How to Convert from Base Seven to Base Five  Summary and Q&A
TL;DR
Learn how to convert a number from base 7 to base 5 by first converting it to base 10 and then performing repeated divisions.
Key Insights
 ⚾ Converting a number from base 7 to base 5 involves first converting it to base 10 and then converting the base 10 number to base 5 using repeated divisions.
 ⚾ The process of converting to base 5 requires dividing the number by 5 and noting the remainder at each step.
 🗂️ Repeatedly dividing and subtracting multiples of 5 helps determine the remainders in the conversion process.
 ⚾ The order of the remainders obtained from the repeated divisions is crucial, as it determines the digits of the number in base 5.
 ⚾ Checking the accuracy of the conversion can be done by converting the resulting number from base 5 back to base 7 and comparing it to the original number.
 ✊ Understanding the powers of 7 and their corresponding digits in base 7 is essential in the conversion process.
 👻 Converting numbers between different bases allows for easier manipulation and understanding of numeric representations.
Transcript
hi everyone in this problem we're going to convert this number 3164 and base 7 to base 5. so step 1 will be to convert this to base 10 then we'll convert it to base 5. so to convert it to base 10 the way i like to do it is i like to start with this number here so 4 and we multiply by 7 to the 0 power okay then you put a plus sign then you go to the... Read More
Questions & Answers
Q: How do you convert a number from base 7 to base 5?
To convert a number from base 7 to base 5, first convert it to base 10 by multiplying each digit with the corresponding power of 7. Then, convert the obtained base 10 number to base 5 by repeatedly dividing and noting the remainders.
Q: What is the process of converting from base 10 to base 5?
Converting from base 10 to base 5 involves repeatedly dividing the number by 5 and noting the remainders. The remainders are then written down in reverse order to obtain the number in base 5.
Q: What is the significance of the repeated divisions in converting to base 5?
The repeated divisions in converting to base 5 help determine the remainders at each step, which are necessary to represent the number in base 5. By dividing the number by 5 multiple times, we can identify the remainders and write them in reverse order to obtain the base 5 form.
Q: How can you check the accuracy of the conversion process?
To check the accuracy of the conversion process, you can convert the resulting number from base 5 back to base 7 and verify if it matches the original number. By following the reverse process of conversion, you can ensure the correctness of your calculations.
Summary & Key Takeaways

Convert the given number from base 7 to base 10 by multiplying each digit with the corresponding power of 7 and adding them up.

After obtaining the base 10 form, convert it to base 5 by repeatedly dividing and noting the remainders.

Write down the remainders in reverse order to obtain the number in base 5.