# Converting 43.3 from Base 7 to Base 8

• ccky
In summary, the conversation discusses converting the number 43.3 base 7 to base 8 using no more than one octal digit to the right of the radix point, truncating any remainder by chopping excess digits, and using an ordinary unsigned octal representation. The correct answer is 37.3... base 8, with the remaining decimal part needing to be converted into a sum of negative powers of 8.

## Homework Statement

Convert(43.3)7to base 8?using no more than one octal digit to the right of the radix point.Truncate any remainder by chopping excess digits.Use an ordinary unsigned octal representation.

Base8,decimal.

## The Attempt at a Solution

(43.3）7 .Than,(31.42857)8, My answer is 37.42684 non-terminating.
Is it right or not?
Thanks.

'...using no more than one octal digit to the right of the radix point.'

43.3 base 7 is equal to 31.42857 decimal, not octal. Check your conversion of 0.3 base 7 to octal.

The part to the right of the decimal is still decimal, not yet converted to octal (and the 37 is correct)

phinds said:
The part to the right of the decimal is still decimal, not yet converted to octal (and the 37 is correct)
71x3 =0.42857...
Is it that?

ccky said:
71x3 =0.42857...
?
You must have meant 7-1 x 3
ccky said:
Is it that?
.4285710 = 4 * 10-1 + 2 * 10-2 + 8 * 10-3 + 5 * 10-4 + 7 * 10-5

Now you need to convert this into a sum of negative powers of 8.

## 1. How do you convert a number from Base 7 to Base 8?

To convert a number from Base 7 to Base 8, you can follow these steps:

• Step 1: Write the given number in expanded form, with each digit multiplied by its corresponding power of 7.
• Step 2: Group the digits into sets of three, starting from the rightmost digit.
• Step 3: Convert each set of three digits into its Base 8 equivalent.
• Step 4: Write the converted sets of digits together to get the final answer.

## 2. What is the expanded form of 43.3 in Base 7?

The expanded form of 43.3 in Base 7 is 4 x 7^1 + 3 x 7^0 + 3 x 7^-1.

## 3. How do you convert a number with a decimal point from Base 7 to Base 8?

To convert a number with a decimal point from Base 7 to Base 8, you can follow the same steps as converting a whole number. Once you have the expanded form in Base 8, simply place the decimal point in the appropriate position according to the power of 8.

## 4. What is the Base 8 equivalent of 43.3 in Base 7?

The Base 8 equivalent of 43.3 in Base 7 is 53.5.

## 5. Can you convert a number directly from Base 7 to Base 8?

No, you cannot convert a number directly from one base to another. You must first convert the number to its decimal equivalent and then convert it to the desired base.