Which of the following measurements are not equivalent?
[tex]$25 mg =0.025 g$[/tex]
[tex]$183 L=0.183 kL$[/tex]
[tex]$150 ms=0.150 s$[/tex]
[tex]$84 cm=8.4 mm$[/tex]
[tex]$24 dL =2.4 L$[/tex]
Answer (2)
Convert each measurement to a common unit.
Compare the converted value to the given value.
Identify the measurement where the converted value does not match the given value.
The measurement that is not equivalent is 84 cm = 8.4 mm .
Explanation
Understanding the Problem We are given a list of measurements and asked to identify which ones are not equivalent. To do this, we will convert each measurement to a common unit and compare it to the given value.
Converting mg to g
25 mg = 0.025 g
To convert milligrams (mg) to grams (g), we use the conversion factor 1 g = 1000 mg . Therefore, 25 mg = 1000 25 g = 0.025 g . This measurement is equivalent.
Converting L to kL
183 L = 0.183 kL
To convert liters (L) to kiloliters (kL), we use the conversion factor 1 kL = 1000 L . Therefore, 183 L = 1000 183 kL = 0.183 kL . This measurement is equivalent.
Converting ms to s
150 ms = 0.150 s
To convert milliseconds (ms) to seconds (s), we use the conversion factor 1 s = 1000 ms . Therefore, 150 ms = 1000 150 s = 0.150 s . This measurement is equivalent.
Converting cm to mm
84 cm = 8.4 mm
To convert centimeters (cm) to millimeters (mm), we use the conversion factor 1 cm = 10 mm . Therefore, 84 cm = 84 × 10 mm = 840 mm . This measurement is not equivalent, since 84 cm = 840 mm = 8.4 mm .
Converting dL to L
24 dL = 2.4 L
To convert deciliters (dL) to liters (L), we use the conversion factor 1 L = 10 dL . Therefore, 24 dL = 10 24 L = 2.4 L . This measurement is equivalent.
Final Answer The measurement that is not equivalent is 84 cm = 8.4 mm . The correct equivalent measurement is 84 cm = 840 mm .
Examples
In everyday life, we often need to convert between different units of measurement. For example, when cooking, you might need to convert grams to milligrams to measure a precise amount of an ingredient. Similarly, in construction, you might need to convert centimeters to millimeters when working on detailed designs. Understanding these conversions ensures accuracy and precision in various tasks.
The measurements that are not equivalent is 84 cm = 8.4 mm , as the correct value is 84 cm = 840 mm . All other measurements in the list are equivalent. Therefore, the correct choice is the measurement involving centimeters and millimeters.
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