POWERS OF TEN - DIVISION

Concept: Use division when you need to separate a whole into equal parts. The answer to a division problem is called a quotient. When dividing large multiple digit numbers ending with zeros, first divide the non-zero numbers, and then add to that quotient the difference of the number of zeros from both original numbers (difference expressed in zeros). Follow these steps to divide.

Quotient

2

Divisor 4

Dividend

Steps for Division of Large Multiple Digit Numbers Ending in Multiple Zeros

Step 1 | Count the number of zeros in the first number, and then remove them.
Step 2 | Count the number of zeros in the second number, and then remove them.
Step 3 | Subtract the number of zeros in the second number from the number of zeros in the first number.
Step 4 | Place the number to be divided (the dividend), without the zeros, inside the bracket.
Step 5 | Place the number by which you are dividing (the divisor), without the zeros, outside the bracket on the left.
Step 6 | Determine how many times the divisor can be divided into the dividend, one dividend digit at a time, working from left to right, and place the answer (the quotient) above the bracket.
Step 7 | Add the number of zeros determined in Step 3 to the quotient. If neither of the original numbers was signed, you have reached the end of the problem. You have your answer.
Step 8 | If either, or both, of the original numbers is signed, follow these rules: If the signs of both numbers are the same, the sign of the answer is positive. If the signs of both numbers are different, the sign of the answer is negative.

Example Divide: – 480000000 3000

Step 1 | Count the number of zeros in the first number, and then remove them. | – 4 8 0, 0 0 0, 0 0 0 1 2 3 4 5 6 7 There are 7 zeros.
Step 2 | Count the number of zeros in the second number, and then remove them. | 3, 0 0 0 1 2 3 There are 3 zeros.
Step 3 | Subtract the number of zeros in the second number from the number of zeros in the first number. | 7 (first number) –3 (second number) 4 (difference)
Step 4 | Place the number to be divided (the dividend), without the zeros, inside the bracket. |
Step 5 | Place the number by which you are dividing (the divisor), without the zeros, outside the bracket on the left. | 3
Step 6 | Determine how many times the divisor (3) can be divided into the dividend (4), one dividend digit at a time, working from left to right, and place the answer (the quotient) (1)above the bracket. The quotient is 1 since 1 x 3 = 3, which is as close as we can get to 4 without going over. Write 1 above the bracket over the 4, and 3 under the 4. | 1 3 – 3
| Subtract 3 from 4. Place the answer, 1, under the Results line. | 1 3 – 3 1
| Drop the next number of the dividend, 8, into the spot to the right of the 1. | 1 3 – 3 18
Step 6 | Determine how many times the divisor (3) can be divided into the new dividend (18) and place that number (6) above the bracket in the quotient area. 18 divided by 3 equals 6, since 3 times 6 equals 18, so place 6 above the bracket, and 18 under the 18. | 16 3 – 3 18 – 18
| Subtract 18 from 18. Place the answer, 00, under the Results line. | 16 3 – 3 18 –18 00
Step 7 | Add the number of zeros determined in Step 3 (4) to the quotient. If neither of the original numbers was signed, you have reached the end of the problem. You have your answer. | 1 6 0, 0 0 0 1 2 3 4
Step 8 | If either, or both, of the original numbers is signed, follow these rules: If the signs of both numbers are the same, the sign of the answer is positive. If the signs of both numbers are different, the sign of the answer is negative. | – 1 6 0, 0 0 0 Since the first of the two numbers is a negative number, and the second is a positive number, the answer is negative.