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: mostly shaded, but some white squares at the bottom.

Count unshaded squares in third grid:
- Looks like 4 squares are unshaded → so shaded = 100 - 4 = 96

Total shaded = 100 + 100 + 96 = 296 squares
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 compute exactly)

Actually:
$ \frac{296}{300} = \frac{296 ÷ 4}{300 ÷ 4} = \frac{74}{75} $

Now, $ \frac{74}{75} = 0.98666... $ → rounds to 0.987 if to 3 decimal places.

But since it's exact, we can write:
- Decimal: 0.986̅ (repeating), but typically we round to three decimals.

However, for consistency with the format, we’ll write:
- Fraction: $ \frac{74}{75} $
- Decimal: 0.987

But wait — maybe better to keep as $ \frac{296}{300} $, but simplified is preferred.

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

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🔹 Problem 3

Visuals:
- Four bars, each divided into 10 equal parts (like tenths).
- First three bars: fully shaded
- Fourth bar: 9 out of 10 parts shaded

So:
- Total shaded = 3 full bars + 9/10 of one bar
- That’s $ 3 + \frac{9}{10} = 3.9 $

As a fraction:
- $ 3 + \frac{9}{10} = \frac{30}{10} + \frac{9}{10} = \frac{39}{10} $

✔ Answer:
- Fraction: $ \frac{39}{10} $
- Decimal: 3.9

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🔹 Problem 4

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

So:
- Total shaded = 2 full bars + 3/10 of a bar
- $ 2 + \frac{3}{10} = 2.3 $

As a fraction:
- $ 2 + \frac{3}{10} = \frac{20}{10} + \frac{3}{10} = \frac{23}{10} $

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

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🔹 Problem 5

Visuals:
- Four 10×10 grids.
- First three: fully shaded
- Fourth: almost fully shaded, but a few small squares are unshaded.

Look closely:
- Each grid has 100 squares.
- First three: 100 × 3 = 300 shaded
- Fourth grid: Count unshaded squares.

From image: There are 3 small white squares (likely in corners), so shaded = 100 - 3 = 97

Total shaded = 300 + 97 = 397 squares
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{39}{10} $ | 3.9 |
| 4 | $ \frac{23}{10} $ | 2.3 |
| 5 | $ \frac{397}{400} $ | 0.9925 |

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📝 Notes:

- In problems 1–2, we're dealing with hundredths (10×10 grids).
- In problems 3–4, tenths (bars divided into 10 parts).
- In problem 5, again hundredths.
- Always simplify fractions when possible.
- Decimals should be accurate — use exact values or rounded appropriately.

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