Page 36 - Arithmetic

Estimation
Rounding off is expressing a decimal to the nearest tenth, hundredth, and thousandth place. Interestingly, rounding off is not limited to just decimals. In terms of whole numbers, you round the numbers to the nearest tens, hundreds, or thousands.
REMEMBER:
When rounding whole numbers or decimals, look at the digit to the right of the place. If the digit is 5 or higher, round the number to the left by one or the next value.
If the digit is less than 5, keep the number unchanged.
Worked Example 16
Round off 1756.8978 to the nearest thousand and thousandth.
Solution:
To nearest thousands = 2000
To nearest thousandth = 1756.898
Percentage
Percentage is how many parts per one hundred. For converting decimal to percentage, multiply the decimal by 100 or move the decimal point two digits to the right. Replace the decimal point with a percentage (%) sign.
REMEMBER:
Change in prices:
When the price of any item increases by R%, there is always a decrease in consumption. The decrease in consumption can be found out using: 𝑅 × 100
(100+𝑅)
And, when the price decreases by R%, the increase is consumption is: 𝑅 (100−𝑅)
Result of population:
× 100
When the population of a town increases by R% per annum,
Population of the town after ‘n’ years = P (1 + 𝑅 )n where P is the present population of the town.
100
Population of the town ‘n’ year ago = P 𝑃 (1+ 𝑅 )𝑛
100
Result of depreciation
If ‘P’ is the present value of an equipment, and it depreciates at a rate of R% per annum
𝑅n Price of machine after ‘n’ years = P (1 - )
100
Price of machine ‘n’ year ago = P 𝑃
(1−
)
100 𝑅𝑛
If M is R% more than N, then N is less than M by (: If M is R% less than N, then N is more than M by (:
𝑅 × 100)% 𝑅+100
𝑅 × 100)% 100∗𝑅
Page 35 of 55
Arithmetic Concept