Grade 5 · Number & Operations in Base Ten · MAT-05-NBT-002
Read and Write Decimals to Thousandths
Represent and solve read and write decimals to thousandths problems using accurate mathematical models, notation, and reasoning.
Learning objectives
What you should be able to do
- Represent and solve read and write decimals to thousandths problems using accurate mathematical models, notation, and reasoning.
- Explain why a strategy for read and write decimals to thousandths 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.
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
Read and Write Decimals to Thousandths 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 read and write decimals to thousandths 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 101/1000 as a decimal.
101/1000 = 0.101Thousandths are recorded in the third place to the right of the decimal point.
Write 138/1000 as a decimal.
138/1000 = 0.138Thousandths are recorded in the third place to the right of the decimal point.
Write 175/1000 as a decimal.
175/1000 = 0.175Thousandths are recorded in the third place to the right of the decimal point.
Write 212/1000 as a decimal.
212/1000 = 0.212Thousandths are recorded in the third place to the right of the decimal point.
Write 249/1000 as a decimal.
249/1000 = 0.249Thousandths are recorded in the third place to the right of the decimal point.
Write 286/1000 as a decimal.
286/1000 = 0.286Thousandths are recorded in the third place to the right of the decimal point.
Write 323/1000 as a decimal.
323/1000 = 0.323Thousandths are recorded in the third place to the right of the decimal point.
Write 360/1000 as a decimal.
360/1000 = 0.360Thousandths are recorded in the third place to the right of the decimal point.
Write 397/1000 as a decimal.
397/1000 = 0.397Thousandths are recorded in the third place to the right of the decimal point.
Write 434/1000 as a decimal.
434/1000 = 0.434Thousandths are recorded in the third place to the right of the decimal point.
Write 471/1000 as a decimal.
471/1000 = 0.471Thousandths are recorded in the third place to the right of the decimal point.
Write 508/1000 as a decimal.
508/1000 = 0.508Thousandths are recorded in the third place to the right of the decimal point.
Write 545/1000 as a decimal.
545/1000 = 0.545Thousandths are recorded in the third place to the right of the decimal point.
Write 582/1000 as a decimal.
582/1000 = 0.582Thousandths are recorded in the third place to the right of the decimal point.
Write 619/1000 as a decimal.
619/1000 = 0.619Thousandths are recorded in the third place to the right of the decimal point.
Write 656/1000 as a decimal.
656/1000 = 0.656Thousandths are recorded in the third place to the right of the decimal point.
Write 693/1000 as a decimal.
693/1000 = 0.693Thousandths are recorded in the third place to the right of the decimal point.
Write 730/1000 as a decimal.
730/1000 = 0.730Thousandths are recorded in the third place to the right of the decimal point.
Write 767/1000 as a decimal.
767/1000 = 0.767Thousandths are recorded in the third place to the right of the decimal point.
Write 804/1000 as a decimal.
804/1000 = 0.804Thousandths are recorded in the third place to the right of the decimal point.
Practice
Guided practice with hints
01Write 841/1000 as a decimal.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 841/1000 = 0.841
02Write 878/1000 as a decimal.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 878/1000 = 0.878
03Write 915/1000 as a decimal.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 915/1000 = 0.915
04Write 952/1000 as a decimal.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 952/1000 = 0.952
05Write 989/1000 as a decimal.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 989/1000 = 0.989
06Write 27/1000 as a decimal.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 27/1000 = 0.027
Practice
Independent practice
01Write 64/1000 as a decimal.
Answer: 64/1000 = 0.064
02Write 101/1000 as a decimal.
Answer: 101/1000 = 0.101
03Write 138/1000 as a decimal.
Answer: 138/1000 = 0.138
04Write 175/1000 as a decimal.
Answer: 175/1000 = 0.175
05Write 101/1000 as a decimal.
Answer: 101/1000 = 0.101
06Write 138/1000 as a decimal.
Answer: 138/1000 = 0.138
07Write 175/1000 as a decimal.
Answer: 175/1000 = 0.175
08Write 212/1000 as a decimal.
Answer: 212/1000 = 0.212
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 249/1000 as a decimal.
249/1000 = 0.249
Write 286/1000 as a decimal.
286/1000 = 0.286
Write 323/1000 as a decimal.
323/1000 = 0.323
Write 360/1000 as a decimal.
360/1000 = 0.360
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Grade 5 Math Strategy Sprint
Solve and explain read and write decimals to thousandths problems accurately, then check each result with a second method.
Practice
Mastery check
01Write 397/1000 as a decimal.
Answer: 397/1000 = 0.397
02Write 434/1000 as a decimal.
Answer: 434/1000 = 0.434
03Write 471/1000 as a decimal.
Answer: 471/1000 = 0.471
04Write 508/1000 as a decimal.
Answer: 508/1000 = 0.508
05Write 545/1000 as a decimal.
Answer: 545/1000 = 0.545
06Write 582/1000 as a decimal.
Answer: 582/1000 = 0.582
07Write 619/1000 as a decimal.
Answer: 619/1000 = 0.619
08Write 656/1000 as a decimal.
Answer: 656/1000 = 0.656
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.