Math Problem Statement

Berikut ini hasil pengukuran panjang dua batang kayu. Tentukan jumlah panjang kedua batang dan selisih kedua panjang batang kayu tersebut sesuai dengan aturan angka penting, semua pengukuran dalam satuan meter.

Solution

The image shows a set of math problems involving measurements and operations on numbers, specifically addition, subtraction, multiplication, and division. The instruction in Indonesian asks to calculate the sum and the difference between the two measurements for each pair of values while following significant figure rules and expressing all measurements in meters.

Let's break down the tasks one by one:

1. First Column (Addition):

  • 5.678+1.11085.678 + 1.1108

Sum: 5.678+1.1108=6.78885.678 + 1.1108 = 6.7888

Result with significant figures: Since the least precise value (5.678) has three decimal places, we round the result to three decimal places: 6.789m6.789 \, \text{m}

2. Second Column (Addition):

  • 0.6343+1.8870.6343 + 1.887

Sum: 0.6343+1.887=2.52130.6343 + 1.887 = 2.5213

Result with significant figures: The least precise value (1.887) has three decimal places, so we round the result to three decimal places: 2.521m2.521 \, \text{m}

3. Third Column (Subtraction):

  • 5.6783.235.678 - 3.23

Difference: 5.6783.23=2.4485.678 - 3.23 = 2.448

Result with significant figures: The least precise value (3.23) has two decimal places, so we round the result to two decimal places: 2.45m2.45 \, \text{m}

4. Fourth Column (Subtraction):

  • 7.9982.04347.998 - 2.0434

Difference: 7.9982.0434=5.95467.998 - 2.0434 = 5.9546

Result with significant figures: The least precise value (7.998) has three decimal places, so we round the result to three decimal places: 5.955m5.955 \, \text{m}

5. Fifth Column (Multiplication):

  • 3.1×0.113.1 \times 0.11

Product: 3.1×0.11=0.3413.1 \times 0.11 = 0.341

Result with significant figures: The least precise value (0.11) has two significant figures, so the result is rounded to two significant figures: 0.34m0.34 \, \text{m}

6. Sixth Column (Multiplication):

  • 6.978×0.236.978 \times 0.23

Product: 6.978×0.23=1.605946.978 \times 0.23 = 1.60594

Result with significant figures: The least precise value (0.23) has two significant figures, so the result is rounded to two significant figures: 1.6m1.6 \, \text{m}

7. Seventh Column (Division):

  • 3.3333÷0.333.3333 \div 0.33

Quotient: 3.3333÷0.33=10.1013.3333 \div 0.33 = 10.101

Result with significant figures: The least precise value (0.33) has two significant figures, so the result is rounded to two significant figures: 10m10 \, \text{m}

8. Eighth Column (Division):

  • 6.28÷0.3146.28 \div 0.314

Quotient: 6.28÷0.314=20.0006.28 \div 0.314 = 20.000

Result with significant figures: The least precise value (0.314) has three significant figures, so the result remains: 20.0m20.0 \, \text{m}

Let me know if you want further details or explanations!


Here are five related questions to expand your understanding:

  1. How do you determine the number of significant figures in an addition or subtraction problem?
  2. Why is it important to round to the least precise measurement in multiplication and division?
  3. Can you explain the difference between significant figures and decimal places?
  4. What happens if one of the values in the problem is exact (e.g., a counting number)?
  5. How would rounding errors impact real-life measurements?

Tip:

Always remember to round your final result based on the least number of significant figures in any of the values involved in the operation!

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Math Problem Analysis

Mathematical Concepts

Addition
Subtraction
Multiplication
Division
Significant Figures

Formulas

Addition: a + b
Subtraction: a - b
Multiplication: a × b
Division: a ÷ b

Theorems

Significant Figures Rule

Suitable Grade Level

Grades 10-12