glamrockqueen7

2021-02-21

A measurement using a ruler marked in centimeters is reported as 6 cm. What is the range of values for the actual measurement?

pierretteA

Step 1
The ruler have markings in centimeters.
The given reading is 6 cm.
Step 2
To find: The range of actual measurement.
The ruler measures in centimeters, so any value between 5.5 cm and 6.5 cm will be measured as 6 cm.
Thus, the range of our actual measurement is 5.5 cm to 6.5 cm or the range of actual measurement is .

Jazz Frenia

Let's denote the actual measurement as $x$ (in centimeters). The reported measurement is 6 cm.
Since the ruler is marked in centimeters, the reported measurement can be considered as an approximation of the actual measurement. Therefore, the range of values for the actual measurement can be determined by considering the possible error in the reported measurement.
Let's assume the maximum possible error in the reported measurement is $\Delta$. The actual measurement $x$ can then range from $6-\Delta$ to $6+\Delta$.
In mathematical notation, the range of values for the actual measurement can be expressed as:
$6-\Delta \le x\le 6+\Delta$
Thus, the range of values for the actual measurement is $\overline{)6-\Delta \le x\le 6+\Delta }$.

Mr Solver

The range of values for the actual measurement depends on the precision and accuracy of the ruler when a measurement made with a ruler marked in centimeters is reported as 6 cm.
Assuming the ruler is accurate and the measurement is reported to the nearest centimeter, the range of values for the actual measurement would include all values between 5.5 cm and 6.5 cm. This is because the reported value of 6 cm means that the actual measurement could be slightly less than 6 cm or slightly more than 6 cm, but not less than 5.5 cm or greater than 6.5 cm.
However, if the ruler is not accurate or the measurement is not reported to the nearest centimeter, the range of values for the actual measurement could be larger. For example, if the ruler has significant measurement errors or if the measurement is reported with rounding errors, the range of values for the actual measurement could extend beyond the 5.5 cm to 6.5 cm range. In such cases, it would be necessary to consider the limitations of the measuring instrument or the precision of the measurement technique to determine the range of values for the actual measurement accurately.

Andre BalkonE

If a measurement using a ruler marked in centimeters is reported as 6 cm, the range of values for the actual measurement can vary due to possible measurement errors. In this case, the range would typically include values slightly above and below 6 cm.
The uncertainty in the measurement can be influenced by various factors, such as the precision of the ruler, human error, or the conditions under which the measurement was taken. To determine the range, we need to consider the potential error associated with the measurement.
If we assume a small measurement error of ±0.5 cm, the range of values for the actual measurement would be between 5.5 cm and 6.5 cm. This means that the actual measurement could be as low as 5.5 cm or as high as 6.5 cm, considering the margin of error.
It's important to note that the range of values provided here is just an example based on a specific assumed error. The actual range could differ depending on the specific circumstances and the precision of the measurement instrument used.

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