A student claims that to divide a number with the units digit 0 by 10, she just crosses out the 0 to get the answer. She wants to know if this is always true and why and if the 0 has to be the units digit. How do you respond?
dividing by 10 shifts the decimal point to the left. That puts the zero after the decimal point, effectively erasing it.
Or, if the number ends in zero, it has the form N0 = N(10) So, dividing by 10 gives
N(10)/10 and the 10's cancel, leaving just N (the number without the zero.)
If the zero is anywhere else, it can't just be dropped, because the factor of 10 isn't there.
To determine if the student's claim is always true, let's consider the concept of dividing a number with the units digit 0 by 10.
When you divide a number by 10, you are essentially moving the decimal point one place to the left. This means that each digit in the number shifts one place to the right, and a 0 is added as the units digit.
To illustrate this, let's take an example:
If we have the number 240 and divide it by 10, we move the decimal point one place to the left, resulting in 24.0.
Now, if we remove the 0 from the units digit of 24.0, we are left with 24.
As you can see, removing the 0 from the units digit does give us the correct answer in this case. However, it's important to note that this method only works when the number being divided has a units digit of 0.
If the number being divided has more than one digit and the units digit is not 0, then you cannot simply remove the units digit and get the correct result.
For example, if we take the number 250 and divide it by 10, we move the decimal point one place to the left, resulting in 25.0. However, if we remove the 0 from the units digit, we would be left with 25, which is incorrect.
In summary, the student's claim is only true when dividing a number with a units digit of 0 by 10. In all other cases, simply crossing out the 0 will not give the correct answer.
To verify whether the student's claim is always true, we can test it with a few examples.
Let's take a number with the units digit of 0, such as 50, and divide it by 10. According to the student's claim, you would just need to cross out the 0 to get the answer, which in this case would be 5. This is indeed correct, as dividing 50 by 10 gives you 5.
Now, let's test it with a number not ending in 0. Consider the number 34. According to the student's claim, to divide 34 by 10, you would cross out the 4 and get 3. However, this claim is incorrect. Dividing 34 by 10 results in 3.4, not 3.
Therefore, the student's claim is only true when the number has a units digit of 0. The units digit is crucial because dividing by 10 simply shifts the decimal point one place to the left, effectively removing the units digit.
In conclusion, to divide a number with the units digit 0 by 10, you can indeed remove the 0 to get the answer. However, this rule does not hold true for numbers that do not end in 0.