The length of a steel tape for measurements of buildings is `10m` and its width is `2.4cm`. What is the ratio of its length to width?

Options

A. `1130:3`
B. `1250:7`
C. `1250:3`
D. `1130:7`

Answer

To find the ratio of the length of the steel tape to its width, we will follow these steps:

### Step 1: Convert the Length to the Same Unit
The length of the steel tape is given as 10 meters, and the width is given as 2.4 centimeters. To find the ratio, we need to convert the length from meters to centimeters.

- **Conversion**: 1 meter = 100 centimeters
- Therefore, 10 meters = 10 × 100 = 1000 centimeters.

### Step 2: Set Up the Ratio
Now that both measurements are in centimeters, we can set up the ratio of length to width.

- **Length**: 1000 centimeters
- **Width**: 2.4 centimeters
- The ratio of length to width = Length : Width = 1000 : 2.4

### Step 3: Simplify the Ratio
To simplify the ratio, we can divide both parts of the ratio by the width (2.4).

- First, we can express 2.4 as a fraction: 2.4 = 24/10
- Therefore, the ratio becomes:
\[ 1000 : 2.4 = 1000 : \frac{24}{10} \]

- When we divide, we can multiply by the reciprocal:
\[ 1000 \div \frac{24}{10} = 1000 \times \frac{10}{24} \]

### Step 4: Perform the Multiplication
Now we will perform the multiplication:
- \( 1000 \times \frac{10}{24} = \frac{10000}{24} \)

### Step 5: Simplify the Fraction
Next, we simplify \( \frac{10000}{24} \):
- Divide both the numerator and the denominator by 4:
\[ \frac{10000 \div 4}{24 \div 4} = \frac{2500}{6} \]

### Step 6: Write the Final Ratio
The final ratio of the length to width is:
- \( 2500 : 6 \)

### Conclusion
Thus, the ratio of the length of the steel tape to its width is \( 2500 : 6 \).

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