3.2 Comparing, Ordering, and Rounding Decimals (195)
Objectives:
Compare decimals
Place decimals in order from smallest to largest
Round decimals to a specified decimal place
3.2.1 Comparing Decimals (195)
We can place all numbers (even decimals or irrational numbers) on the number line.
If a number m is to the right of a number n, then m is larger than n { m > n }
n
m
If a number m is to the left of a number n, then m is smaller than n { m < n }
m
n
Comparing two numbers in decimal notation
1. Start at the left and compare corresponding digits. If the digits are the same, move 1 →
2. When two digits are different, the larger number is the one with the larger digit.
Example. Compare 31.234 and 31.24 - same through 31.2, then we get a 3 vs 4 31.234 < 31.24
PP1 Write an inequality statement with 5.74 and 5.75.
5.74 < 5.75 or 5.75 > 5.74 (201)
PP2 Fill in the blank with one of the symbols >, <, or =
0.894 ___ 0.89
>
(201)
3.2.2 Placing Decimals in Order from Smallest to Largest (seldom largest to smallest) (201)
We set them up so that a < b < c < d etc.
PP3 Place the following five decimal numbers in order from smallest to largest (201)
2.45, 2.543, 2.46, 2.54, 2.5
2.45, 2.46, 2.5, 2.54, 2.543
3.2.3 Rounding Decimals to a Specified Decimal Place
We don’t have mils (1/1000 of a dollar) any more. If we have a 7% tax on $1.10, the total is
$1.177 . So you end up spending $1.18 . If it were $1.20 instead, the total is $1.354, or $1.35 .
Rounding Decimals (202)
1. Find the decimal place to which you want to round (tenths, hundredths, etc.)
2. If the 1st digit to the right of that value is < 4, set all digits from there right to 0s
3. If the 1st digit to the right of that value is > 5, increase the desired digit up one and set
remaining digits to 0s (actually drop them)
Examples: 23.44 to nearest 10th 23.4
PP4 Round 723.88 to the nearest tenth.
PP5 Round to the nearest thousandth
45.679 to nearest 100th 45.68
723.9
1.96 to nearest 10th 2.0
(203)
a) 12.92647 12.926
b) 0.007892
0.008
(203)
PP6 Round to the nearest tenth. Last month the college gym used 15,699.953 hours (204)
15,700.0
PP7 Round the following figures to the nearest whole dollar. (204)
Medical bills
$375.50
$376. {decimal optional}
Retirement contributions $980.49
$980.
Taxes
$971.39
$971.
Contributions to charity $817.65
$818
Warning, only go one digit right of the accuracy required.
4.545 to nearest 10th 4.5