Solve 49.268+14/0.1*1.1^6*(1-1/1.1^44)

$$49.268+ \frac{ 14 }{ 0.1 \times { 1.1 }^{ 6 } } \times (1- \frac{ 1 }{ { 1.1 }^{ 44 } } )$$

Evaluate

$$\frac{373014579762703159977770244708748377057972017025571203317}{2934771321992382912666662399758957998474553474680750250}\approx 127.101753028$$

Solution Steps

Calculate 1.1 to the power of 6 and get 1.771561.

$$49.268+\frac{14}{0.1\times 1.771561}\left(1-\frac{1}{1.1^{44}}\right)$$

Multiply 0.1 and 1.771561 to get 0.1771561.

$$49.268+\frac{14}{0.1771561}\left(1-\frac{1}{1.1^{44}}\right)$$

Expand \frac{14}{0.1771561} by multiplying both numerator and the denominator by 10000000.

$$49.268+\frac{140000000}{1771561}\left(1-\frac{1}{1.1^{44}}\right)$$

Calculate 1.1 to the power of 44 and get 66.26407607736641103900260617069258125403649041.

$$49.268+\frac{140000000}{1771561}\left(1-\frac{1}{66.26407607736641103900260617069258125403649041}\right)$$

Expand \frac{1}{66.26407607736641103900260617069258125403649041} by multiplying both numerator and the denominator by 100000000000000000000000000000000000000000000.

$$49.268+\frac{140000000}{1771561}\left(1-\frac{100000000000000000000000000000000000000000000}{6626407607736641103900260617069258125403649041}\right)$$

Convert 1 to fraction \frac{6626407607736641103900260617069258125403649041}{6626407607736641103900260617069258125403649041}.

$$49.268+\frac{140000000}{1771561}\left(\frac{6626407607736641103900260617069258125403649041}{6626407607736641103900260617069258125403649041}-\frac{100000000000000000000000000000000000000000000}{6626407607736641103900260617069258125403649041}\right)$$

Since \frac{6626407607736641103900260617069258125403649041}{6626407607736641103900260617069258125403649041} and \frac{100000000000000000000000000000000000000000000}{6626407607736641103900260617069258125403649041} have the same denominator, subtract them by subtracting their numerators.

$$49.268+\frac{140000000}{1771561}\times \frac{6626407607736641103900260617069258125403649041-100000000000000000000000000000000000000000000}{6626407607736641103900260617069258125403649041}$$

Subtract 100000000000000000000000000000000000000000000 from 6626407607736641103900260617069258125403649041 to get 6526407607736641103900260617069258125403649041.

$$49.268+\frac{140000000}{1771561}\times \frac{6526407607736641103900260617069258125403649041}{6626407607736641103900260617069258125403649041}$$

Multiply \frac{140000000}{1771561} times \frac{6526407607736641103900260617069258125403649041}{6626407607736641103900260617069258125403649041} by multiplying numerator times numerator and denominator times denominator.

$$49.268+\frac{140000000\times 6526407607736641103900260617069258125403649041}{1771561\times 6626407607736641103900260617069258125403649041}$$

Do the multiplications in the fraction \frac{140000000\times 6526407607736641103900260617069258125403649041}{1771561\times 6626407607736641103900260617069258125403649041}.

$$49.268+\frac{913697065083129754546036486389696137556510865740000000}{11739085287969531650666649599035831993898213898723001}$$

Convert decimal number 49.268 to fraction \frac{49268}{1000}. Reduce the fraction \frac{49268}{1000} to lowest terms by extracting and canceling out 4.

$$\frac{12317}{250}+\frac{913697065083129754546036486389696137556510865740000000}{11739085287969531650666649599035831993898213898723001}$$

Least common multiple of 250 and 11739085287969531650666649599035831993898213898723001 is 2934771321992382912666662399758957998474553474680750250. Convert \frac{12317}{250} and \frac{913697065083129754546036486389696137556510865740000000}{11739085287969531650666649599035831993898213898723001} to fractions with denominator 2934771321992382912666662399758957998474553474680750250.

$$\frac{144590313491920721341261123111324342668844300590571203317}{2934771321992382912666662399758957998474553474680750250}+\frac{228424266270782438636509121597424034389127716435000000000}{2934771321992382912666662399758957998474553474680750250}$$

Since \frac{144590313491920721341261123111324342668844300590571203317}{2934771321992382912666662399758957998474553474680750250} and \frac{228424266270782438636509121597424034389127716435000000000}{2934771321992382912666662399758957998474553474680750250} have the same denominator, add them by adding their numerators.

$$\frac{144590313491920721341261123111324342668844300590571203317+228424266270782438636509121597424034389127716435000000000}{2934771321992382912666662399758957998474553474680750250}$$

Add 144590313491920721341261123111324342668844300590571203317 and 228424266270782438636509121597424034389127716435000000000 to get 373014579762703159977770244708748377057972017025571203317.

$$\frac{373014579762703159977770244708748377057972017025571203317}{2934771321992382912666662399758957998474553474680750250}$$

Factor

$$\frac{373014579762703159977770244708748377057972017025571203317}{2 \cdot 5 ^ {3} \cdot 11 ^ {50}} = 127\frac{2.9862186967051008 \times 10^{53}}{2.934771321992383 \times 10^{54}} = 127.10175302839875$$