ESTIMATION & ROUNDING Using approximation in number contexts. Grade 7 Mathematics: Estimation and Rounding Subtopic Navigator Introduction Rounding Numbers Estimating with Whole Numbers Estimation in Multiplication and Division Rounding Decimals Applications and Mixed Problems Cumulative Exercises Conclusion Lesson Objectives Understand the rules of rounding numbers to given place values. Develop estimation strategies in addition, subtraction, multiplication, and division. Use approximation to simplify real-life calculations. Recognize the importance of estimation in checking the reasonableness of results. Lesson Introduction Estimation and rounding are powerful mathematical tools that help us approximate values quickly and check the reasonableness of calculations. Rounding involves reducing a number to a nearby, simpler value, while estimation involves using rounded numbers or mental strategies to simplify complex calculations. Rounding Numbers To round a number, look at the digit in the place you are rounding to and check the next digit: If the next digit is less than 5, keep the rounding digit the same and change all digits to the right to zero. If the next digit is 5 or more, increase the rounding digit by 1 and change all digits to the right to zero. Example 1: Round [latex]4672[/latex] to the nearest hundred. Solution: The digit in the hundreds place is 6. The next digit is 7 (≥ 5). Increase 6 to 7 → [latex]4700[/latex]. Example 2: Round [latex]825[/latex] to the nearest ten. Solution: The digit in the tens place is 2. The next digit is 5 (≥ 5). Increase 2 to 3 → [latex]830[/latex]. Example 3: Round [latex]13948[/latex] to the nearest thousand. Solution: Thousands digit is 9. The next digit is 4 (< 5). Keep 9 → [latex]13000[/latex]. Exercises (Rounding Numbers) Round [latex]5846[/latex] to the nearest hundred. Round [latex]692[/latex] to the nearest ten. Estimating with Whole Numbers Estimation uses rounded values to simplify calculations mentally and quickly. Example 4: Estimate [latex]467 + 289[/latex] by rounding to the nearest hundred. Solution: [latex]467 approx 500[/latex], [latex]289 approx 300[/latex]. So [latex]500 + 300 = 800[/latex]. Example 5: Estimate [latex]1235 - 678[/latex]. Solution: [latex]1235 approx 1200[/latex], [latex]678 approx 700[/latex]. So [latex]1200 - 700 = 500[/latex]. Example 6: Estimate [latex]245 + 387[/latex]. Solution: [latex]245 approx 200[/latex], [latex]387 approx 400[/latex]. So [latex]200 + 400 = 600[/latex]. Exercises (Estimating with Whole Numbers) Estimate [latex]763 + 426[/latex] by rounding to the nearest hundred. Estimate [latex]984 - 457[/latex]. Estimation in Multiplication and Division In multiplication and division, rounding numbers helps simplify large calculations. Example 7: Estimate [latex]48 times 19[/latex]. Solution: [latex]48 approx 50[/latex], [latex]19 approx 20[/latex]. So [latex]50 times 20 = 1000[/latex]. Example 8: Estimate [latex]362 div 9[/latex]. Solution: [latex]362 approx 360[/latex]. Since [latex]360 div 9 = 40[/latex], the estimated answer is [latex]40[/latex]. Example 9: Estimate [latex]598 times 41[/latex]. Solution: [latex]598 approx 600[/latex], [latex]41 approx 40[/latex]. So [latex]600 times 40 = 24000[/latex]. Exercises (Estimation in Multiplication and Division) Estimate [latex]73 times 48[/latex]. Estimate [latex]892 div 29[/latex]. Rounding Decimals Decimals are rounded in a similar way as whole numbers by checking the next digit. Example 10: Round [latex]12.678[/latex] to 2 decimal places. Solution: Look at the hundredths place (7). The next digit is 8 (≥ 5). So [latex]12.68[/latex]. Example 11: Round [latex]3.2451[/latex] to 3 decimal places. Solution: Thousandths digit is 5. Next digit is 1 (< 5). Keep 5 → [latex]3.245[/latex]. Example 12: Round [latex]7.498[/latex] to 1 decimal place. Solution: Tenths digit is 4. Next digit is 9 (≥ 5). Increase 4 to 5 → [latex]7.5[/latex]. Exercises (Rounding Decimals) Round [latex]18.276[/latex] to 2 decimal places. Round [latex]4.995[/latex] to 2 decimal places. Applications and Mixed Problems Example 13: A shirt costs [latex]$19.85[/latex]. Estimate the cost of 6 shirts. Solution: Round [latex]19.85 approx 20[/latex]. [latex]20 times 6 = 120[/latex]. Estimated cost: [latex]$120[/latex]. Example 14: A car travels [latex]247 text{ km}[/latex] daily. Estimate distance in 7 days. Solution: [latex]247 approx 250[/latex]. [latex]250 times 7 = 1750[/latex] km. Example 15: A family spends [latex]$53.90[/latex] weekly on groceries. Estimate for 4 weeks. Solution: [latex]53.90 approx 54[/latex]. [latex]54 times 4 = 216[/latex]. Exercises (Applications) Estimate the total cost of 9 items each costing [latex]$11.95[/latex]. A bus carries [latex]478[/latex] passengers daily. Estimate the total in 5 days. Cumulative Exercises Round [latex]4756[/latex] to the nearest hundred. Round [latex]9.786[/latex] to 2 decimal places. Estimate [latex]498 + 623[/latex] by rounding to the nearest hundred. Estimate [latex]1247 - 896[/latex]. Estimate [latex]67 times 52[/latex]. Estimate [latex]450 div 48[/latex]. A mobile phone costs [latex]$249.90[/latex]. Estimate the cost of 3 phones. A train travels [latex]368 text{ km}[/latex] daily. Estimate distance for 10 days. Round [latex]1234.567[/latex] to 1 decimal place. Round [latex]6789[/latex] to the nearest thousand. Conclusion/Recap Estimation and rounding simplify calculations, help in decision-making, and ensure results are reasonable. They are vital in real-life situations such as budgeting, shopping, and distance measurement. Mastering these skills boosts mental math speed and confidence. Clip It! Share your ANSWER in the Chat. Indicate TITLE e.g Linear Equation 1. .....2. e.t.c
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