Grade 4 · Fractions & Decimals · MAT-04-FD-013
Compare Decimals to Hundredths
Represent and solve compare decimals to hundredths problems using accurate mathematical models, notation, and reasoning.
Learning objectives
What you should be able to do
- Represent and solve compare decimals to hundredths problems using accurate mathematical models, notation, and reasoning.
- Explain why a strategy for compare decimals to hundredths 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
Compare Decimals to Hundredths 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
Verify comparisons with a second representation such as a number line, common unit, or place-value expansion. A comparison is not justified by one digit or one numerator alone.
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 compare decimals to hundredths 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.
Compare 0.12 and 0.18.
0.12 < 0.18Line up decimal points and compare tenths, then hundredths, then thousandths when needed.
Compare 0.15 and 0.20.
0.15 < 0.20Line up decimal points and compare tenths, then hundredths, then thousandths when needed.
Compare 0.18 and 0.22.
0.18 < 0.22Line up decimal points and compare tenths, then hundredths, then thousandths when needed.
Compare 0.21 and 0.24.
0.21 < 0.24Line up decimal points and compare tenths, then hundredths, then thousandths when needed.
Compare 0.24 and 0.26.
0.24 < 0.26Line up decimal points and compare tenths, then hundredths, then thousandths when needed.
Compare 0.27 and 0.28.
0.27 < 0.28Line up decimal points and compare tenths, then hundredths, then thousandths when needed.
Compare 0.30 and 0.30.
0.30 = 0.30Line up decimal points and compare tenths, then hundredths, then thousandths when needed.
Compare 0.33 and 0.32.
0.33 > 0.32Line up decimal points and compare tenths, then hundredths, then thousandths when needed.
Compare 0.36 and 0.34.
0.36 > 0.34Line up decimal points and compare tenths, then hundredths, then thousandths when needed.
Compare 0.39 and 0.36.
0.39 > 0.36Line up decimal points and compare tenths, then hundredths, then thousandths when needed.
Compare 0.42 and 0.38.
0.42 > 0.38Line up decimal points and compare tenths, then hundredths, then thousandths when needed.
Compare 0.45 and 0.40.
0.45 > 0.40Line up decimal points and compare tenths, then hundredths, then thousandths when needed.
Compare 0.48 and 0.42.
0.48 > 0.42Line up decimal points and compare tenths, then hundredths, then thousandths when needed.
Compare 0.51 and 0.44.
0.51 > 0.44Line up decimal points and compare tenths, then hundredths, then thousandths when needed.
Compare 0.54 and 0.46.
0.54 > 0.46Line up decimal points and compare tenths, then hundredths, then thousandths when needed.
Compare 0.57 and 0.48.
0.57 > 0.48Line up decimal points and compare tenths, then hundredths, then thousandths when needed.
Compare 0.60 and 0.50.
0.60 > 0.50Line up decimal points and compare tenths, then hundredths, then thousandths when needed.
Compare 0.63 and 0.52.
0.63 > 0.52Line up decimal points and compare tenths, then hundredths, then thousandths when needed.
Compare 0.66 and 0.54.
0.66 > 0.54Line up decimal points and compare tenths, then hundredths, then thousandths when needed.
Compare 0.69 and 0.56.
0.69 > 0.56Line up decimal points and compare tenths, then hundredths, then thousandths when needed.
Practice
Guided practice with hints
01Compare 0.72 and 0.58.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 0.72 > 0.58
02Compare 0.75 and 0.60.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 0.75 > 0.60
03Compare 0.78 and 0.62.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 0.78 > 0.62
04Compare 0.81 and 0.64.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 0.81 > 0.64
05Compare 0.84 and 0.66.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 0.84 > 0.66
06Compare 0.87 and 0.68.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 0.87 > 0.68
Practice
Independent practice
01Compare 0.90 and 0.70.
Answer: 0.90 > 0.70
02Compare 0.93 and 0.72.
Answer: 0.93 > 0.72
03Compare 0.96 and 0.74.
Answer: 0.96 > 0.74
04Compare 0.99 and 0.76.
Answer: 0.99 > 0.76
05Compare 0.12 and 0.18.
Answer: 0.12 < 0.18
06Compare 0.15 and 0.20.
Answer: 0.15 < 0.20
07Compare 0.18 and 0.22.
Answer: 0.18 < 0.22
08Compare 0.21 and 0.24.
Answer: 0.21 < 0.24
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
Compare 0.24 and 0.26.
0.24 < 0.26
Compare 0.27 and 0.28.
0.27 < 0.28
Compare 0.30 and 0.30.
0.30 = 0.30
Compare 0.33 and 0.32.
0.33 > 0.32
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Grade 4 Math Strategy Sprint
Solve and explain compare decimals to hundredths problems accurately, then check each result with a second method.
Practice
Mastery check
01Compare 0.36 and 0.34.
Answer: 0.36 > 0.34
02Compare 0.39 and 0.36.
Answer: 0.39 > 0.36
03Compare 0.42 and 0.38.
Answer: 0.42 > 0.38
04Compare 0.45 and 0.40.
Answer: 0.45 > 0.40
05Compare 0.48 and 0.42.
Answer: 0.48 > 0.42
06Compare 0.51 and 0.44.
Answer: 0.51 > 0.44
07Compare 0.54 and 0.46.
Answer: 0.54 > 0.46
08Compare 0.57 and 0.48.
Answer: 0.57 > 0.48
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.