Lesson 5: Significant Figures and Scientific Notations

This flashcard set covers the rules for determining significant figures, rounding methods, and calculation rules for addition, subtraction, multiplication, and division based on Lesson 5.

What is the definition of significant figures?

These are the digits in a measurement that include all certain digits plus one estimated digit, used to represent precision.

What is the rule regarding non-zero digits in significant figures?

All non-zero digits are always significant, such as in the numbers $4.5137$ and $1.2345$.

How are zeros that appear between non-zero digits (e.g., $5.07$ or $2005$) treated?

Zeros between non-zero digits are always significant.

What is the rule for leading zeros that appear before all non-zero digits?

Leading zeros are never significant, as seen in examples like $0.00456$ and $0001.25$.

When are trailing zeros at the end of a number considered significant?

Zeros at the end of a number are significant only if the number contains a decimal point (e.g., $1300.0$ is significant, but $1300$ is not).

What is the difference in focus between decimal place rounding and significant figure rounding?

Decimal place rounding focuses on the number of digits after the decimal point, while significant figure rounding focuses on the number of meaningful digits.

Round $45.678$ to $3$ significant figures.

$$45.7$$

Round $0.00456$ to $2$ significant figures.

$$0.0046$$

Round $1.997$ to $2$ significant figures.

$$2.0$$

Round $5600$ to $2$ significant figures.

$$5600$$

Round $2.71828$ to $3$ significant figures.

$$2.72$$

What is the rule for the result when multiplying or dividing measured values?

The result should have the same number of significant figures as the measurement with the fewest significant figures.

What is the rule for the result when adding or subtracting measured values?

The result should have the same number of decimal places as the measurement with the fewest decimal places.