Page 223 - Math_Genius_V1.0_C7_Flipbook

D:\Surender Prajapati\CBSE_ICSE_Book_New\CBSE\Grade-7\Math_Genius-7\Open_File\10_Chapter\10_Chapter
\ 15-Nov-2024 Surender Prajapati Proof-6 Reader’s Sign _______________________ Date __________

Converting Percentages into Decimals

To convert a given percentage into a decimal number, divide the given percentage by 100 and

remove the symbol %. Alternatively, put the decimal point two places to the left from the right
end and remove % symbol.

Example 6: Convert each of the following percentages into decimals.
(a) 83% (b) 1% (c) 4.5% (d) 0.18%

Solution: We have,

83
(a) 83% = = 0.83 Alternative Method:
100
1 (a) 83% = 0.83
(b) 1% = = 0.01 (b) 1% = 0.01
100
45 45 (c) 4.5% = 0.045
.
(c) 4.5% = = = 0.045 (d) 0.18% = 0.0018
100 1000
18 18 18
(d) 0.18% = % = = = 0.0018
100 100 100 10000
×

Note: On converting percentages into decimals, remove % sign and shift the decimal point two places to the left.

Converting Ratios into Percentages

To convert the given ratio into a percentage, first convert the ratio into a fraction, then multiply
the obtained fraction by 100 and put the symbol %.
Example 7: Convert each of the following ratios into a percentage:

(a) 12 : 35 (b) 9 : 11 (c) 248 : 155 (d) 14 : 5

12  12  240 2
Solution: (a) 12 : 35 = =  × 100 % = % = 34 %

35  35  7 7
9  9  900 9
(b) 9 : 11 = =  × 100 % = % = 81 %

11  11  11 11
×
248  248   248 20
(c) 248 : 155 = =  × 100 % =   % = (8 × 20)% = 160 %

155  155   31 
14  14 
(d) 14 : 5 = =  × 100 % = (14 × 20)% = 280%

5  5 
Converting Percentages into Ratios

To convert the given percentage into a ratio:
1. Convert the given percent into a fraction by dividing the number by 100, remove the % sign.
2. Consider the numerator as the first term and the denominator as the second term and
simplify if required.

221 Percentage and Its Applications