Hi! I'm Vidi. Let's learn Place Value with Decimals (Thousandths) together — read with me, then play the games to win a ⭐!
🔵Reading & Writing Decimals to 3 Places
What is a Decimal?
A decimal is a way to show numbers less than 1 using a decimal point (•). The decimal point separates whole numbers from parts of a whole.
Place Value Chart:
| Hundreds | Tens | Ones | • | Tenths | Hundredths | Thousandths |
|---|---|---|---|---|---|---|
| 100 | 10 | 1 | • | 1/10 | 1/100 | 1/1000 |
| 0 | 0 | 3 | • | 4 | 2 | 5 |
Reading Decimals:
- 0.425 = "four hundred twenty-five thousandths"
- 3.7 = "three and seven tenths"
- 5.082 = "five and eighty-two thousandths"
Writing Decimals:
- "Six and fifteen hundredths" = 6.15
- "Two hundred thirty-four thousandths" = 0.234
DECIMAL PLACE VALUE CHART:
┌────┬────┬────┬───┬────┬─────┬──────┐
│ H │ T │ O │ • │ t │ h │ th │
├────┼────┼────┼───┼────┼─────┼──────┤
│100 │10 │1 │ • │1/10│1/100│1/1000│
├────┼────┼────┼───┼────┼─────┼──────┤
│ 4 │ 2 │ 7 │ • │ 3 │ 6 │ 9 │
└────┴────┴────┴───┴────┴─────┴──────┘
4 2 7 . 3 6 9 = Four hundred twenty-seven AND three hundred sixty-nine thousandths
VISUAL REPRESENTATION OF 0.425:
WHOLE SQUARE (1.00)
┌─────────────────┐
│░░░░░░░░░░░░░░░░░│ 42.5% shaded
│░░░░░░░░░░░░░░░░░│ = 0.425
│░░░░░░░░░░░░░░░░░│
│░░░░░░░░░░░░░░░░░│
│░░░░░░░░░░░░░░░ │
└─────────────────┘
4 tenths (0.4) + 2 hundredths (0.02) + 5 thousandths (0.005) = 0.425👀 See a worked example
Write the decimal: 3 tenths + 4 hundredths + 7 thousandths
- 3 tenths = 0.3
- 4 hundredths = 0.04
- 7 thousandths = 0.007
- Add: 0.3 + 0.04 + 0.007 = 0.347
Read the decimal: 25.406
- Whole number part: 25 = "twenty-five"
- Decimal part: 406 thousandths
- Complete: "Twenty-five and four hundred six thousandths"
Write as decimal: "Eight and fifteen thousandths"
- "Eight" = 8
- "fifteen thousandths" = 0.015
- Complete: 8.015 (not 8.15, which is fifteen hundredths!)
🤖 Vidi's Key Points
- Decimal point separates whole from part
- First place after decimal = tenths (1/10)
- Second place = hundredths (1/100)
- Third place = thousandths (1/1000)
- Always say "and" for the decimal point when reading
- 0.235 = two hundred thirty-five thousandths
🟢Rounding Decimals
What is Rounding?
Rounding makes numbers easier to work with by finding the closest "nice" number.
Steps to Round Decimals:
- Find the place value you're rounding to (tenths, hundredths)
- Look at the digit to the right
- If it's 5 or more → round UP
- If it's 4 or less → round DOWN (stay same)
Rounding to Tenths:
- 3.47 → Look at hundredths place (7 ≥ 5) → round up → 3.5
- 3.42 → Look at hundredths place (2 ≤ 4) → round down → 3.4
Rounding to Hundredths:
- 5.673 → Look at thousandths place (3 ≤ 4) → round down → 5.67
- 5.678 → Look at thousandths place (8 ≥ 5) → round up → 5.68
ROUNDING NUMBER LINE (to nearest tenth):
3.40 3.45 3.50
│ │ │
▼ ▼ ▼
├───────┼───────┤
│ │ │
3.42 → closer to 3.40 → rounds to 3.4
3.47 → closer to 3.50 → rounds to 3.5
ROUNDING DECISION TREE:
Start: Find rounding place
│
▼
Look at digit to the right
│
┌─────┴─────┐
▼ ▼
Is it ≥ 5? Is it ≤ 4?
│ │
▼ ▼
Round UP Round DOWN
(add 1) (stay same)👀 See a worked example
Round 7.348 to nearest tenth
- Tenths place: 3 (7.3__)
- Look at hundredths: 4
- 4 ≤ 4 → round down
- Answer: 7.3
Round 12.567 to nearest hundredth
- Hundredths place: 6 (12.56_)
- Look at thousandths: 7
- 7 ≥ 5 → round up (6 becomes 7)
- Answer: 12.57
Round 0.999 to nearest tenth
- Tenths place: 9 (0.9__)
- Look at hundredths: 9
- 9 ≥ 5 → round up (9 becomes 10, carry over)
- 0.9 + 0.1 = 1.0
- Answer: 1.0
🤖 Vidi's Key Points
- 5 or more? Round up! (5,6,7,8,9)
- 4 or less? Round down! (0,1,2,3,4)
- Rounding to tenths → look at hundredths
- Rounding to hundredths → look at thousandths
- Rounding can cause carries (0.999 → 1.0)
🟣Comparing Decimals
How to Compare Decimals:
Method 1: Use Place Value
- Compare whole numbers first
- If whole numbers are equal, compare tenths
- If tenths are equal, compare hundredths
- Continue to thousandths if needed
Method 2: Use Common Denominator
- 0.8 = 8/10 = 80/100
- 0.79 = 79/100
- 80/100 > 79/100, so 0.8 > 0.79
Method 3: Use Number Line
- Numbers to the right are greater
COMPARING DECIMALS NUMBER LINE:
0.79 0.8
│ │
▼ ▼
├──────────┤
│ │
0.75 0.76 0.77 0.78 0.79 0.80 0.81 0.82
│ │ │ │ │ │ │ │
0.79 < 0.8 (0.79 is to the left)
PLACE VALUE COMPARISON:
Number A: 5 . 6 7 8
Number B: 5 . 6 8 2
Step 1: Whole numbers = (5 = 5) ✓
Step 2: Tenths = (6 = 6) ✓
Step 3: Hundredths: 7 vs 8 → 7 < 8
Conclusion: 5.678 < 5.682👀 See a worked example
Compare: 0.8 and 0.79
Solution (Place Value):
- 0.8 = 0.80 (add zero to compare)
- Compare tenths: 8 vs 7
- 8 > 7, so 0.8 > 0.79
Compare: 3.245 and 3.25
- Write with same places: 3.250
- Compare: 3.245 vs 3.250
- Hundredths: 4 vs 5 → 4 < 5
- So 3.245 < 3.25
Arrange in ascending order: 0.5, 0.52, 0.502
- Write with same decimal places: 0.500, 0.520, 0.502
- Compare: 0.500 < 0.502 < 0.520
- Answer: 0.5, 0.502, 0.52
🤖 Vidi's Key Points
- Add zeros to make same number of decimal places
- Compare left to right (whole → tenths → hundredths → thousandths)
- > means "greater than"
- < means "less than"
- = means "equal to"
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