When dividing decimals by 0.1, 0.01, and 0.001, __ in the dividend to the number of zeros in the power of 10. A. Move the decimal point B. Divide directly C. Add zeros to the divisor and dividend D. Add zeros to the divisor
The correct answer and explanation is:
Correct Answer: A. Move the decimal point
When dividing decimals by numbers like 0.1, 0.01, or 0.001, the correct method is to move the decimal point in the dividend to the right. The number of places the decimal point is moved depends on the number of zeros in the divisor. This technique is based on the fact that dividing by a number less than 1 actually makes the result larger. The smaller the divisor, the greater the result.
Here is how it works:
- Dividing by 0.1 is the same as multiplying by 10. This moves the decimal one place to the right.
- Dividing by 0.01 is the same as multiplying by 100. This moves the decimal two places to the right.
- Dividing by 0.001 is the same as multiplying by 1000. This moves the decimal three places to the right.
For example:
- 2.3 ÷ 0.1 = 23
- 6.56 ÷ 0.01 = 656
- 76.563 ÷ 0.001 = 76563
Each of these follows the pattern of moving the decimal point rightward based on how many zeros are in the divisor. This happens because a smaller divisor fits into the dividend more times. Dividing by a decimal can be tricky if not approached this way, but understanding this relationship makes mental math quicker and more accurate.
This method avoids the need for long division and helps students gain a better conceptual understanding of place value and powers of ten. It also shows that dividing is closely related to multiplying when working with powers of ten. Moving the decimal is a shortcut based on these mathematical rules.