Question
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\( 2600 \times 900 \), and Maria estimates by cark both estimates. a) Work b) Use the column method to find the exact number of litres c) Whose estimate was more accurate? How much closer wos this estimate to the exact answer? a) How many seconds are there in a day? b) Use an estimate and then compensate, to calculate how many seconds there are in a month of 31 days.

Ask by Gibbs Bowman. in South Africa
Mar 13,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

**Part 1: Calculate \( 2600 \times 900 \)** - **Exact Answer**: \( 2600 \times 900 = 2,340,000 \) **Part 2: Estimate and Column Method** a) **Estimation**: - Maria estimates \( 2600 \) as \( 3000 \) and \( 900 \) as \( 1000 \). - **Estimated Product**: \( 3000 \times 1000 = 3,000,000 \) b) **Column Method**: - **Exact Calculation**: \[ \begin{array}{r} 2600 \\ \times 900 \\ \hline 0000 \\ 234000 \\ \hline 2,340,000 \\ \end{array} \] - **Result**: \( 2,340,000 \) **Part 3: Accuracy Comparison** - **Maria's Estimate**: \( 3,000,000 \) - **Exact Answer**: \( 2,340,000 \) - **Difference**: \( 3,000,000 - 2,340,000 = 660,000 \) - **Conclusion**: Maria's estimate was less accurate, being \( 660,000 \) more than the exact answer. **Part 4: Seconds in a Day** - **Total Seconds in a Day**: \( 24 \) hours \( \times 60 \) minutes \( \times 60 \) seconds \( = 86,400 \) seconds **Part 5: Seconds in a 31-Day Month Using Estimate and Compensation** - **Estimate**: - Assume \( 30 \) days in a month. - \( 30 \) days \( \times 86,400 \) seconds/day \( = 2,592,000 \) seconds - **Compensation**: - \( 31 - 30 = 1 \) extra day. - \( 1 \) day \( \times 86,400 \) seconds/day \( = 86,400 \) seconds - **Total Seconds**: \( 2,592,000 + 86,400 = 2,678,400 \) seconds

Solution

Calculate the value by following steps: - step0: Calculate: \(24\times 60\times 60\) - step1: Multiply the terms: \(1440\times 60\) - step2: Multiply the numbers: \(86400\) Calculate or simplify the expression \( 31 * 24 * 60 * 60 \). Calculate the value by following steps: - step0: Calculate: \(31\times 24\times 60\times 60\) - step1: Multiply the terms: \(744\times 60\times 60\) - step2: Multiply the terms: \(44640\times 60\) - step3: Multiply the numbers: \(2678400\) Calculate or simplify the expression \( 2600 * 900 \). Calculate the value by following steps: - step0: Calculate: \(2600\times 900\) - step1: Multiply the numbers: \(2340000\) Let's break down the problem step by step. ### Part 1: Calculate \( 2600 \times 900 \) 1. **Exact Calculation**: \[ 2600 \times 900 = 2340000 \] ### Part 2: Estimate and Column Method a) **Estimation**: - Maria might estimate \( 2600 \) as \( 3000 \) and \( 900 \) as \( 1000 \). - Therefore, the estimated product would be: \[ 3000 \times 1000 = 3000000 \] b) **Column Method**: - To find the exact number of litres using the column method, we can break it down: \[ \begin{array}{c} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

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The Deep Dive

To estimate \(2600 \times 900\), Maria might round \(2600\) to \(3000\) and \(900\) to \(1000\). Then, she calculates \(3000 \times 1000 = 3,000,000\). Officially, the exact answer for \(2600 \times 900\) using the column method is \(2,340,000\). Comparing the estimates, Maria's estimate is higher, making it less accurate since it overshot by \(660,000\). The exact answer is noticeably lower and weighs more with accuracy. Now, for seconds in a day: there are \(24\) hours, each with \(60\) minutes, and each minute has \(60\) seconds. So, it’s \(24 \times 60 \times 60 = 86,400\) seconds in a day. For estimating seconds in 31 days, one can round \(31\) days to \(30\) and calculate \(30 \times 86,400 = 2,592,000\) seconds. Then, compensate by adding back the value for the extra day, which is \(86,400\). So, \(2,592,000 + 86,400 = 2,678,400\) seconds in a month of \(31\) days.

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