Work Out ${ 97.974436 \div 14\$} And Give Your Answer To 2 Decimal Places.

In this article, we will delve into the world of mathematical operations, specifically focusing on dividing a decimal number. We will work out the calculation of $97.974436 \div 14$ and provide the answer to 2 decimal places.

Understanding the Problem

The problem at hand involves dividing a decimal number by another decimal number. In this case, we are required to divide $97.974436$ by $14$. To solve this problem, we will use the standard division algorithm, which involves dividing the dividend (the number being divided) by the divisor (the number by which we are dividing).

Step 1: Divide the Dividend by the Divisor

To begin, we will divide the dividend $97.974436$ by the divisor $14$. We will perform long division to find the quotient (result of the division).

97.974436 ÷ 14 = ?

To divide $97.974436$ by $14$, we will start by dividing the whole number part of the dividend ( $97$ ) by the divisor ( $14$ ). This will give us the first digit of the quotient.

97 ÷ 14 = 6

Next, we will multiply the divisor ( $14$ ) by the quotient digit we obtained in the previous step ( $6$ ) and subtract the result from the dividend ( $97.974436$ ). This will give us a remainder.

14 × 6 = 84

97.974436 - 84 = 13.974436

We will then bring down the next digit of the dividend ( $9$ ) and repeat the process.

13.974436 ÷ 14 = 0.99

14 × 0.99 = 13.86

13.974436 - 13.86 = 0.134436

We will then bring down the next digit of the dividend ( $7$ ) and repeat the process.

0.134436 ÷ 14 = 0.0096

14 × 0.0096 = 0.1344

0.134436 - 0.1344 = 0.000036

We will then bring down the next digit of the dividend ( $4$ ) and repeat the process.

0.000036 ÷ 14 = 0.00000257

14 × 0.00000257 = 0.00003598

0.000036 - 0.00003598 = 0.00000002

Since the remainder is very small, we can stop here and round the quotient to 2 decimal places.

Quotient: 7.00

Rounded Quotient: 7.00

Answer to 2 Decimal Places: 7.00

Conclusion

In this article, we worked out the calculation of $97.974436 \div 14$ and provided the answer to 2 decimal places. We used the standard division algorithm to find the quotient and rounded the result to 2 decimal places. The final answer is 7.00.

Additional Tips and Variations

• When dividing a decimal number by another decimal number, it is often helpful to multiply both numbers by a power of 10 to eliminate the decimal points.
• In this case, we could have multiplied both $97.974436$ and $14$ by $100$ to eliminate the decimal points and make the calculation easier.
• However, in this article, we chose to perform the division as is, without multiplying by a power of 10, to demonstrate the standard division algorithm.

Final Thoughts

In this article, we will address some of the most common questions and concerns related to dividing decimal numbers. Whether you are a student, a teacher, or simply someone who wants to improve their math skills, this article will provide you with the answers you need.

Q: What is the difference between dividing a decimal number by a whole number and dividing a decimal number by another decimal number?

A: When dividing a decimal number by a whole number, the result is a decimal number. However, when dividing a decimal number by another decimal number, the result can be a whole number, a decimal number, or even a repeating decimal.

Q: How do I divide a decimal number by a whole number?

A: To divide a decimal number by a whole number, you can simply divide the decimal number by the whole number using long division or a calculator. For example, if you want to divide $23.45$ by $5$, you can use long division to get the result.

Q: How do I divide a decimal number by another decimal number?

A: To divide a decimal number by another decimal number, you can use the standard division algorithm, as we demonstrated in the previous article. You can also use a calculator or a computer program to perform the division.

Q: What is the rule for dividing decimal numbers?

A: The rule for dividing decimal numbers is to divide the dividend (the number being divided) by the divisor (the number by which we are dividing). The result is the quotient (the result of the division).

Q: How do I round the result of a division problem involving decimal numbers?

A: To round the result of a division problem involving decimal numbers, you can round the quotient to the desired number of decimal places. For example, if you want to round the result of $23.45 \div 5$ to 2 decimal places, you can round the result to $4.69$.

Q: What is the difference between a repeating decimal and a non-repeating decimal?

A: A repeating decimal is a decimal number that has a repeating pattern of digits. For example, $0.33333...$ is a repeating decimal. A non-repeating decimal is a decimal number that does not have a repeating pattern of digits. For example, $0.12345$ is a non-repeating decimal.

Q: How do I convert a repeating decimal to a fraction?

A: To convert a repeating decimal to a fraction, you can use the following steps:

1. Identify the repeating pattern of digits.
2. Let x be the repeating decimal.
3. Multiply x by 10 to shift the decimal point one place to the right.
4. Subtract the original decimal from the new decimal to eliminate the repeating pattern.
5. Solve for x to get the fraction.

Q: How do I convert a non-repeating decimal to a fraction?

A: To convert a non-repeating decimal to a fraction, you can use the following steps:

1. Identify the decimal number.
2. Let x be the decimal number.
3. Multiply x by 10 to shift the decimal point one place to the right.
4. Subtract the original decimal from the new decimal to get a whole number.
5. Solve for x to get the fraction.

Conclusion

In this article, we addressed some of the most common questions and concerns related to dividing decimal numbers. We hope this article has provided you with the answers you need and has helped you to understand the concept better. Whether you are a student, a teacher, or simply someone who wants to improve their math skills, we hope this article has been helpful.

Additional Resources

• For more information on dividing decimal numbers, please refer to the previous article.
• For more information on converting decimals to fractions, please refer to the article on converting decimals to fractions.
• For more information on math concepts, please refer to the math concepts section of our website.

Final Thoughts

In conclusion, dividing decimal numbers can be a challenging task, but with the right approach and techniques, it can be done accurately and efficiently. We hope this article has provided a clear and concise explanation of the process and has helped you to understand the concept better.