Significant Figures, Scientific Notation, and the Metric System

Significant Figures (SF)

Digits that carry meaning contributing to their measurement accuracy.

The Four Rules of Significant Figures

1. All nonzero digits are significant; 2. Zeros between nonzero digits are significant; 3. Leading zeros are NOT significant; 4. Trailing zeros are significant when a decimal point is present.

Scientific Notation

A way to express very large or very small numbers compactly, using powers of ten.

Rule for Multiplying with Significant Figures

The result should have the same number of significant figures as the factor with the least significant figures.

Leading Zeros

Zeros that precede all nonzero digits; they are NOT considered significant.

Trailing Zeros

Zeros at the end of a number that are significant if a decimal point is present.

Metric System

A system of measurement based on meters, liters, grams, and seconds.

Conversion from Deka to Hecto

Moves the decimal left ONE time, equivalent to a change of 10¹ to 10².

Conversion from kilo to micro

Moves the decimal right NINE times, equivalent to a change of 10³ to 10^-6.

Moving the decimal point to the left in Scientific Notation

The exponent becomes POSITIVE.

Moving the decimal point to the right in Scientific Notation

The exponent becomes NEGATIVE.

Zeroes between nonzero digits

Always considered significant.

Rounding in Multiplication

The product is rounded to the significant figures of the number that has the least significant figures.

Significant Figures in 17

2 SF, as both digits are non-zero.

Significant Figures in 0.0045

2 SF, as leading zeros are not significant.

Significant Figures in 4009

4 SF, as zeros between nonzero digits are significant.

Unit for Volume in Metric System

Liter.

Unit for Mass in Metric System

Gram.

Unit for Length in Metric System

Meter.