tenths digit stays the same or increases by one.
Round 2.706 to the nearest tenth.
2.706 → 2.7The hundredths digit determines whether the tenths digit stays the same or increases by one.
Round 2.819 to the nearest tenth.
2.819 → 2.8The hundredths digit determines whether the tenths digit stays the same or increases by one.
Round 2.932 to the nearest tenth.
2.932 → 2.9The hundredths digit determines whether the tenths digit stays the same or increases by one.
Round 3.045 to the nearest tenth.
3.045 → 3.0The hundredths digit determines whether the tenths digit stays the same or increases by one.
Round 3.158 to the nearest tenth.
3.158 → 3.2The hundredths digit determines whether the tenths digit stays the same or increases by one.
Round 3.271 to the nearest tenth.
3.271 → 3.3The hundredths digit determines whether the tenths digit stays the same or increases by one.
Round 3.384 to the nearest tenth.
3.384 → 3.4The hundredths digit determines whether the tenths digit stays the same or increases by one.
Practice
Guided practice with hints
01Round 3.497 to the nearest tenth.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 3.497 → 3.5
02Round 3.610 to the nearest tenth.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 3.610 → 3.6
03Round 3.723 to the nearest tenth.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 3.723 → 3.7
04Round 3.836 to the nearest tenth.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 3.836 → 3.8
05Round 3.949 to the nearest tenth.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 3.949 → 3.9
06Round 4.062 to the nearest tenth.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 4.062 → 4.1
Practice
Independent practice
01Round 4.175 to the nearest tenth.
Answer: 4.175 → 4.2
02Round 4.288 to the nearest tenth.
Answer: 4.288 → 4.3
03Round 4.401 to the nearest tenth.
Answer: 4.401 → 4.4
04Round 4.514 to the nearest tenth.
Answer: 4.514 → 4.5
05Round 1.237 to the nearest tenth.
Answer: 1.237 → 1.2
06Round 1.350 to the nearest tenth.
Answer: 1.350 → 1.4
07Round 1.463 to the nearest tenth.
Answer: 1.463 → 1.5
08Round 1.576 to the nearest tenth.
Answer: 1.576 → 1.6
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
Round 1.689 to the nearest tenth.
1.689 → 1.7
Round 1.802 to the nearest tenth.
1.802 → 1.8
Round 1.915 to the nearest tenth.
1.915 → 1.9
Round 2.028 to the nearest tenth.
2.028 → 2.0
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Grade 5 Math Strategy Sprint
Solve and explain round decimals to any place problems accurately, then check each result with a second method.
Practice
Mastery check
01Round 2.141 to the nearest tenth.
Answer: 2.141 → 2.1
02Round 2.254 to the nearest tenth.
Answer: 2.254 → 2.3
03Round 2.367 to the nearest tenth.
Answer: 2.367 → 2.4
04Round 2.480 to the nearest tenth.
Answer: 2.480 → 2.5
05Round 2.593 to the nearest tenth.
Answer: 2.593 → 2.6
06Round 2.706 to the nearest tenth.
Answer: 2.706 → 2.7
07Round 2.819 to the nearest tenth.
Answer: 2.819 → 2.8
08Round 2.932 to the nearest tenth.
Answer: 2.932 → 2.9
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.