Powerful Patterns 11: Putting Zeroes in Fractions

1/4 = 0.25

10/4 = 2.5

100/4 = 25

1,000/4 = 250

10,000/4 = 2,500

100,000/4 = 25,000

1,000,000/4 = 250,000

10,000,000/4 = 2,500,000

When a zero is added to the numerator, the fraction gets bigger in size, considering the decimal point! In fact, the non-zero digits shift to the left as the quotient gets more zeroes! Notice how the decimal point disappeared after 100 was divided by 4.

In the next pattern below, zeroes are added to the denominator instead of the numerator! Observe what happens:

1/4 = 0.25

1/40 = 0.025

1/400 = 0.0025

1/4,000 = 0.00025

1/40,000 = 0.000025

1/400,000 = 0.0000025

In this 2nd pattern, (which also started with 1/4 = 0.25) the non-zero digits shift to the right instead of the left, adding more zeroes to the right of the decimal point & making the quotient (or fraction) smaller! The decimal point doesn't disappear this time!

There's 1 more list with a pattern like this! Let's add zeroes to both the numerator & denominator this time!

(Again, we'll start with 1/4 = 0.25)

1/4 = 0.25

10/40 = 0.25

100/400 = 0.25

1,000/4,000 = 0.25

10,000/40,000 = 0.25

100,000/400,000 = 0.25

1,000,000/4,000,000 = 0.25

10,000,000/40,000,000 = 0.25

Holy Macaroni! The quotient/fraction stayed the exact same size in absolute value this time! However, the beginning of this pattern shows the fraction in its simplest terms. Anyway, since zeroes were added to both the numerator & the denominator, the exponential ratio, considering the powers of ten(10), remained the same as well so the quotient couldn't change in this final pattern!

What if the numerator & denominator both have zeroes but different numbers of zeroes? Well, that determines where the decimal point will be shifted in the quotient, which I'll show you in this final example:

10,000/40 = 250

10/40,000 = 0.00025

10/400 = 0.025

1,000,000/40 = 25,000

If the numerator has more zeroes, the quotient will be bigger; if the denominator has more zeroes, the quotient will be smaller.

Surely, you can make other patterns like these with other non-zero numbers in the numerator or the denominator of the fraction! And I especially do mean "non-zero" with the denominator because division by zero is normally undefined! The quotient will remain zero if the numerator is equal to zero, too!

Graham Cracker the Gingerbread Man explains with his joke that multiplying by zero is the same as multiplying a number by nothing! Division by zero is undefined due to how multiplication by zero works. See Math Trick #48: Multiplication Vs. Division By Zero for more details.

Powerful Patterns 11: Putting Zeroes in Fractions

Look at the list in the virtual chalkboard below. You should notice a pattern...

When a zero is added to the numerator, the fraction gets bigger in size, considering the decimal point! In fact, the non-zero digits shift to the left as the quotient gets more zeroes! Notice how the decimal point disappeared after 100 was divided by 4.

In the next pattern below, zeroes are added to the denominator instead of the numerator! Observe what happens:

In this 2nd pattern, (which also started with 1/4 = 0.25) the non-zero digits shift to the right instead of the left, adding more zeroes to the right of the decimal point & making the quotient (or fraction) smaller! The decimal point doesn't disappear this time!

There's 1 more list with a pattern like this! Let's add zeroes to both the numerator & denominator this time!

(Again, we'll start with 1/4 = 0.25)

What if the numerator & denominator both have zeroes but different numbers of zeroes? Well, that determines where the decimal point will be shifted in the quotient, which I'll show you in this final example:

Speaking of patterns, maybe you already seen some other numerical math patterns that other mathematicians already discovered & published! (Besides me or you; any open-minded person can be a great mathematician, like me!)