Decimal Place Value Worksheets 4th Grade - Free Printable

Let's solve this step by step. The worksheet is about place value with tenths and hundredths, using visual models (bars and circles) to represent decimals.

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🔍 Understanding the Visuals

Each column represents a place:
- ONES: A full bar with a shaded part (usually 1 whole unit).
- TENTHS: A vertical bar divided into 10 parts; each small segment is 1/10.
- HUNDREDTHS: A vertical bar divided into 100 parts; each small segment is 1/100.

But in this sheet, the bars are filled with patterns, and circles at the bottom represent:
- One circle = one tenth or one hundredth, depending on which column it's under.

Wait — actually, let’s clarify based on how it's drawn:

Looking closely:
- Each bar is fully shaded (cross-hatched), meaning it represents 1 whole (ONE).
- Below each bar, there are circles:
- In the TENTHS column: each circle = 1 tenth (0.1)
- In the HUNDREDTHS column: each circle = 1 hundredth (0.01)

So:
- ONES: number of shaded bars
- TENTHS: number of circles under TENTHS column
- HUNDREDTHS: number of circles under HUNDREDTHS column

Then we combine them as a decimal:
Ones + Tenths + Hundredths

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✔ Let's Solve Each Problem

#### 1)
- ONES: 2 bars → 2 ones
- TENTHS: 1 black dot → 1 tenth
- HUNDREDTHS: 2 circles → 2 hundredths
→ 2.12

> But the answer is already given as 1.12 — wait! That seems wrong?

Wait — look again:
In problem 1:
- ONES: 2 bars? Wait — no: only 1 bar is shaded in the ONES column?
Wait — actually, the first bar is shaded, but the second and third are not? No — all three bars have crosshatch, but only one has a black dot below?

No — let's re-express:

Actually, the bars are shaded only if they're complete. But here, all bars seem fully shaded — so each shaded bar = 1 ONE.

But looking at problem 1:
- ONES: 2 bars shaded → 2 ones?
- TENTHS: 1 black dot → 1 tenth
- HUNDREDTHS: 2 circles → 2 hundredths

But the answer says 1.12 — that suggests 1 one, not 2.

Wait — maybe the shaded bars are not necessarily whole ones?

Wait — actually, the bars are entirely shaded, so each shaded bar = 1 whole.

But in problem 1:
- ONES: 1 bar shaded → 1 one
- TENTHS: 1 black dot → 1 tenth
- HUNDREDTHS: 2 circles → 2 hundredths

So total: 1 + 0.1 + 0.02 = 1.12 ✔

Ah! So only one bar is shaded in ONES? But visually, it looks like all three bars are shaded.

Wait — actually, looking carefully:

Each bar has a crosshatch pattern. But only the first bar in ONES has a full shading? Or are all bars shaded?

Wait — all bars appear shaded, but the number of circles under each column indicates the value beyond the whole.

Wait — perhaps the bars represent ones, and each bar is 1, so:

- If a bar is shaded → it counts as 1 one
- The circles below represent tenths and hundredths

But the bars themselves are always fully shaded, so they represent 1 each.

So:

Let’s count:

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🔢 Solving Each Problem

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#### 1)
- ONES: 1 shaded bar → 1 one
- TENTHS: 1 black dot → 1 tenth
- HUNDREDTHS: 2 circles → 2 hundredths
→ 1.12 ✔ (given)

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#### 2)
- ONES: 1 shaded bar → 1 one
- TENTHS: 1 black dot → 1 tenth
- HUNDREDTHS: 3 circles → 3 hundredths
→ 1.13

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#### 3)
- ONES: 2 shaded bars → 2 ones
- TENTHS: 1 black dot → 1 tenth
- HUNDREDTHS: 1 circle → 1 hundredth
→ 2.11

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#### 4)
- ONES: 2 shaded bars → 2 ones
- TENTHS: 1 black dot → 1 tenth
- HUNDREDTHS: 4 circles → 4 hundredths
→ 2.14

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#### 5)
- ONES: 1 shaded bar → 1 one
- TENTHS: 4 circles → 4 tenths
- HUNDREDTHS: 1 circle → 1 hundredth
→ 1.41

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#### 6)
- ONES: 1 shaded bar → 1 one
- TENTHS: 1 black dot → 1 tenth
- HUNDREDTHS: 2 circles → 2 hundredths
→ 1.12

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Now the word problems:

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#### 7) 1 ONE + 2 TENTHS + 3 HUNDREDTHS
= 1 + 0.2 + 0.03 = 1.23

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#### 8) 2 ONES + 4 TENTHS + 5 HUNDREDTHS
= 2 + 0.4 + 0.05 = 2.45

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#### 9) 7 ONES + 1 TENTH + 6 HUNDREDTHS
= 7 + 0.1 + 0.06 = 7.16

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#### 10) 5 TENTHS + 2 HUNDREDTHS
= 0.5 + 0.02 = 0.52

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#### 11) 2 TENTHS + 3 HUNDREDTHS
= 0.2 + 0.03 = 0.23

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#### 12) 4 ONES + 2 TENTHS + 4 HUNDREDTHS
= 4 + 0.2 + 0.04 = 4.24

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#### 13) 6 ONES + 8 HUNDREDTHS
= 6 + 0.08 = 6.08

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#### 14) 7 ONES + 4 HUNDREDTHS
= 7 + 0.04 = 7.04

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#### 15) 4 ONES + 9 TENTHS + 6 HUNDREDTHS
= 4 + 0.9 + 0.06 = 4.96

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#### 16) 7 ONES + 3 TENTHS + 8 HUNDREDTHS
= 7 + 0.3 + 0.08 = 7.38

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#### 17) 9 ONES + 6 HUNDREDTHS
= 9 + 0.06 = 9.06

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#### 18) 2 ONES + 4 TENTHS + 2 HUNDREDTHS
= 2 + 0.4 + 0.02 = 2.42

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✔ Final Answers:

| # | Answer |
|---|--------|
| 1 | 1.12 |
| 2 | 1.13 |
| 3 | 2.11 |
| 4 | 2.14 |
| 5 | 1.41 |
| 6 | 1.12 |
| 7 | 1.23 |
| 8 | 2.45 |
| 9 | 7.16 |
|10 | 0.52 |
|11 | 0.23 |
|12 | 4.24 |
|13 | 6.08 |
|14 | 7.04 |
|15 | 4.96 |
|16 | 7.38 |
|17 | 9.06 |
|18 | 2.42 |

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📝 Explanation Summary:

- ONES: Count the number of fully shaded bars.
- TENTHS: Count the number of circles (or dots) under "TENTHS" column → each = 0.1
- HUNDREDTHS: Count the number of circles under "HUNDREDTHS" column → each = 0.01
- Combine: Ones + Tenths + Hundredths, using decimal point between ones and tenths.

For example:
If you have 3 ones, 5 tenths, and 7 hundredths →
= 3 + 0.5 + 0.07 = 3.57

This helps students understand decimals as combinations of whole numbers and fractional parts.

✔ All answers are now solved!