147326 = 147326
1
147326 = 14732 + 6
10 10
147326 = 1473 + 2 + 6
100 10100
147326 = 147 + 3 + 2 + 6
1000 101001000
147326 = 14 + 7 + 3 + 2 + 6
10000 10100100010000
147326 = 1 + 4 + 7 + 3 + 2 + 6
10000010100100010000100000
147326 = 1 + 4 + 7 + 3 + 2 + 6
1000000 101001000100001000001000000
147326 = 1 + 4 + 7 + 3 + 2 + 6
10000000 100100010000100000100000010000000

N.B. The student should write this table himself, and then proceed to make similar tables from the following exercises.

EXERCISES.

Reduce the following fractions into a series of numbers and more simple fractions:

31415926, 31415926,&c.
10100
2700031, 2700031,&c.
10100
2073000, 2073000,&c.
10100
3331303, 3331303,&c.
100010000

133. If, in this table, and others made in the same manner, you look at those fractions which contain a whole number, you will see that they may be made thus: Mark off, from the right hand of the numerator, as many figures as there are ciphers in the denominator by a point, or any other convenient mark.

This will give14732·6when the fraction is147326
10
1473·26 147326
100
147·326 147326
1000
&c. &c.

The figures on the left of the point by themselves make the whole number which the fraction contains. Of those on its right, the first is the numerator of the fraction whose denominator is 10, the second of that whose denominator is 100, and so on. We now come to those fractions which do not contain a whole number.

134. The first of these is ¹⁴⁷³²⁶/₁₀₀₀₀₀₀ which the number of ciphers in the denominator is the same as the number of figures in the numerator. If we still follow the same rule, and mark off all the figures, by placing the point before them all, thus, ·147326, the observation in (133) still holds good; for, on looking at ¹⁴⁷³²⁶/₁₀₀₀₀₀₀ in the table, we find it is

1 + 4 + 7 + 3 + 2 + 6
101001000100001000001000000