A scale is calibrated to centimeters and the following measurements are stored by the scale. Find out significant digits.
(i) 200 m
(ii) 92.80 m
(iii) 80.26 m
(iv) 8.23 cm
(v) 8.91 mm
(vi) 6.001 mm

Answer

To find the significant digits in the given measurements, we will analyze each measurement step by step.

### Step-by-Step Solution:

1. **Measurement (i): 200 m**
- Convert to centimeters: \( 200 \, \text{m} = 20000 \, \text{cm} \)
- Significant digits: The number "200" can be ambiguous. If it is written as "200." (with a decimal point), it has 3 significant digits. However, without a decimal point, it typically has 1 significant digit. Therefore, we consider it has **1 significant digit**.

2. **Measurement (ii): 92.80 m**
- Convert to centimeters: \( 92.80 \, \text{m} = 9280 \, \text{cm} \)
- Significant digits: The number "92.80" has 4 significant digits (the trailing zero after the decimal counts as significant). Thus, it has **4 significant digits**.

3. **Measurement (iii): 80.26 m**
- Convert to centimeters: \( 80.26 \, \text{m} = 8026 \, \text{cm} \)
- Significant digits: The number "80.26" has 4 significant digits. Thus, it has **4 significant digits**.

4. **Measurement (iv): 8.23 cm**
- Significant digits: The number "8.23" has 3 significant digits. Thus, it has **3 significant digits**.

5. **Measurement (v): 8.91 mm**
- Convert to centimeters: \( 8.91 \, \text{mm} = 0.891 \, \text{cm} \)
- Significant digits: The number "0.891" has 3 significant digits (the leading zero does not count). Thus, it has **3 significant digits**.

6. **Measurement (vi): 6.001 mm**
- Convert to centimeters: \( 6.001 \, \text{mm} = 0.6001 \, \text{cm} \)
- Significant digits: The number "0.6001" has 4 significant digits (the leading zero does not count). Thus, it has **4 significant digits**.

### Summary of Significant Digits:
- (i) 200 m: **1 significant digit**
- (ii) 92.80 m: **4 significant digits**
- (iii) 80.26 m: **4 significant digits**
- (iv) 8.23 cm: **3 significant digits**
- (v) 8.91 mm: **3 significant digits**
- (vi) 6.001 mm: **4 significant digits**