Question

My teacher said that if we're given for example 1.82,then we can derive its reciprocal by using this chart(without using calculator).

He told us that by looking at this chart, the reciprocal if 1.82 is 0.55. Also, the reciprocal of 1.67 is 0.60z But how?? I don't understand how he did it. Please explain the mathematical concept for this

Some numbers you night need: 1/1.5 1/2 1/2.5 1/3 1/3.5 1/4 1/4.5 1/5 1/5.5 1/6 1/6.5 1/7 1/7.5 1/8 0.667 1/8.5 1/9 1/9.5 0.118 0.500 0.111 0.4 0.105 1/10 1/11 1/12 1/13 1/14 1/15 1/16 1/17 1/18 1/19 0.333 0.1 0.286 0.091 0.083 0.25 0.077 0.222 0.071 0.2 0.067 0.182 0.0625 0.167 0.059 0.154 0.056 0.143 0.053 0.133 0.125

This chart is called "double reciprocal chart"

It's for Line weaver burk plot

Answer 1

See, Firstly for 1.82.

in the chart, we can see 0.182 which is just 1.82 multiplied by 0.1.

so what we can do in the equation $1/5.5=0.182$

multiply both sides by 10,$10/5.5=1.82$

and now since we have got 1.82 on one side we can simply reciprocate the whole equation $5.5/10=1/1.82$

so we get reciprocal of $1.82=0.55$

Now for the case of 1.67,

in the chart, we see 0.167 which is again 1.67 divided by 10

we can simply do the above procedure again and get answer = 0.6

and all we did is see the chart properly and find values related to the question value. No calculator is required