Identify Place Value Grids as Fractions & Decimals - Math ... - Free Printable

Let's solve each problem step by step. The goal is to write the shaded portions as fractions and decimals based on the visual representations.

Each grid or bar represents a whole, and we need to determine what fraction (and decimal) of the total is shaded.

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🔹 Problem 1

Visuals:
- Two 10×10 grids.
- First grid: Fully shaded → 100 out of 100 squares.
- Second grid: Mostly shaded, but missing a few squares.

Counting:
- Each 10×10 grid has 100 squares.
- First grid: 100 shaded.
- Second grid: Let’s count the unshaded squares.
- It looks like only 3 squares are unshaded in the bottom right corner.
- So, shaded = 100 - 3 = 97 squares.

Total shaded = 100 + 97 = 197 squares
Total possible = 100 + 100 = 200 squares

So:

- Fraction: $ \frac{197}{200} $
- Decimal: $ \frac{197}{200} = 0.985 $

✔ Answer:
- Fraction: $ \frac{197}{200} $
- Decimal: 0.985

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🔹 Problem 2

Visuals:
- Three 10×10 grids.
- First two: fully shaded
- Third: almost fully shaded, but with a small portion unshaded.

Count:
- First two: 100 + 100 = 200 shaded
- Third: Only a few squares unshaded — look at the bottom right.
- Looks like 4 squares are unshaded → so 96 shaded

Total shaded = 200 + 96 = 296
Total possible = 300

So:
- Fraction: $ \frac{296}{300} $
- Simplify: divide numerator and denominator by 4 → $ \frac{74}{75} $
- Decimal: $ \frac{296}{300} = 0.98666... \approx 0.987 $

But let's calculate exactly:
$ \frac{296}{300} = 0.986\overline{6} $, which rounds to 0.987 if rounded to three decimal places.

However, since this is likely expecting exact values, we can write:

- Fraction: $ \frac{74}{75} $ (simplified)
- Decimal: 0.9867 (rounded to four decimal places), but often written as 0.987

But let's check: $ \frac{296}{300} = \frac{148}{150} = \frac{74}{75} $

And $ \frac{74}{75} = 0.98666... $

So:
- Fraction: $ \frac{74}{75} $
- Decimal: 0.987 (rounded)

✔ Answer:
- Fraction: $ \frac{74}{75} $
- Decimal: 0.987

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🔹 Problem 3

Visuals:
- Four bars, each divided into 10 equal parts (tenths).
- First three: fully shaded
- Fourth: shaded for 8 out of 10 parts

So:
- Total shaded: 3 full bars + 8/10 of a bar = 3 + 0.8 = 3.8

As a fraction:
- 3 full bars = $ \frac{30}{10} $
- Plus $ \frac{8}{10} $
- Total = $ \frac{38}{10} = \frac{19}{5} $

So:
- Fraction: $ \frac{19}{5} $ or $ \frac{38}{10} $
- Decimal: 3.8

✔ Answer:
- Fraction: $ \frac{19}{5} $ or $ \frac{38}{10} $
- Decimal: 3.8

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🔹 Problem 4

Visuals:
- Three bars, each divided into 10 parts.
- First two: fully shaded
- Third: shaded for 3 out of 10 parts

So:
- Shaded = 2 full bars + 3/10 = 2 + 0.3 = 2.3

As a fraction:
- $ 2 + \frac{3}{10} = \frac{23}{10} $

So:
- Fraction: $ \frac{23}{10} $
- Decimal: 2.3

✔ Answer:
- Fraction: $ \frac{23}{10} $
- Decimal: 2.3

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🔹 Problem 5

Visuals:
- Four 10×10 grids.
- First three: fully shaded
- Fourth: mostly shaded, but only 3 squares unshaded

Each grid = 100 squares
- First three: 3 × 100 = 300 shaded
- Fourth: 100 - 3 = 97 shaded
- Total shaded = 300 + 97 = 397
- Total possible = 400

So:
- Fraction: $ \frac{397}{400} $
- Decimal: $ \frac{397}{400} = 0.9925 $

✔ Answer:
- Fraction: $ \frac{397}{400} $
- Decimal: 0.9925

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✔ Final Answers:

| Problem | Fraction | Decimal |
|--------|------------------|-------------|
| 1 | $ \frac{197}{200} $ | 0.985 |
| 2 | $ \frac{74}{75} $ | 0.987 |
| 3 | $ \frac{19}{5} $ | 3.8 |
| 4 | $ \frac{23}{10} $ | 2.3 |
| 5 | $ \frac{397}{400} $ | 0.9925 |

> 💡 Note: For Problem 2, $ \frac{296}{300} $ simplifies to $ \frac{74}{75} $, and $ \frac{74}{75} = 0.98666... $, which rounds to 0.987 when rounded to three decimal places.

Let me know if you'd like these written in a printable format!