# When can Mathematica simplify fractions with large constants?

I cannot get Mathematica (version 11.3.0.0 on Mac OS) to simplify this:

c = (2.71*^10*a)/(1.23*^14*a + 3.14*^12*b)


$$\frac{2.71\times 10^{10} a}{1.23\times 10^{14} a+3.14\times 10^{12} b}$$

Simplify[c]


$$\frac{2.71\times 10^{10} a}{1.23\times 10^{14} a+3.14\times 10^{12} b}$$

Simplify[N[c]]


$$\frac{2.71\times 10^{10} a}{1.23\times 10^{14} a+3.14\times 10^{12} b}$$

I just want it to divide the top and bottom by $10^{10}$.

Is this a bug?

I ask because this does simplify:

c = ( 1.23*^14*a^2)/(3.14*^10*a + 2.71*^8*b)


$$\frac{1.23\times 10^{14} a^2}{3.14\times 10^{10} a+2.71\times 10^8 b}$$

Simplify[c]


$$\frac{3917.2 a^2}{1. a+0.00863057 b}$$

I can't figure out in which cases it simplifies, and in which it doesn't.

• Are either of these acceptable? Expand[Numerator[c]/10^10]/Expand[Denominator[c]/10^10] or Simplify[Numerator[c]/10^10]/Simplify[Denominator[c]/10^10] – Bill Aug 16 '18 at 1:50
• related/possible duplicate: How to give a better looking output result?. – AccidentalFourierTransform Aug 16 '18 at 2:10

factorReal from here, thought it divides by powers of 2 instead of 10 to avoid rounding errors:
factorReal = Plus[x_, y__] :>

You could change Log2 to Log10 and 2.^... to 10.^... if desired.