CCSS: CCSS.MATH.CONTENT.5.NBT.A.3 · Difficulty: medium
Fast Track
19 min
Standard
25 min
Thorough
31 min
Learning Objectives (What You'll Master Today)
Read and write decimals to thousandths using base-ten numerals, number names, and expanded form
Compare two decimals to thousandths based on the value of each digit
Identify the place value of each digit in a decimal number up to thousandths
Round decimals to any place using understanding of place value
I Can... I can read and write decimals to thousandths using base-ten numerals, number names, and expanded form
(A) Mathematical Concepts - Self-Learning Guide
Big Idea: Key Concept
Every digit in a number has a value based on its position, or place. To the left of the decimal point, we have ones, tens, hundreds, and so on — each place is 10 times greater than the one to its right. To the right of the decimal point, we have tenths, hundredths, and thousandths — each place is 10 times smaller than the one to its left. For example, in the number 3.745, the 7 is in the tenths place (worth 0.7), the 4 is in the hundredths place (worth 0.04), and the 5 is in the thousandths place (worth 0.005). Understanding place value helps us compare decimals correctly: 0.35 is greater than 0.305 because 5 hundredths is more than 0 hundredths, even though 0.305 has more digits.
🧪 Interactive Simulation
How-To Methods
Identify the Decimal Point: Find the dot that separates the whole-number part from the fractional part.
Name Each Place: Starting from the decimal point, move right: tenths, hundredths, thousandths. Each place is 1/10 of the place to its left.
Read the Value of Each Digit: A digit's value equals the digit times its place value. For example, 4 in the hundredths place = 4 x 0.01 = 0.04.
Write in Expanded Form: Break the number into the sum of each digit's value. Example: 2.36 = 2 + 0.3 + 0.06.
Compare Decimals: Line up the decimal points and compare digits from left to right, starting with the largest place value.
Use Zeros as Placeholders: Remember that 0.5 = 0.50 = 0.500. Adding zeros after the last decimal digit does not change the value.
Key Formula/Rule:
Decimal Place Value Pattern: Ones (1) → Tenths (0.1) → Hundredths (0.01) → Thousandths (0.001). Each place is 1⁄10 of the place to its left.
Worked Example:
Problem: Write 4.208 in expanded form and identify the value of each digit.
Identify the whole number part: The digit 4 is in the ones place, so its value is 4.
Identify the tenths digit: The digit 2 is in the tenths place, so its value is 0.2.
Identify the hundredths digit: The digit 0 is in the hundredths place, so its value is 0.00.
Identify the thousandths digit: The digit 8 is in the thousandths place, so its value is 0.008.
Answer: 4.208 = 4 + 0.2 + 0.008. The 4 is worth 4 ones, the 2 is worth 2 tenths, the 0 is worth 0 hundredths, and the 8 is worth 8 thousandths.
Why This Matters
Decimal place value is the foundation of how we work with money, measurements, and science. When you read a price tag of $3.49, you are reading a decimal. When a scientist measures 2.375 liters of liquid, every digit after the decimal matters for accuracy. Understanding that each place to the right is ten times smaller helps you compare, round, add, and subtract decimals confidently. This knowledge connects directly to fractions, percentages, and all higher-level math.
I am a decimal number between 2 and 3. My tenths digit is 6. My hundredths digit is the same as my ones digit. My thousandths digit is 4. What number am I?
Jayden saved $24.50 in January and $18.75 in February. He wants to buy a book that costs $45.00. He says he has enough because 24 + 18 = 42 and 42 is close to 45. Is Jayden's reasoning correct?
A. No — he has exactly $42.00, which is $3.00 short
B. Yes — $24.50 + $18.75 = $44.25, which rounds up to $45.00
A bakery lists these prices per cookie: Chocolate Chip at $1.25, Oatmeal Raisin at $1.052, Sugar Cookie at $1.205, and Peanut Butter at $1.50. Which cookie costs the LEAST?
In a long jump competition, the top 3 results were: 1st place with 4.__ 2 __ meters, 2nd place with 4.506 meters, and 3rd place with 4.497 meters. The first-place jump was exactly 0.015 meters longer than second place. What was the first-place distance?
In a science lab, a student needs to measure exactly 3.500 mL of liquid. She has measured 3.465 mL so far. She can add liquid in drops of 0.005 mL each. How many more drops does she need, and what will the display show after adding just 4 drops?
A. She needs 5 drops; after 4 drops the display shows 3.495 mL
B. She needs 7 drops; after 4 drops the display shows 3.490 mL
C. She needs 35 drops; after 4 drops the display shows 3.469 mL
D. She needs 7 drops; after 4 drops the display shows 3.485 mL
(E) Mini Quiz - Check Your Understanding!
Mini Quiz
E1. What is the place value of the digit 7 in 0.371?
A. Ones
B. Tenths
C. Hundredths
D. Thousandths
E2. Which decimal is between 4.56 and 4.57?
A. 4.555
B. 4.559
C. 4.565
D. 4.571
E3. Which symbol makes this statement true? 0.620 ___ 0.62
A. >
B. <
C. =
D. Cannot be determined
Self-Reflection
How did you feel about this topic?
Confident / Okay / Confused - Circle one
What is one thing you must remember?
Problem-Solving Strategy (4-Step Process)
Challenge Problem: A jeweler weighs three gemstones. Ruby weighs 2.358 grams, Sapphire weighs 2.4 grams, and Emerald weighs 2.35 grams. First, arrange the gemstones from lightest to heaviest. Then, find the difference in weight between the heaviest and lightest stones. Finally, write the weight of the Ruby in expanded form. Show your work for each step and explain your reasoning.
