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NOTES: SIGNIFICANT FIGURES

(Ch5.2 p133-139)

. A. Uncertainty in Measurement

▪ Significant Figures

• A measurement always has some degree of uncertainty (the last digit is estimated)

. B. Significant Figures

▪ Counting Significant figures

• Significant figures include all the numbers that are certain plus the last digit that is estimated

• Rules for counting significant figures

1) Nonzero integers always count as significant figures

2) Never count leading zeros (the ones on the left)

3) Always count captive zeros (the ones in between nonzero integers)

4) Only count trailing zeros when there is a decimal point (the ones to the right)

5) Exact numbers or definitions have unlimited significant figures

• Scientific Notation: don’t count the 10 or the exponent (Ex: 2.1 ( 1013 only has 2, not 4)

▪ Rules for Rounding Off

• If the digit to be removed…

- is less than 5, the preceding digit stays the same. For example, 1.33 rounds to 1.3

- is equal to or greater than 5, the preceding digit is increased by 1. For example, 1.36 rounds to 1.4, and 3.15 rounds to 3.2

• In a series of calculations, you should carry all the digits from your calculator till the end and then only round the final answer

▪ Rules when Multiplying or Dividing

• For multiplication and division, number of significant figures are counted

• Only keep as many significant figures as the one with the least

- For example:

4.56 ( 1.4 = 6.384 [pic] 6.4

[pic]0.0279027 [pic] 0.0279

▪ Rules for Adding or Subtracting

• For addition and subtraction, the decimal places are counted (regardless of how many digits are to the left of the decimal place)

• Only keep as many decimal places as the one with the least

- For example:

12.11 + 18.0 + 1.013 = 31.123 [pic] 31.1

0.6875 – 0.1 = 0.5875 [pic] 0.6

NOTES: SIGNIFICANT FIGURES

(Ch5.2 p133-139)

. A. Uncertainty in Measurement

▪ Significant Figures

• A measurement always has some degree of uncertainty (the last digit is estimated)

. B. Significant Figures

▪ Counting Significant figures

• Significant figures include all the numbers that are certain plus the last digit that is estimated

• Rules for counting significant figures

1) Nonzero integers always count as significant figures

2) Never count leading zeros (the ones on the left)

3) Always count captive zeros (the ones in between nonzero integers)

4) Only count trailing zeros when there is a decimal point (the ones to the right)

5) Exact numbers or definitions have unlimited significant figures

• Scientific Notation: don’t count the 10 or the exponent (Ex: 2.1 ( 1013 only has 2, not 4)

▪ Rules for Rounding Off

• If the digit to be removed…

- is less than 5, the preceding digit stays the same. For example, 1.33 rounds to 1.3

- is equal to or greater than 5, the preceding digit is increased by 1. For example, 1.36 rounds to 1.4, and 3.15 rounds to 3.2

• In a series of calculations, you should carry all the digits from your calculator till the end and then only round the final answer

▪ Rules when Multiplying or Dividing

• For multiplication and division, number of significant figures are counted

• Only keep as many significant figures as the one with the least

- For example:

4.56 ( 1.4 = 6.384 [pic] 6.4

[pic]0.0279027 [pic] 0.0279

▪ Rules for Adding or Subtracting

• For addition and subtraction, the decimal places are counted (regardless of how many digits are to the left of the decimal place)

• Only keep as many decimal places as the one with the least

- For example:

12.11 + 18.0 + 1.013 = 31.123 [pic] 31.1

0.6875 – 0.1 = 0.5875 [pic] 0.6

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