# How to Convert from Base Seven to Base Five | Summary and Q&A

12.2K views
October 26, 2020
by
The Math Sorcerer
How to Convert from Base Seven to Base Five

## 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

### 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.