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Answer :
Sure, let's look at each division problem and determine whether a zero needs to be written in the dividend to find the quotient.
### 17a. [tex]\(1.4 \div 0.05\)[/tex]
1. Understanding the Divisor: The divisor here is 0.05. To work more comfortably, we make the divisor a whole number by moving the decimal point two places to the right.
2. Adjusting the Dividend: As we moved the decimal in the divisor two places to the right, we must do the same for the dividend. Moving the decimal in 1.4 two places to the right results in 140.
3. Calculation: Now, perform [tex]\(140 \div 5\)[/tex]. The division can proceed without any further adjustments. After dividing, we find the quotient is 28.
4. Conclusion: A zero was indeed added to the dividend during the process to accommodate moving the decimal point.
Answer: Yes
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### 17b. [tex]\(2.52 \div 0.6\)[/tex]
1. Understanding the Divisor: The divisor here is 0.6. We will move the decimal one place to the right to make it 6, a whole number.
2. Adjusting the Dividend: Similarly, move the decimal one place in the dividend, 2.52, resulting in 25.2.
3. Calculation: Now, perform [tex]\(25.2 \div 6\)[/tex]. After division, the quotient is 4.2.
4. Conclusion: No zeros were added to the dividend during this process as only the existing digits were utilized after moving the decimal.
Answer: No
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### 17c. [tex]\(2.61 \div 0.3\)[/tex]
1. Understanding the Divisor: The divisor here is 0.3. Move the decimal one place to the right to make it 3, a whole number.
2. Adjusting the Dividend: Move the decimal in 2.61 one place to the right, which results in 26.1.
3. Calculation: Now, perform [tex]\(26.1 \div 3\)[/tex]. The quotient, 8.7, is obtained directly from this division.
4. Conclusion: No extra zeros were needed during this division process.
Answer: No
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I hope this step-by-step guide helps you understand how to determine if a zero is needed in the dividend to find the quotient for these calculations!
### 17a. [tex]\(1.4 \div 0.05\)[/tex]
1. Understanding the Divisor: The divisor here is 0.05. To work more comfortably, we make the divisor a whole number by moving the decimal point two places to the right.
2. Adjusting the Dividend: As we moved the decimal in the divisor two places to the right, we must do the same for the dividend. Moving the decimal in 1.4 two places to the right results in 140.
3. Calculation: Now, perform [tex]\(140 \div 5\)[/tex]. The division can proceed without any further adjustments. After dividing, we find the quotient is 28.
4. Conclusion: A zero was indeed added to the dividend during the process to accommodate moving the decimal point.
Answer: Yes
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### 17b. [tex]\(2.52 \div 0.6\)[/tex]
1. Understanding the Divisor: The divisor here is 0.6. We will move the decimal one place to the right to make it 6, a whole number.
2. Adjusting the Dividend: Similarly, move the decimal one place in the dividend, 2.52, resulting in 25.2.
3. Calculation: Now, perform [tex]\(25.2 \div 6\)[/tex]. After division, the quotient is 4.2.
4. Conclusion: No zeros were added to the dividend during this process as only the existing digits were utilized after moving the decimal.
Answer: No
---
### 17c. [tex]\(2.61 \div 0.3\)[/tex]
1. Understanding the Divisor: The divisor here is 0.3. Move the decimal one place to the right to make it 3, a whole number.
2. Adjusting the Dividend: Move the decimal in 2.61 one place to the right, which results in 26.1.
3. Calculation: Now, perform [tex]\(26.1 \div 3\)[/tex]. The quotient, 8.7, is obtained directly from this division.
4. Conclusion: No extra zeros were needed during this division process.
Answer: No
---
I hope this step-by-step guide helps you understand how to determine if a zero is needed in the dividend to find the quotient for these calculations!
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