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 -3.1478654 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: 0.009587 m has 4 significant figures 0.0000009 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 – 9.0700 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 . -2000 m has 1 significant figure or has 4 significant figure depending on if the zeros are place holders -2000. m has 4 significant figures because of the decimal point. Rounding Rules • Use only the 1st 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. 2.37 cm x 15.67 cm x 7.4 cm = 274.82046 (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. 34.039 m + 0.24 m + 1.332 m + 12.7 m = 48.311 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 103 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 TOMORROW! - Bring Calculator!
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