A student skipped a step when she tried to convert 26 hours into seconds, and she got the following incorrect result:
26 hours [tex]$\left(\frac{60 \text { seconds }}{1 \text { minute }}\right)=1560$[/tex] seconds
What conversion ratio did she skip in this multiple-step conversion?
A. [tex]$\frac{60 \text { minutes }}{1 \text { hour }}$[/tex]
B. [tex]$\frac{1 \text { minute }}{60 \text { seconds }}$[/tex]
C. [tex]$\frac{60 \text { seconds }}{1 \text { minute }}$[/tex]
D. [tex]$\frac{1 \text { hour }}{60 \text { minutes }}$[/tex]
Answer (2)
The student incorrectly converted 26 hours to seconds by skipping a conversion step.
The complete conversion requires converting hours to minutes and then minutes to seconds.
The student only converted minutes to seconds, missing the hours to minutes conversion.
The missing conversion ratio is 1 hour 60 minutes .
Explanation
Problem Analysis The problem is to identify the missing conversion factor when converting 26 hours into seconds. The student's incorrect calculation only included the conversion from minutes to seconds, skipping the necessary step to convert hours to minutes first.
Identifying the Missing Conversion Factor To convert hours to seconds, we need two conversion factors: one to convert hours to minutes and another to convert minutes to seconds. The correct conversion should be: 26 hours × 1 hour 60 minutes × 1 minute 60 seconds The student's calculation was: 26 hours × 1 minute 60 seconds = 1560 seconds Comparing the correct conversion with the student's calculation, we can identify the missing conversion factor.
Determining the Missing Step The student skipped the conversion from hours to minutes. The missing conversion factor is: 1 hour 60 minutes This conversion factor is needed to change hours into minutes before converting minutes into seconds.
Final Answer Therefore, the correct answer is A. 1 hour 60 minutes
Examples
In real life, unit conversions are essential in many fields, such as cooking, construction, and science. For example, when following a recipe, you might need to convert ounces to grams or cups to milliliters. In construction, you might need to convert feet to meters when working with international blueprints. In physics, you often need to convert between different units of time, distance, and mass to solve problems. Understanding unit conversions ensures accuracy and consistency in these applications.
The student skipped the conversion from hours to minutes when converting 26 hours into seconds. The needed conversion ratio is 1 hour 60 minutes . Therefore, the correct answer is A.
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