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\begin{tabular}{l} 4. The following set of measurements (in cm) was recorded during \\ experiment: \\ 56,\( 8 ; 55,4 ; 78,9 ; 47,8 ; 34,2 ; 67,6 ; 45,5 ; 34,5 ; 64,5 \) \\ 88 \\ (a) Find the sum of the measurements and round it off to the nearest \\ whole number. \\ \( \begin{array}{l}\text { (ind }\end{array} \) \\ First round off each measurement to the nearest whole number and \\ en find the sum. \\ \hline\end{tabular}

Ask by Paul Christensen. in South Africa
Mar 12,2025

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Tutor-Verified Answer

Answer

The sum of the rounded measurements is 575.

Solution

1. List the original measurements: \(56.8,\; 55.4,\; 78.9,\; 47.8,\; 34.2,\; 67.6,\; 45.5,\; 34.5,\; 64.5,\; 88\). 2. Round each measurement to the nearest whole number: - \(56.8 \to 57\) - \(55.4 \to 55\) - \(78.9 \to 79\) - \(47.8 \to 48\) - \(34.2 \to 34\) - \(67.6 \to 68\) - \(45.5 \to 46\) - \(34.5 \to 35\) - \(64.5 \to 65\) - \(88\) is already a whole number. 3. The rounded measurements are: \(57,\; 55,\; 79,\; 48,\; 34,\; 68,\; 46,\; 35,\; 65,\; 88\). 4. Find the sum: \[ 57 + 55 + 79 + 48 + 34 + 68 + 46 + 35 + 65 + 88 \] Compute step-by-step: - \(57 + 55 = 112\) - \(112 + 79 = 191\) - \(191 + 48 = 239\) - \(239 + 34 = 273\) - \(273 + 68 = 341\) - \(341 + 46 = 387\) - \(387 + 35 = 422\) - \(422 + 65 = 487\) - \(487 + 88 = 575\) 5. The sum of the rounded measurements is \(575\).

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To find the sum of the measurements, let's first round each value to the nearest whole number. The rounded measurements are: 56, 55, 79, 48, 34, 68, 46, 35, 65, and 88. Adding these up gives us a total of 55 + 79 + 48 + 34 + 68 + 46 + 35 + 65 + 88 = 511. So, the sum of the measurements rounded to the nearest whole number is 511 cm. Now, let’s calculate the sum without rounding initially. The original measurements sum up to: 56.8 + 55.4 + 78.9 + 47.8 + 34.2 + 67.6 + 45.5 + 34.5 + 64.5 + 88 = 469.7 cm. When we round 469.7 to the nearest whole number, we also get 470 cm. Thus, rounding before or after can lead to different results, so it’s important to be consistent in our approach!

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