Basic Math Operations - Mathematics and Statistics for the Environment - page 45

■ EXAMPLE 2.9
Problem: Calculate pounds per million gallons for 1 ppm (1 mg/L) of water.

Solution: Because 1 gal of water = 8.34 lb,

1
10

gal
gal

1 gal lb/gal

1,000,000 ga

× . 8 34

1 ppm = = = 834 . lb/1,000,000 gal

6

l

■ EXAMPLE 2.10
Problem: How many pounds of activated carbon (AC) are needed with 42 lb of sand to make the
mixture 26% AC?

Solution: Let x be the weight of AC; thus,

x

= 026 .

42 + x

x = 02642 .( + x ) = 1092026 . + . x

10 92
0

.
.74

x = = 14 76 . lb

■ EXAMPLE 2.11
Problem: A pipe is laid at a rise of 140 mm in 22 m. What is the grade?

Solution:

140
22

mm
m

140 mm

Grade = × 100 % = × 100 % = 0 .64%

22 m × 1000 mm

■ EXAMPLE 2.12
Problem: A motor is rated as 40 horsepower (hp). However, the output horsepower of the motor is
only 26.5 hp. What is the efficiency of the motor?

Solution:

hp output
hp input

26.5 hp
40

Efficiency = × 100% = × 100 6%% =

hp

2.5 SIGNIFICANT DIGITS
When rounding numbers, the following key points are important:

• Numbers are rounded to reduce the number of digits to the right of the decimal point. This
is done for convenience, not for accuracy.
• A number is rounded off by dropping one or more numbers from the right and adding
zeroes if necessary to place the decimal point. If the last figure dropped is 5 or more,
increase the last retained figure by 1. If the last digit dropped is less than 5, do not increase
the last retained figure. If the digit 5 is dropped, round off preceding digit to the nearest
even number.