First, divide “4” into 3. 0, which you can think of as 30. The closest you can get is 4 x 7, or 28, which will give you a remainder of 2. So, write a 7 after the “0. " above the division bracket and “28” below the “3. 0” under the division bracket. Under that, write 2, your remainder, or what you have left when you subtract 28 from 30. Next, add another “0” to the “3. 0” so you have “3. 00”, or what you can think of as “300,” under the division bracket. This will allow you to drop down another 0 to the right of the “2” so you can divide “4” into “20. " Divide “4” into “20” to get 5. Write the “5” to the right of the “0. 7” above the division bracket, so you have “0. 75” written there.
Simply divide 10 by 3. You’ll get 3 x 3, or 9, with a remainder of 1. So, write a 3 after the “0. " above the division bracket, and subtract the answer, 9, from 10 to get a remainder of 1. Add another “0” after the “1” below the “10” to get “10” again. When you divide “3” into “10” again, you’ll have to repeat the process, placing another “3” after the first “3” above the division bracket along with subtracting another “9” from the new “10” you have left. Keep going until you notice a pattern. Notice something funny yet? You’ll see that this can go on forever. You can keep dividing 3 into 10, getting a remainder of 1, and writing yet another “3” after the decimal point above the division bracket.
There are many fractions that have repeating decimals, such as 2/9 (”. 2” repeating), 5/6 (”. 83" with the “3” repeating), or 7/9 (". 7" repeating). This will happen any time you have a denominator that is a multiple of 3 with a numerator that won’t go into it cleanly.
3/5. 10/5 = 2, which is a full number. You know you can multiply 5 x 2 to get 10, so 2 will be your magic number. 3/4. 10/4 = 2. 5, so that’s not a full number, but 100/4 = 25, which is a full number. So, now you know you can multiply 4 by 25 to get 100, so 25 will be the number you use. 5/16. 10/16 = . 625, 100/16 = 6. 25, 1000/16 = 62. 5, 10,000/16 = 625, which is your first full number. So, now you know you can multiply 16 by 625 to get 10,000, so 625 is your magic number.
3/5 x 2/2 = 6/10 3/4 x 25/25 = 75/100 5/16 x 625/625 = 3,125/10,000
3/5 = 6/10 = . 6 3/4 = 75/100 = . 75 5/16 = 3,125/10,000 = . 3125
