Page 304 - Basic College Mathematics with Early Integers

S E C T ION 4 .1 I INTRODUCTION TO DECIMALS 281

If you have trouble comparing two negative decimals, try the following: Compare
their absolute values. Then to correctly compare the negative decimals, reverse
the direction of the inequality symbol.

0.586 0.586
0.568 0.568

1 0.5 0 0.5 1
0.568 0.586 so 0.568 0.586

Example 14 Insert 6, 7, or = to form a true statement. PRACTICE 14
Insert 6, 7, or = to form a
-0.0101 -0.00109 true statement.
-0.029 -0.0209
Solution: Since 0.0101 7 0.00109, then -0.0101 6 -0.00109 .
c c c c
Work Practice 14

Objective Rounding Decimals
We round the decimal part of a decimal number in nearly the same way as we round
whole numbers. The only difference is that we drop digits to the right of the round-
ing place, instead of replacing these digits with 0s. For example,
36.954 rounded to the nearest hundredth is 36.95
c

Rounding Decimals to a Place Value to the Right
of the Decimal Point
Step 1: Locate the digit to the right of the given place value.

Step 2: If this digit is 5 or greater, add 1 to the digit in the given place value and
drop all digits to its right. If this digit is less than 5, drop all digits to the
right of the given place.

Example 15 Round 736.2359 to the nearest tenth. PRACTICE 15
Round 123.7817 to the nearest
Solution: thousandth.

Step 1: We locate the digit to the right of the tenths place.
tenths place
736.2 3 59
digit to the right
Step 2: Since the digit to the right is less than 5, we drop it and all digits to its
right.

Thus, 736.2359 rounded to the nearest tenth is 736.2.
Work Practice 15
Answers
The same steps for rounding can be used when the decimal is negative. 14. 6 15. 123.782