# A question about orders of magnitude

I'm reading a book in which the author compares two pairs of numbers $(0.31, 0.39)$ and $(6.10,0.39)$ and multiplies the second member of each pair by a factor $R_1 = 2$ and $R_2 = 20$ so that both members of the pair "have the same order of magnitude". Consequently the pairs of numbers become $(0.31, 2 \times 0.39)$ and $(6.10 , 20 \times 0.39)$. How do these factors ensure that both numbers in the pair have the same order of magnitude?

"Order of magnitude" can be just a synonym for "approximately equal" or it can be "the same number of digits in front of the decimal point". I don't know why the author multiplied $0.39$ by $2$-it was already close to $0.31$ and this takes it farther away. Certainly $20 \times 0.39 = 7.8$ is much closer to $6.1$ than without multiplying by $20$.