Complete the following metric conversions using the correct number of significant figures: (a) 28.0 cm to m (b) 1000. m to km (c) 9.28 cm to mm (d) 10.68 g to mg (e) 6.8 \times 10^4 mg to kg (f) 8.54 g to kg (g) 25.0 mL to L (h) 22.4 L to µL
The Correct Answer and Explanation is:
Here are the conversions with the correct number of significant figures:
- (a) 28.0 cm = 0.280 m
- (b) 1000. m = 1.000 km
- (c) 9.28 cm = 92.8 mm
- (d) 10.68 g = 10,680 mg
- (e) 6.8 × 10⁴ mg = 0.068 kg
- (f) 8.54 g = 0.00854 kg
- (g) 25.0 mL = 0.0250 L
- (h) 22.4 L = 2.24 × 10⁷ µL
Explanation:
Metric conversions are streamlined because the system is based entirely on multiples of ten. To move between units, you either multiply or divide by powers of ten depending on whether you’re moving up or down the prefix scale.
Preserving significant figures is essential since it reflects how precise a measurement is. For instance, 28.0 cm has three significant figures. When you divide by 100 to convert to meters, the result (0.280 m) must also retain three significant figures. This rule applies throughout — your final answer must carry the same number of significant figures as the original value unless otherwise dictated by mathematical operations.
Take part (b): 1000. m has four significant figures because of the decimal point. Dividing by 1000 to convert to kilometers gives 1.000 km, where the trailing zeros are significant because they reflect the precision of the original measurement.
In part (e), you’re converting from milligrams to kilograms — a leap across six powers of ten. Therefore, divide by 10⁶. Starting with 6.8 × 10⁴ mg (two significant figures), your result is 0.068 kg, keeping the same level of precision.
In part (h), you multiply by 10⁶ to go from liters to microliters. Since 22.4 L has three significant figures, the result must also have three, which gives 2.24 × 10⁷ µL.
These conventions ensure scientific communication remains clear and precise across contexts and disciplines.
