How to Multiply 1/7 by 10: Exploring Rational and Decimal Forms

Multiplication involving fractions is a fundamental concept in mathematics that is widely used in various real-life applications. This article will explore how to multiply the fraction 1/7 by 10, providing both rational and decimal forms of the answer.

Step-by-Step Multiplication of 1/7 by 10

Multiplying the fraction 1/7 by 10 is a straightforward process. Here’s how you can do it:

First, express the multiplication as a fraction: 1/7 times; 10. Next, rewrite 10 as a fraction with a denominator of 1: 10/1. Now, multiply the two fractions by multiplying the numerators together and the denominators together: 10/7. The result is 10/7, which is the rational form of the answer.

Converting to Decimal Form

While the rational form is useful for precision, converting it to a decimal form can provide a more intuitive understanding, especially in practical applications. To convert 10/7 to a decimal:

Divide the numerator by the denominator: 10 ÷ 7. The result is approximately 1.42857142857, which can be written as 1.43 when rounded to two decimal places.

However, it's worth noting that 10/7 is a repeating decimal. Specifically, it is 1.428571428571428571..., which can be truncated to 1.428571, 1.42857, or 1.4 with some repetition.

Replication of Digits in Decimal Form

When expressing 10/7 as a repeating decimal, you may observe that the digit 4 repeats:

The decimal form of 10/7 is 1.428571428571428571..., which can be truncated to 1.4285714, 1.428571, or 1.42857 if you decide to round it off. The fourth decimal place and beyond repeat the digit 4, giving it a repeating pattern of 1.42857142857.

Practical Applications

Understanding how to multiply 1/7 by 10 and working with both the rational and decimal forms can be valuable in various fields:

Finance: When dealing with currency conversions or budgeting, understanding fractions and decimals is essential. Science: In scientific calculations, especially in fields like chemistry and physics, working with fractions and decimals can help in precise measurements and calculations. Engineering: Engineers often need to work with fractions and decimals when designing structures or operations.

Conclusion

In summary, multiplying 1/7 by 10 yields a rational number 10/7, which can be converted to the recurring decimal 1.42857142857. Understanding how to convert between these forms is a crucial skill in mathematics and its applications. Whether you need precision or an intuitive understanding, both forms of the answer can be useful.

Frequently Asked Questions

Q: Why is 10/7 a repeating decimal?
A: The fraction 10/7 is a repeating decimal because the numerator (10) does not have any factors in common with the denominator (7). When dividing, the remainder never reaches zero, leading to a repeating pattern in the decimal form.

Q: How do you convert fractions to decimals?
A: To convert a fraction to a decimal, divide the numerator by the denominator. If the division results in a repeating pattern, you can represent it with a bar over the repeating digits.

Q: How do you multiply fractions?
A: To multiply two fractions, simply multiply the numerators together and the denominators together. This results in a new fraction. If the result is not in its simplest form, simplify it by dividing both the numerator and the denominator by their greatest common divisor.