1. Understand:
2. Plan:
3. Execute:
4. Check:
(F) Answer Key & Detailed Explanations
#
Answer
Type
Solution
1
C
Apply
final_step: The expanded form is 6 + 0.03 + 0.009. Answer: C step_1: Identify each digit's place in 6.039: 6 is in ones, 0 is in tenths, 3 is in hundredths, 9 is in thousandths. step_2: Calculate each digit's value: 6 = 6, 0 x 0.1 = 0, 3 x 0.01 = 0.03, 9 x 0.001 = 0.009. step_3: Write expanded form: 6 + 0 + 0.03 + 0.009 = 6 + 0.03 + 0.009.
2
A
Apply
final_step: The digit 9 in $1.259 is in the thousandths place, worth 0.009. Answer: A step_1: Write out the place values for 1.259: 1 = ones, 2 = tenths, 5 = hundredths, 9 = thousandths. step_2: The digit 9 is in the thousandths place. step_3: Its value is 9 x 0.001 = 0.009.
3
D
Apply
final_step: 0.50 and 0.5 have exactly the same value. Answer: D step_1: Check option A: 0.40 vs 0.4. Since 0.40 = 0.4, they are equal, not greater. A is FALSE. step_2: Check option B: More digits doesn't mean larger. 0.1 has fewer digits than 0.099 but 0.1 > 0.099. B is FALSE. step_3: Check option C: Compare 0.9 and 0.12. Tenths: 9 > 1, so 0.9 > 0.12. C is FALSE. step_4: Check option D: 0.50 = 0.5 because the trailing zero adds no value. D is TRUE.
4
B
Apply
final_step: Bella finished fastest with 13.099 seconds. Answer: B step_1: Compare tenths digits: Alex 13.4_, Bella 13.0_, Carlos 13.4_, Diana 13.5_. step_2: Bella has 0 in the tenths place, which is the smallest tenths digit. So 13.099 < 13.4_ < 13.5. step_3: Verify: 13.099 < 13.41 < 13.45 < 13.5. Bella's time is the lowest.
5
A
Apply
final_step: The mystery number is 2.624. Answer: A step_1: The number is between 2 and 3, so the ones digit is 2: 2.___. step_2: Tenths digit is 6: 2.6__. step_3: Hundredths digit equals the ones digit (2): 2.62_. step_4: Thousandths digit is 4: 2.624.
6
C
Apply
final_step: Monday's measurement is larger by 0.045 cm. Answer: C step_1: Monday: 12.750 cm. Friday: 12.705 cm. Compare: both start with 12.7. step_2: Hundredths: Monday has 5, Friday has 0. Since 5 > 0, Monday's measurement is larger. step_3: Difference: 12.750 - 12.705 = 0.045 cm.
7
D
Apply
final_step: Jayden has $43.25, which is $1.75 short of $45.00. His reasoning was incorrect because he ignored the decimal parts. Answer: D step_1: Add the whole dollars: $24 + $18 = $42. step_2: Add the cents: $0.50 + $0.75 = $1.25. step_3: Total: $42 + $1.25 = $43.25. step_4: Compare to $45.00: $45.00 - $43.25 = $1.75 short.
8
B
Apply
final_step: Oatmeal Raisin at $1.052 costs the least. Answer: B step_1: Write all prices with three decimal places: Choc Chip = 1.250, Oatmeal = 1.052, Sugar = 1.205, PB = 1.500. step_2: Compare tenths: Oatmeal has 0, all others have 2 or 5. So Oatmeal (1.052) is the smallest. step_3: Verify order: 1.052 < 1.205 < 1.250 < 1.500.
9
A
Apply
final_step: The first-place distance was 4.521 meters. Answer: A step_1: Second place jumped 4.506 meters. First place was 0.015 meters longer. step_2: Add: 4.506 + 0.015. Line up decimals: 6 + 5 thousandths = 11 thousandths → write 1, carry 1. 0 + 1 hundredths + 1 carry = 2 hundredths. 5 + 0 tenths = 5 tenths. step_3: Result: 4.521 meters.
10
D
Apply
final_step: She needs 7 more drops. After 4 drops, the display shows 3.485 mL. Answer: D step_1: Find the remaining amount: 3.500 - 3.465 = 0.035 mL. step_2: Each drop is 0.005 mL. Number of drops: 0.035 ÷ 0.005 = 7 drops. step_3: After 4 drops: 4 x 0.005 = 0.020 mL added. Display: 3.465 + 0.020 = 3.485 mL.
(G) Mini Quiz Answers
Multiple Choice:
E1. C
E2. C
E3. C
Self-Reflection:
I learned that every spot after the decimal has a name and a value — tenths, hundredths, thousandths. The trickiest part for me was comparing decimals like 0.305 and 0.35, because I thought more digits meant a bigger number. Now I know to compare place by place from left to right, just like reading a number.
Problem-Solving Strategy (4-Step):
1. Understand: A scientist recorded two temperature readings: 36.450°C and 36.405°C. We need to determine which temperature is higher and find the difference between them.
2. Plan: First, compare the two decimals digit by digit starting from the left. Then subtract the smaller from the larger to find the difference.
3. Execute: Step 1: Both start with 36.4. Step 2: Compare hundredths: 36.450 has 5 in hundredths, 36.405 has 0 in hundredths. Since 5 > 0, the first reading (36.450) is higher. Step 3: Subtract: 36.450 - 36.405 = 0.045°C.
4. Check: Verify: 36.405 + 0.045 = 36.450. Correct. The difference of 0.045 makes sense because it is less than one-tenth of a degree.
(H) Error Analysis Notebook (Growth Mindset Tool)
Problem #
My Score
Error Type
What I Learned / How to Improve
#9
0/15
Concept
"I forgot to check my answer. Next time I will verify my solution."