POWERS OF TEN - MULTIPLICATION

Concept: Use multiplication when you need to add the same number many times. The answer to a multiplication problem is called the product. When multiplying large multiple digit numbers ending with zeros, first multiply the non-zero numbers, and then add the total number of zeros from all numbers to the product. Follow these steps to multiply.

Steps for Multiplication 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 | Add together the number of zeros in both the first and second numbers.
Step 4 | Arrange the first and second numbers, without the zeros, so that digits with the same place value are aligned.
Step 5 | Multiply all the digits in the top number by the digit in the ones column (furthest to the right) of the bottom number, working from right to left. Place this partial product below the Results Line. (If the product in any column is greater than 9, place the right-most digit of the product below the Results line in the appropriate column, and carry the rest to the top of the next column to the left.)
Step 6 | Next, multiply the digits in the top number by the digit in the tens column of the bottom number. Place this new partial product below the first partial product, with a zero to the right of the second partial product, as a placeholder. For each additional partial product, place an additional zero to the right of the partial product, as a placeholder. Continue this process until all the digits of the top number have been multiplied by all of the digits of the bottom number.
Step 7 | Add all the partial products together to get the total product.
Step 8 | Add the total number of zeros from Step 3 to the total product. If neither of the original numbers was signed, you have reached the end of the problem. You have your answer.
Step 9 | 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 Multiply: –75,000,000 x 3,000

Step 1 | Count the number of zeros in the first number, and then remove them. | – 7 5, 0 0 0, 0 0 0 1 2 3 4 5 6 = 6
Step 2 | Count the number of zeros in the second number, and then remove them. | 3, 0 0 0 1 2 3 = 3
Step 3 | Add together the number of zeros in both the first and second numbers. | 6 + 3 = 9
Step 4 | Arrange the first and second numbers, without the zeros, so that digits with the same place value are aligned. | –75 3
Step 5 | Multiply all the digits in the top number by the digit in the ones column (furthest to the right) of the bottom number, working from right to left. Place this partial product below the Results Line. (If the product in any column is greater than 9, place the right-most digit of the product below the Results line in the appropriate column, and carry the rest to the top of the next column to the left.) 3 x 5 = 1 5 | 1 –75 x 3 5
| Step 5 continued. 3 x 7 = 21 + 1 = 22 | 1 –75 x 3 22 5
Step 6 | Next, multiply the digits in the top number by the digit in the tens column of the bottom number. Place this new partial product below the first partial product, with a zero to the right of the second partial product, as a placeholder. For each additional partial product, place an additional zero to the right of the partial product, as a placeholder. Continue this process until all the digits of the top number have been multiplied by all of the digits of the bottom number. | Step 6 and 7 do not apply in this problem, since there is only one digit in the bottom number. Move to Step 8.
Step 7 | Add all the partial products together to get the total product. | Does not apply.
Step 8 | Add the total number of zeros from Step 3 to the total product. If neither of the original numbers was signed, you have reached the end of the problem. You have your answer. | 225,000,000,000
Step 9 | 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. | – 225,000,000,000 Since the first of the two numbers is a negative number, and the second is a positive number, the answer is negative.