12 Stretch Your Thinking Look at the division problem 112 / 0.056. Without solving, how many zeros will be in the quotient? How do you know?
The Correct Answer and Explanation is:
When dividing 112 by 0.056, we need to first consider the decimal places involved. The problem asks how many zeros will be in the quotient, without actually performing the division. Here’s the thought process:
- Understanding the numbers: The dividend is 112 (which is a whole number), and the divisor is 0.056 (which is a decimal number).
- Making the divisor a whole number: To simplify the division, it’s useful to remove the decimal in the divisor. We can multiply both the numerator (112) and the denominator (0.056) by a factor of 1000. This shifts the decimal point three places to the right, converting 0.056 into 56.
- 112 × 1000 = 112,000
- 0.056 × 1000 = 56
- Analyzing the quotient: Now, instead of worrying about decimals, we simply need to divide 112,000 by 56. Without actually solving the division, you can observe that:
- 112,000 divided by 56 will give you a quotient where the result has no decimal points because both numbers are now whole numbers.
- You are essentially dividing by a number that is slightly less than 100, which means the quotient will be smaller than 112,000, but not by an enormous factor.
- Conclusion: Since 112,000 divided by 56 results in a quotient of 2,000, there will be three zeros in the quotient. This conclusion arises because we multiplied the divisor by 1000 and simplified the division by a factor close to 100.
In short, the quotient has three zeros, as we shifted the decimal and ended up dividing 112,000 by 56.
