Express the following quotients in scientific notation to correct number of significant figures

Express the following quotients in scientific notation to correct number of significant figures. 0.524 / 0.022 16.04 1.333E5 2.54E-3 0.02544 25.4 / 6.78E-5 73,449 / 1.000E-2 0.06038 / 3.0778E6 2,909,112 3.14E0 A.3 Significant Figures. Express the following Results in normal notation to the correct number of decimal places. 0.524+0.22 28.309-4.9 123+25.045 88.678-22.0456 4390+15.5 2.34-5.369

The Correct Answer and Explanation is :

Let’s address each calculation, ensuring the results are expressed with the correct number of significant figures or decimal places as specified.

Part A: Expressing Quotients in Scientific Notation with Correct Significant Figures

1. 0.524 / 0.022

• Calculation: 0.524 ÷ 0.022 = 23.81818181818182
• Significant Figures: Both numbers have 3 significant figures.
• Result: 2.38 × 10¹

1. 25.4 / 6.78E-5

• Calculation: 25.4 ÷ 6.78 × 10⁻⁵ = 374631.26843657816
• Significant Figures: Both numbers have 3 significant figures.
• Result: 3.75 × 10⁵

1. 73,449 / 1.000E-2

• Calculation: 73,449 ÷ 1.000 × 10⁻² = 7344900.0
• Significant Figures: 73,449 has 5 significant figures; 1.000 has 4 significant figures.
• Result: 7.3449 × 10⁶

1. 0.06038 / 3.0778E6

• Calculation: 0.06038 ÷ 3.0778 × 10⁶ = 1.9617908895964652 × 10⁻⁸
• Significant Figures: 0.06038 has 4 significant figures; 3.0778 has 5 significant figures.
• Result: 1.962 × 10⁻⁸

Part B: Expressing Results in Normal Notation with Correct Decimal Places

1. 0.524 + 0.22

• Calculation: 0.524 + 0.22 = 0.744
• Decimal Places: 0.22 has 2 decimal places.
• Result: 0.74

1. 28.309 – 4.9

• Calculation: 28.309 – 4.9 = 23.409
• Decimal Places: 4.9 has 1 decimal place.
• Result: 23.4

1. 123 + 25.045

• Calculation: 123 + 25.045 = 148.045
• Decimal Places: 123 has 0 decimal places.
• Result: 148

1. 88.678 – 22.0456

• Calculation: 88.678 – 22.0456 = 66.6324
• Decimal Places: 88.678 has 3 decimal places.
• Result: 66.632

1. 4390 + 15.5

• Calculation: 4390 + 15.5 = 4405.5
• Decimal Places: 4390 has 0 decimal places.
• Result: 4406

1. 2.34 – 5.369

• Calculation: 2.34 – 5.369 = -3.029
• Decimal Places: 2.34 has 2 decimal places.
• Result: -3.03

Explanation

Significant Figures in Division: When dividing numbers, the result should have the same number of significant figures as the number with the fewest significant figures in the operation. For example, in 0.524 ÷ 0.022, both numbers have 3 significant figures, so the result is rounded to 3 significant figures.

Decimal Places in Addition/Subtraction: When adding or subtracting, the result should have the same number of decimal places as the number with the fewest decimal places. For instance, in 0.524 + 0.22, the number 0.22 has 2 decimal places, so the result is rounded to 2 decimal places.

This approach ensures that the precision of the result reflects the precision of the least precise measurement, maintaining the integrity of significant figures and decimal places in calculations.