Chapter CSB1.12, Problem 5E

To determine

To calculate: The estimated length of the line segment to nearest half, quarter, eight or sixteenth inch.

  

Answer to Problem 5E

The length of line segment to nearest half is approximately $2\frac{1}{2}$ inch, to nearest quarter is approximately $2$ inches, to nearest eight is approximately $2\frac{1}{8}$ inch and to nearest eight is approximately $2\frac{1}{16}$ inch.

The most precise measurement is when measured nearest to sixteenth inch.

Explanation of Solution

Given information:

The line segment is provided below,

  

Consider the line segment is provided below,

  

The estimated length of line segment could be 6 centimeters.

To measure the length of line segment, put end of line at zero of scale and see the point up to which the other end of the segment is stretched.

  

For nearest half inch divide the inch in two equal parts.

Observe the measurement of line segment on inch scale. The length is close to $2\frac{1}{2}$ inch rather than 1 inch or 2 inch.

Therefore, length of line segment to nearest half is approximately $2\frac{1}{2}$ inch.

For nearest quarter inch divide the inch in four equal parts and each part measures $\frac{1}{4}\text{th}$ of an inch.

Observe the measurement of line segment on inch scale. The length is close to $2$ inches rather than $2\frac{1}{4}$ inch.

Therefore, length of line segment to nearest quarter is approximately $2$ inches.

For nearest eight inch divide the inch in eight equal parts and each part measures $\frac{1}{8}\text{th}$ of an inch.

Observe the measurement of line segment on inch scale. The length is close to $2\frac{1}{8}$ inch rather than $2$ inches.

Therefore, length of line segment to nearest eight is approximately $2\frac{1}{8}$ inch.

For nearest sixteenth inch divide the inch in sixteen equal parts and each part measures $\frac{1}{16}\text{th}$ of an inch.

Observe the measurement of line segment on inch scale. The length is close to $2\frac{1}{16}$ inch rather than $2$ inches.

Therefore, length of line segment to nearest eight is approximately $2\frac{1}{16}$ inch.

Thus, the most precise measurement is when measured nearest to sixteenth inch.