Rounding 3.76 to the nearest whole number requires noting that the decimal portion, 0.76, is greater than 0.5. Therefore, the number is rounded up to 4, exemplifying basic rounding techniques.

To convert 0.00456 to scientific notation, first identify the significant digits. Rounding to two significant figures gives 4.6 x 10^-3, ensuring proper use of scientific notation.

Since 1 kilometer equals 1000 meters, multiplying 2 by 1000 gives 2000 meters. This straightforward conversion reinforces basic unit conversion skills.

The absolute error is the absolute difference between the true value and the measured value. Here, |100 - 98| equals 2 cm, clearly illustrating the concept of measurement error.

Accuracy refers to how near a measurement is to the accepted or true value. This is distinct from precision, which describes how consistent repeated measurements are.

When rounding 4567 to the nearest hundred, the tens digit is 6, which is 5 or more, so the number rounds up to 4600. This reinforces correct place value rounding.

With an uncertainty of ±0.05 L, the measurement may be 0.05 L less than or greater than 3.25 L, resulting in a range from 3.20 L to 3.30 L. This demonstrates how instrument precision affects measurement ranges.

Multiplying 2.5 (which has 2 significant figures) by 3.42 (with 3 significant figures) necessitates that the answer be rounded to 2 significant figures. Thus, 2.5 x 3.42 = 8.55 rounds to 8.6.

Distributing 3 over the parentheses gives 12x - 15, and adding the 2x yields 14x - 15. This problem tests fundamental skills in algebraic simplification.

Adding 3 to both sides of the equation results in 2x = 10. Dividing both sides by 2 then yields x = 5, demonstrating a basic approach to solving linear equations.

Multiplying the length and width (8.5 cm x 3.2 cm) gives 27.2 cm², which when expressed to two decimal places is 27.20 cm². This problem reinforces the application of geometric formulas and rounding rules.

Cross-multiplication of 4/x = 2/3 gives 4 × 3 = 2 × x, leading to 12 = 2x and thus x = 6. This standard technique in solving proportions is key in algebra.

The area of a triangle is found using the formula ½ × base × height. Substituting the given values yields ½ × 10 cm × 6 cm = 30 cm².

Subtracting 3.1 from 7.2 gives 4.1, and multiplying by 2.5 results in 10.25, which rounds to 10.3 when rounded to one decimal place. The problem emphasizes the importance of following the correct order of operations.

Adding the numbers (4 + 8 + 6 + 10 + 12) gives 40, which when divided by the number of values (5) results in a mean of 8. This reinforces fundamental concepts in statistics.

A small standard deviation indicates that the measurements cluster closely around the mean, which signifies high precision. This is distinct from accuracy, which compares measurements to the true value.

Expanding the left side gives 6y - 12, and the right side simplifies to 3y + 10. Solving the equation 6y - 12 = 3y + 10 leads to 3y = 22, so y = 22/3.

In addition and subtraction, absolute errors are added directly to determine the overall uncertainty. This contrasts with multiplication and division, where relative errors are used.

The measurement should be rounded to match the precision indicated by the uncertainty. Here, rounding 12.3456 m to the thousandth place yields 12.346 m, which is consistent with an uncertainty of ±0.001 m.

For A = πr², the relative uncertainty in A is 2 times the relative uncertainty in r. Calculating with r = 5.00 cm and an uncertainty of ±0.02 cm gives an uncertainty in A of approximately ±0.63 cm², following error propagation rules.