Introduction :
Reciprocal is simply defined as the inverse of a number Or a value i.e. the reciprocal of a number is 1 divided by that number. If n is a real number, then its inverse will be 1/n or n⁻¹. A reciprocal is also a number taken to the power of -1.
For Example , the reciprocal (or inverse) of 5 is 1 divided by 5 , which is 1/5 or 5⁻¹.
1/5 or 5⁻¹ = 0.2 ( from chart 0.2000 four- figure number )
The table of reciprocal numbers is also known as the table of reciprocal four-figure numbers. We can find reciprocal with values ranging from 1.0 to 9.9 at intervals of 0.1. The table of reciprocal four- figure numbers is essentially divided into three sections, as shown in the following tables.
(i) at intervals of 0.1, the number in the table's extreme left vertical column ranges from 1.1 to 9.9.
(ii) the horizontal row at the top of the chart is from 0 to 9 at intervals 1.
(iii) at intervals of 1, the number in the horizontal row at the top of the chart are from 1 to 9 .This portion of the chart is referred to as the mean differences column.
Find the reciprocal of following numbers, using the reciprocal four-figure numbers chart.
If x ≥ 1
(i) 1/1.722 = ?
⇒ SOLUTION : The number in the reciprocal four-figure numbers table extreme left vertical column in 1.7 ,the horizontal row at the top of the chart in 2 consist of containing four digits number 0.5814 and horizontal row at the top of the chart in number 2 consist of containing one digit number 7 [= 0.0007 mean difference subtract ]
1/1.722 = 0.5814 - 0.0007
= 0.5821 .... Ans
(ii) 1/17.22 = ?
⇒SOLUTION : 1/1.722 x 10¹(decimal place change right to left and multiply 10¹ )
= ( 1/1.722 ) x 10⁻¹ (·.· 1/10¹ = 10⁻¹ )
= 0.5821 x 10⁻¹
= 0.05821 ..... Ans
(iii) 1/172.2 = ?
⇒SOLUTION : 1/1.722 x 10² (decimal place change from right to left and multiply 10² )
= ( 1/1.722 ) x 10⁻² ( ·.· 1/10² = 10⁻² )
= 0.5821 x 10⁻²
= 0.005821 ..... Ans
(iv) 1/1722 = ?
⇒SOLUTION : 1/1.722 x 10³ (decimal place change from right to left and multiply x 10³ )
= ( 1/1.722 ) x 10⁻³ ( ·.· 1/10³ = 10⁻³ )
= 0.5821 x 10⁻³
= 0.0005821 ..... Ans
Find the reciprocal of following numbers, using the reciprocal four-figure numbers chart.
If x < 1
(i) 1/0.1722 = ?
⇒SOLUTION : 1/1.722 x 10⁻¹ (decimal place change from left to right and multiply x 10⁻¹ )
= ( 1/1.722 ) x 10¹ ( ·.· 1/10⁻¹ = 10¹ )
= 0.5821 x 10¹
= 5.821 ...... Ans
(ii) 1/0.01722 = ?
⇒SOLUTION : 1/1.722 x 10⁻² (decimal place change from left to right and multiply x 10⁻² )
= ( 1/1.722 ) x 10² ( ·.· 1/10⁻² = 10² )
= 0.5821 x 10²
= 58.21 ..... Ans
(iii) 1/0.001722 = ?
⇒SOLUTION : 1/1.722 x 10⁻³(decimal place change from left to right and multiply x 10⁻³ )
= ( 1/1.722 ) x 10³ ( ·.· 1/10⁻³ = 10³ )
= 0.5821 x 10³
= 582.1 ..... Ans
(iii) 1/0.001722 = ?
⇒ SOLUTION : 1/1.722 x 10⁻⁴ (decimal place changes from left to right and multiply x 10⁻⁴ )
= ( 1/1.722 ) x 10⁴ ( ·.· 1/10⁻⁴ = 10⁴ )
= 0.5821 x 10⁴
= 5821 ...... Ans
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