This decimal numbers worksheet helps students practice converting between fractions and decimals through varied exercises and visual grid representations.

Let's solve each part of the worksheet step by step.

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1. Write each of the following fractions as a decimal

We convert fractions to decimals by dividing the numerator by the denominator.

#### a) $ \frac{118}{1000} $

- Since the denominator is 1000, we move the decimal point three places to the left.
- $ 118 \div 1000 = 0.118 $

✔ Answer: 0.118

#### b) $ \frac{921}{1000} $

- Again, denominator is 1000 → move decimal 3 places left.
- $ 921 \div 1000 = 0.921 $

✔ Answer: 0.921

#### c) $ \frac{301}{500} $

- We can divide 301 by 500:
- $ 301 \div 500 = 0.602 $
- (Alternatively, multiply numerator and denominator by 2 to get $ \frac{602}{1000} = 0.602 $)

✔ Answer: 0.602

#### d) $ \frac{124}{100} $

- Denominator is 100 → move decimal two places left.
- $ 124 \div 100 = 1.24 $

✔ Answer: 1.24

#### e) $ \frac{48}{250} $

- Simplify or divide directly:
- $ 48 \div 250 = 0.192 $
- (Or convert: $ \frac{48}{250} = \frac{48 \times 4}{250 \times 4} = \frac{192}{1000} = 0.192 $)

✔ Answer: 0.192

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2. Write each of the following decimals as a fraction

We write decimals as fractions using place value, then simplify.

#### a) 0.853

- This is 853 thousandths → $ \frac{853}{1000} $
- Check if it simplifies: 853 is a prime number? (Yes, it doesn't divide evenly by 2, 3, 5, etc.)
- So, $ \frac{853}{1000} $ is already in simplest form.

✔ Answer: $ \frac{853}{1000} $

#### b) 0.712

- 712 thousandths → $ \frac{712}{1000} $
- Simplify: divide numerator and denominator by 8
- $ 712 \div 8 = 89 $
- $ 1000 \div 8 = 125 $
- So, $ \frac{89}{125} $

✔ Answer: $ \frac{89}{125} $

#### c) 0.350

- 350 thousandths → $ \frac{350}{1000} $
- Simplify: divide by 50 → $ \frac{7}{20} $

✔ Answer: $ \frac{7}{20} $

#### d) 0.159

- 159 thousandths → $ \frac{159}{1000} $
- Check for simplification: 159 ÷ 3 = 53 → 159 = 3 × 53; 1000 not divisible by 3 → no common factors
- So, $ \frac{159}{1000} $ is simplified.

✔ Answer: $ \frac{159}{1000} $

#### e) 0.110

- 110 thousandths → $ \frac{110}{1000} $
- Simplify: divide numerator and denominator by 10 → $ \frac{11}{100} $

✔ Answer: $ \frac{11}{100} $

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3. For each diagram, write the fraction and decimal that the shaded area represents

Each grid has 100 small squares, so each square is $ \frac{1}{100} $.

#### a) First Diagram

- Count shaded squares:
- The shape is L-shaped.
- Bottom row: 10 full squares
- Second row from bottom: 10 squares
- Third row: 10 squares
- Fourth row: 10 squares
- Fifth row: 10 squares
- Sixth row: 10 squares
- Seventh row: 10 squares
- Eighth row: 10 squares
- Ninth row: 10 squares
- Tenth row: 10 squares

Wait — actually, let’s look more carefully.

Looking at the image:

- The grid is 10×10 = 100 squares.
- The shaded region appears to be missing a white rectangle in the top-left corner.
- The white unshaded area is a 3×3 square (top-left), so:
- White squares: 3 × 3 = 9
- Shaded squares: 100 − 9 = 91

✔ So, shaded area = $ \frac{91}{100} = 0.91 $

#### b) Second Diagram

- There is a white rectangle in the center.
- It appears to be 4 columns wide and 3 rows high → 4 × 3 = 12 white squares
- Total squares: 100
- Shaded squares: 100 − 12 = 88

✔ So, shaded area = $ \frac{88}{100} = \frac{22}{25} = 0.88 $

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✔ Final Answers:

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#### 1. Fractions to Decimals
a) 0.118
b) 0.921
c) 0.602
d) 1.24
e) 0.192

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#### 2. Decimals to Fractions
a) $ \frac{853}{1000} $
b) $ \frac{89}{125} $
c) $ \frac{7}{20} $
d) $ \frac{159}{1000} $
e) $ \frac{11}{100} $

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#### 3. Diagrams
a) Fraction: $ \frac{91}{100} $, Decimal: 0.91
b) Fraction: $ \frac{88}{100} $ or $ \frac{22}{25} $, Decimal: 0.88

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