College Algebra 9th txtbk

SECTION B–1 Scientific Notation and Significant Digits A-15
Using this definition,
7.8 10 3 has two significant digits
7.80 10 3 has three significant digits
7.800 10 3 has four significant digits
All three of these measurements have the same decimal representation (7,800), but each
represents a different accuracy.
Definition 1 tells us how to write a number so that the number of significant digits is
clear, but it does not tell us how to interpret the accuracy of a number that is not written
in scientific notation. We will use the following convention for numbers that are written as
decimal fractions:
Z SIGNIFICANT DIGITS IN DECIMAL FRACTIONS
The number of significant digits in a number with no decimal point is found by
counting the digits from left to right, starting with the first digit and ending with
the last nonzero digit.
The number of significant digits in a number containing a decimal point is
found by counting the digits from left to right, starting with the first nonzero digit
and ending with the last digit.
Applying this rule to the number 7,800, we conclude that this number has two significant
digits. If we want to indicate that it has three or four significant digits, we must use
scientific notation.
EXAMPLE 1 Significant Digits in Decimal Fractions
Underline the significant digits in the following numbers:
(A) 70,007 (B) 82,000 (C) 5.600 (D) 0.0008 (E) 0.000 830
SOLUTIONS (A) 70,007 (B) 82,000 (C) 5.600 (D) 0.0008 (E) 0.000 830
MATCHED PROBLEM 1
Underline the significant digits in the following numbers:
(A) 5,009 (B) 12,300 (C) 23.4000 (D) 0.00050 (E) 0.0012
Z Rounding Convention
In calculations involving multiplication, division, powers, and roots, we adopt the following
convention:
Z ROUNDING CALCULATED VALUES
The result of a calculation is rounded to the same number of significant digits
as the number used in the calculation that has the least number of significant
digits.