the length of a piece of string is known to be exactly 9.84 cm. two students measured the string. student A used a ruler marked in centimeters and got a measurement of 10 cm. student B used a ruler marked in millimeters and centimeters and got a measurement of 9.8 cm. how precise is the ruler originally used to measure the string ? explain
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To determine the precision of the ruler originally used to measure the string, we need to compare the measurements obtained by both students with the known length of the string (9.84 cm).
Student A used a ruler marked in centimeters and measured the string as 10 cm. Since the known length of the string is 9.84 cm, the ruler used by Student A has a precision of 1 cm.
Student B used a ruler marked in millimeters and centimeters and measured the string as 9.8 cm. Comparing it to the known length of 9.84 cm, we can see that Student B's measurement is 0.04 cm shorter than the actual length of the string.
Since Student B's ruler measures in millimeters, we can infer that each millimeter on the ruler represents a smaller unit than 0.04 cm. Therefore, Student B's ruler has a higher precision than Student A's ruler.
In conclusion, based on the measurements obtained by both students, the ruler originally used to measure the string has a lower precision than Student B's ruler, which can measure in millimeters and centimeters.
To determine the precision of the ruler originally used to measure the string, we need to compare the measurements of the students with the known length of the string.
Student A used a ruler marked in centimeters and measured the string as 10 cm. This means that the ruler has markings in centimeters and can measure up to the nearest centimeter. However, since the known length of the string is 9.84 cm, using this ruler may lead to a slight overestimation.
Student B used a ruler marked in millimeters and centimeters and measured the string as 9.8 cm. This ruler has markings in both millimeters and centimeters, which allows for more precise measurements. However, the measurement of 9.8 cm is slightly smaller than the known length of the string, indicating a slight underestimation.
Comparing the two measurements, we see that Student B's measurement of 9.8 cm is closer to the known length of the string at 9.84 cm. This suggests that Student B's ruler is more precise than Student A's ruler.
To determine the precision, we can calculate the difference between the measurement and the known length for each student. Student A's measurement has a difference of 0.16 cm (10 cm - 9.84 cm), while Student B's measurement has a difference of only 0.04 cm (9.8 cm - 9.84 cm).
Therefore, based on the differences, we can conclude that the ruler originally used by Student B, which is marked in millimeters and centimeters, is more precise than the ruler used by Student A, which is marked in centimeters only. The ruler used by Student B allows for measurements with smaller increments (millimeters), resulting in a more accurate measurement.