Why is multiplying by 10, by 100, by 1000, and so on, special in the base-ten system? The answer  lies in how the values of the places in the base-ten system are related. Multiplying by 10, 100, 1000, and so on, is special because of the structure of place value in  the base-ten system: In the base-ten system, the value of each place is 10 times the value of the  place to its immediate right. Consider what happens when we multiply the number 34 by 10. The  number 34 stands for 3 tens and 4 ones and can be represented by 3 bundles of 10 toothpicks  and 4 individual toothpicks, as shown in Figure 4.9. Then 10 x34 stands for the total number  of toothpicks in 10 groups of 34 toothpicks. As Figure 4.10 shows, when we form 10 groups of  34 toothpicks, each of the 3 original tens becomes bundled into 1 group of 100 and each of the  4 original individual toothpicks is bundled into 1 group of 10. Therefore, when we multiply 34  by 10, the 3 in the tens place moves one place over to the hundreds place and the 4 in the ones  place moves one place over to the tens place. Notice that this shifting occurs precisely because the  value of the hundreds place is 10 times the value of the tens place and the value of the tens place is  10 times the value of the ones place. In general, when we multiply a number by 10, all the digits move one place to the left because the  value of each place is 10 times the value of the place to its right.  What about multiplying by 100, or 1000, or 10,000, and so on? Because  100 = 10 x10  multiplying by 100 has the same effect as multiplying by 10 twice. Therefore, multiplying by 100  moves each digit in the decimal representation of a number two places to the left. Similarly, because  1000 = 10 x10 x10  multiplying by 1000 has the same effect as multiplying by 10 three times. Therefore, multiplying by  1000 moves each digit in the base-ten representation of a number three places to the left.