Question

Add the following measurements and round off the answer: (a) \( \begin{array}{lll} 1.55 \mathrm{~cm} & \text { (b) } & 5.0 \mathrm{~cm} \end{array} \) $$ \begin{array}{r} 36.15 \mathrm{~cm} \\ +17.3 \mathrm{~cm} \\ \hline \end{array} \( \)\begin{array}{r} 16.3 \mathrm{~cm} \\ +0.95 \mathrm{~cm} \\ \hline \end{array} $

Short answer

The final rounded measurement is 77.3 cm.

Step-by-step solution

Align the Measurements

Before adding the measurements, ensure all are in the same unit (centimeters), which they already are. Next, align them by their decimal points for proper addition.

Add the Measurements for Group 1

Add the first group of measurements below one another as stated: 1.55 cm + 5.0 cm + 36.15 cm + 17.3 cm. Start by adding from right to left in the decimals and manage the carry if necessary.

Calculate the Total for Group 1

Sum up the values: \[\begin{array}{c}1.55 \+5.0 \36.15 \17.3 \\hline60.0\end{array}\]

Add the Measurements for Group 2

Now add the second group of measurements together: 16.3 cm + 0.95 cm. Just like before, add from right to left.

Calculate the Total for Group 2

Perform the addition: \[\begin{array}{c}16.3 \+0.95 \\hline17.25\end{array}\]

Combine Results from Both Groups

Finally, add the totals of both groups:\[60.0 + 17.25\]

Perform the Final Addition

Add the results from Step 3 and Step 5:\[60.0 + 17.25 = 77.25\]

Round Off the Final Result

Round the total to one decimal place, since the least precise measurement was given to one decimal place. Therefore, round 77.25 to 77.3 cm.

Key concepts

Measurement Addition

When adding measurements, it is crucial to ensure that all numbers are in the same units before any calculations are performed. This guarantees accuracy and avoids the potential for mistakes in interpretation. In this exercise, all measurements are given in centimeters, so they can be directly added together. Proper alignment of digits is also necessary, which means placing the decimal points directly above each other. This alignment makes carrying and borrowing numbers easier, ensuring precision.

For effective addition of measurements:

• Ensure consistency in units (e.g., all measurements in centimeters).
• Line up decimal points before performing addition.
• Add from right to left, carrying over when necessary.

By following these steps, as seen in the provided example, we can confidently add multiple measurements and achieve an accurate result.

Rounding Numbers

Rounding is used in mathematics to make numbers simpler to use and understand without losing significant accuracy. In measurement addition, rounding is particularly applied to maintain consistency with the least precise measurement involved in the calculation.

To round correctly:

• Identify the decimal place to which you are rounding. In our exercise, measurements were correct to one decimal place.
• Look at the number immediately following that place. If it’s 5 or more, increase the rounding digit by one.
• If it’s less than 5, leave the rounding digit unchanged.

This principle ensures that the result conforms to the precision limit of the least accurate measurement, as shown when rounding 77.25 cm to 77.3 cm. Every time, respect the original precision level of the given measurements.

Units of Measurement

Units of measurement standardize the representation of quantities, allowing for clear communication and calculation of measurements. Here, centimeters (cm) were used consistently throughout the exercise. Consistent use of units is vital in any mathematical operation, but when performing addition, it guarantees the validity of the result.

Important aspects of units of measurement include:

• Consistent units across all measurements.
• Understanding the base units for conversions if needed.
• Checking final answers to ensure they are in desired units.

In calculations like this, verifying that all initial and final values are in the correct units (centimeters here) ensures that the mathematical operations give meaningful results applicable in real-world scenarios.