Chapter 3c Numbers in the Real World - Dealing with Uncertainty

Flashcards covering significant digits, measurement errors, accuracy, precision, and rounding rules.

When are zeros NOT significant?

Zeros to the right of the last nonzero digit but before the decimal point (e.g., 40,000 or 210)

When are zeros NEVER significant?

Zeros to the left of the first nonzero digit (e.g., 0.006 or 0.00052)

When are zeros ALWAYS significant?

Zeros between nonzero digits (e.g., 4002 or 3.06) or other significant zeros (such as the first zero in 30.0)

When are zeros ALWAYS significant?

Zeros that follow a nonzero digit and lie to the right of the decimal point (e.g., 4.20 or 3.00)

Are Nonzero digits significant?

Always significant

How many significant digits are in 11.90 seconds, and what does it imply?

4 significant digits, measurement to the nearest 0.01 second

How many significant digits are in 0.000067 meter, and what does it imply?

2 significant digits, measurement to the nearest 0.000001 meter

How many significant digits are in 0.0030 gram, and why?

2 significant digits; leading zeros are placeholders, final zero is measured

How many significant digits are in a population reported as 240,000, and what does it imply?

2 significant digits, measurement to the nearest 10,000 people

How many significant digits are in a population reported as 2.40 × 105, and what does it imply?

3 significant digits, measurement to the nearest 1000 people

What causes random errors?

Random and inherently unpredictable events in the measurement process.

What causes systematic errors?

A problem in the measurement system that affects all measurements in the same way.

What is the formula for absolute error?

measured value – true value

What does relative error do?

Compares the size of the error to the true value.

What does relative error compare the size of?

Size of Errors

If a projected budget surplus of $17 billion turns out to be $25 billion, what is the absolute error?

$8 billion

If a projected budget surplus of $17 billion turns out to be $25 billion, what is the relative error?

47.1%

What does accuracy describe?

How closely a measurement approximates a true value. A measurement with a small relative error.

What does precision describe?

The amount of detail in a measurement.

What is the rounding rule for addition or subtraction?

Round the answer to the same precision as the least precise number in the problem.

What is the rounding rule for multiplication or division?

Round the answer to the same number of significant digits as the measurement with the fewest significant digits.

When should you round to avoid errors?

Round only after completing all the operations, not during the intermediate steps.