Powerful Patterns 6: Dividing Specific Numbers by 3

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

111 ÷ 3 = 37

1,011 ÷ 3 = 337

10,011 ÷ 3 = 3,337

100,011 ÷ 3 = 33,337

1,000,011 ÷ 3 = 333,337

10,000,011 ÷ 3 = 3,333,337

100,000,011 ÷ 3 = 33,333,337

When a zero is added between the 1st & 2nd 1's of the dividend, a 3 is added to the quotient!

Look out, because here comes another list with a similar pattern just below!

111 ÷ 3 = 37

1,101 ÷ 3 = 367

11,001 ÷ 3 = 3,667

110,001 ÷ 3 = 36,667

1,100,001 ÷ 3 = 366,667

11,000,001 ÷ 3 = 3,666,667

110,000,001 ÷ 3 = 36,666,667

When a zero is added between the 2nd & 3rd 1's of the dividend, a 6 is added to the quotient between the 3 & the 7!

Again, Dottie Doll asks you this question:

There's 1 more list with a pattern like this!

111 ÷ 3 = 37

10,101 ÷ 3 = 3,367

1,001,001 ÷ 3 = 333,667

100,010,001 ÷ 3 = 33,336,667

10,000,100,001 ÷ 3 = 3,333,366,667

1,000,001,000,001 ÷ 3 = 333,333,666,667

100,000,010,000,001 ÷ 3 = 33,333,336,666,667

This time, a zero is added into both spaces between the 1's of the dividend, so both of those neat things happen in the quotient! You see both of what happens in the previous 2 lists simultaneously!

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!)

Back to Index Page Back to Math Trick Menu

© Derek Cumberbatch