Unit 1 - Objective 3 - Calculators and Approximate Numbers

Precision, Significant Digits, and Accuracy

The precision of a measurement is indicated by the position of the last digit relative to the decimal point.
The significant digits are those that are determined by measurement.
Accuracy refers to the number of significant digits.

Determining which digits are significant

  1. All nonzero digits are significant.
  2. Zero digits that lie between significant digits are significant. For example, 307 has three significant digits.
  3. Zero digits that lie to the right of both the decimal point and the last nonzero digit are significant. For Example, .860 has three significant digits.
  4. Zeros at the beginning of a decimal fraction are not significant. For example both .045, .0045 and 0.045 have two significant digits since the zeros serve only to locate the decimal point.

Rounding off numbers

To round off a number to a certain number of significant digits, examine the digit in the next place to the right. If this digit is less then 5 (0, 1, 2, 3, 4) then accept the digit in the last place to the left of this digit. If the digit is 5 or more (5, 6, 7, 8, 9) then increase the digit in the last place by one.

Example:
  1. Round off 83.427 to the nearest hundredth. The digit 2 is in the hundredth place. The next digit to the right is a 7. This is more than 5, so the 2 is increased by 1 (to 3) and the 7 is dropped. So 83.427 rounded to the nearest hundredth is 83.43.

  2. Round 5.2348 to the nearest hundredth. The digit in the hundredth place is a 3. The next digit to the right is a 4. Since 4 is less than 5, the 4 and all other digits are dropped. So 5.2348 rounded to the nearest hundredth is 5.23.

  3. Round 7,030.6 to two significant digits. The second digit is a 0. The digit to the right is a 3. Since 3 is less than 5, we accept the second significant digit zero. Each digit between the second significant digit and the decimal point is changed to 0. So 7,030.6 rounded to two significant digits is 7,000.

  4. Round 7,030.6 to three significant digits. The third significant digit is a 3. The digit to the right is a 0. Since 0 is less than 5 we accept the third significant digit 3. So 7,030.6 rounded to three significant digits is 7,030.

  5. Round 7,030.6 to four significant digits. The fourth significant digit is a 0. The digit to the right is a 6. Since 6 is greater than 5, we raise the fourth significant digit by 1 to 1. So 7,030.6 rounded to four significant digits is 7,031.

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