Title: Significant Figures and Rounding Objective: I will be able to determine the amount of significant figures when given a quantifiable number and round appropriately. Questions: What is significant figures and how do I round? Notes:

Significant Figures Some digits in an number may be exact while others may be uncertain, so chemists have devised a way to determine which digits are the most significant.

Rule #1 – All numbers that are not zero are always significant Example: -487 miles has 3 significant figures has 8 significant figures

Rule #2-Zeros appearing between nonzero digits are significant Examples: 40.7 lbs has 3 significant figures 87,009 lbs has 5 significant figures

Rule #3 – Zeros in front of non- zeros digits are NOT significant Examples: m has 4 significant figures m has 1 significant figure

Rule #4-Zeros at the end of a number and to the right of a decimal point are significant Examples: –85.00 g has 4 significant figures – g has 5 significant figures

Rule #5 – Zeros at the end of a number with no decimal may or may not be significant, if there is a decimal point at the end of all of the zeros then the zeros are significant m has 1 significant figure or has 4 significant figure depending on if the zeros are place holders m has 4 significant figures because of the decimal point.

Rounding Rules Use only the 1 st number to the right of the last sig. fig. number to decide whether or not to round. Less than 5, do NOT round More than 5, round the last sig. fig. up by 1 When using a calculator wait until the very end before rounding. Try to keep as many digits in the calculator until you come to the very end.

Multiplying and Dividing Keep as many sig figs in your answer as are in the piece of data with the least number of sig figs cm x cm x 7.4 cm = (keep two sig figs) = 2.7 x 102 cm3

Addition and Subtraction 1. Keep the same number of decimal places in your answer as the least precise measurement in your calculation m m m m = m (keep one decimal place) = 48.3 m

Scientific Notation This is a number that has 1 digit left of the decimal point. –Example 3.4 x 10 3

Exponent: Positive or Negative? When convert expanded numbers into scientific notation: –If you move the decimal to the left the exponent number is postive –If you move the decimal to the right the exponent is negative. When converting from scientific notation back to expanded form: –If you move the decimal to the right the exponent number is negative –If you move the decimal to the left the exponent is positive.

Your Calculator Remember Order of Operations: –Parentheses –Exponents –Multiplication and Division –Addition and Subtraction Use the button “EE” on calculator

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