Ripley told his mom that multiplying whole numbers by multiples of 10 was easy because you just count zeros in the factors and put them in the product. He used these two examples to explain this strategy 7,000 times 600 equals 4,200,000 and 800 times 700 equals 560,000 Ripley's mom said his strategy will not always work. Why not? Give an example.
sometimes there are no zeros in what you are multiplying by or what is being multiplied so it won't always work
Ripley's strategy of counting zeros in the factors and putting them in the product to multiply whole numbers by multiples of 10 is actually a valid shortcut, but it does not work in all cases. The strategy only works when the number being multiplied is a multiple of 10.
An example where Ripley's strategy would not work is multiplying 8,000 by 700. According to his strategy, since there are three zeros in 8,000 and two zeros in 700, the product should have five zeros, resulting in 56,000,000. However, the correct product is actually 5,600,000.
In this example, Ripley's strategy fails because 8,000 is not a multiple of 10. Therefore, it is important to understand that his strategy is only applicable when multiplying a whole number by a multiple of 10.
Ripley's strategy of counting zeros in the factors and putting them in the product for multiplying whole numbers by multiples of 10 is a helpful shortcut, but it is not always reliable. There are cases where it may not work, and I can provide an example to illustrate this.
Let's take the example of multiplying 2,500 by 400 using Ripley's strategy. According to his strategy, we would count the zeros in the factors, which means we have three zeros in 2,500 and two zeros in 400. Therefore, using Ripley's approach, we would expect the product to have a total of five zeros.
However, if we calculate the actual product, 2,500 times 400, we get 1,000,000, which has six zeros. This means Ripley's strategy does not work for this example, and we cannot solely rely on it to determine the number of zeros in the product.
The reason Ripley's strategy does not always work is that it only takes into account the number of zeros in the factors, but not other digits or operations involved in the multiplication. Multiplying by 10 is a special case where Ripley's strategy works because multiplying any number by 10 simply shifts all its digits one place to the left, adding a zero at the end. However, when dealing with larger numbers and different multiples, there are additional calculations involved that affect the number of zeros in the product.
Therefore, while Ripley's strategy can be a useful trick for quick mental calculations, it is not a foolproof method for determining the number of zeros in the product when multiplying whole numbers by multiples of 10. It is always better to perform the actual multiplication to get an accurate result.
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