Page 30 - Mathematics of Business and Finance

10 Chapter 1 | Review of Basic Arithmetic

Example 1.1(h) Rounding Percents
Round the following percents to the indicated number of decimal places:

(i) 12.834% to one decimal place
(ii) 67.386% to two decimal places

(iii) 25.325% to two decimal places

Solution (i) Rounding 12.834% to one decimal place
■ Identify the rounding digit in the tenths place: 12.834%.
■ The digit to the immediate right of the rounding digit is less than 5; therefore, do not
change the value of the rounding digit. Drop all the digits to the right of the rounding
digit, which will result in 12.8%.
Therefore, 12.834% rounded to one decimal place (or nearest tenth) is 12.8%.

(ii) Rounding 67.386% to two decimal places
■ Identify the rounding digit in the hundredths place: 67.386%.
■ The digit to the immediate right of the rounding digit is greater than 5; therefore, increase
the value of the rounding digit by one, from 8 to 9, and drop all the digits that are to the
right of the rounding digit, which will result in 67.39%.
Therefore, 67.386% rounded to two decimal places (or nearest hundredth) is 67.39%.
(iii) Rounding 25.325% to two decimal places
■ Identify the rounding digit in the hundredths place: 25.325%.
■ The digit to the immediate right of the rounding digit is equal to 5; therefore, increase
the value of the rounding digit by one, from 2 to 3, and drop all the digits that are to the
right of the rounding digit, which will result in 25.33%.
Therefore, 25.325% rounded to two decimal places (or nearest hundredth) is 25.33%.

Example 1.1(i) Rounding a Set of Percents which Add Up to 100%
Reya spends 40.18% of her salary on rent, 20.61% on food, 15.62% on travel, 10.15% on entertainment,
5.5% on pet food, and saves the remaining 7.94%. Express these percents rounded to the nearest
percent without decimals.

Solution These percents rounded to the nearest percent without decimals (i.e. a whole percent) would be:
Rent: 40%, Food: 21%, Travel: 16%, Entertainment: 10%, Pet food: 6%, and Savings: 8%.
However, the sum of these percents would be:
40% + 21% + 16% + 10% + 6% + 8% = 101%
We have to round these numbers so that they add up to 100%; therefore, 1% has to be reduced from
one of these rounded numbers such that it does not have a significant effect.
Changing the largest percent will result in the smallest overall effect. If 40% is reduced to 39%,
39% – 40% 5% – 6%
the change is = –2.5%, but if 6% is reduced to 5%, the change is = –16.67%.
40% 6%
Changing 40% has a smaller effect than changing 6%.
Therefore, the percents rounded to the nearest whole numbers are best represented as:
Rent: 39%, Food: 21%, Travel: 16%, Entertainment: 10%, Pet food: 6%, and Savings: 8%, giving us a
Do not round sum of:
intermediate
calculations. 39% + 21% + 16% + 10% + 6% + 8% = 100%
Round your final
answer to two
decimal places. Note: In business and finance applications, final answers are generally rounded to the nearest hundredth
(2 decimal places) for value of money (e.g. $1234.56) and percents (e.g. 4.86%).