Answer :

Certainly! Let's solve the problem step-by-step.

We are given a base 10 number, 71, and several options to check which one correctly represents 71 in a specific base, denoted here as base [tex]\( f \)[/tex]. From the context, it seems base [tex]\( f \)[/tex] could refer to base 8 (octal), which is a common base conversion. Let's convert 71 from base 10 to base 8 and then compare it with the options provided.

Step 1: Convert 71 from base 10 to base 8 (octal).

To convert from base 10 to base 8, you repeatedly divide the number by 8 and record the remainders:

1. Divide 71 by 8:
- 71 ÷ 8 = 8 with a remainder of 7. (Write down 7)

2. Divide the quotient by 8:
- 8 ÷ 8 = 1 with a remainder of 0. (Write down 0)

3. Divide the new quotient by 8:
- 1 ÷ 8 = 0 with a remainder of 1. (Write down 1)

Reading the remainders from last to first, 71 in base 10 is written as [tex]\( 107 \)[/tex] in base 8.

Step 2: Compare with the given options.

Now let's compare the correct base 8 representation, [tex]\( 107 \)[/tex], with the provided options:

- (a) 1078
- (b) 1068
- (c) 718
- (d) 178

None of the options are written solely in base 8 format as some contain digits not valid in base 8 (which ranges from 0-7). This may be due to a misinterpretation or typo in the given options. However, based on the conversion:

The closest match for the number [tex]\( 107 \)[/tex] from our conversion would align with the intent behind:

- (d) 178, interpreting without any base errors, matches the actual conversion.

Thus, the number 71 in base 10 is represented as 178 in base 8 (as interpreted) from the given choices.

Thanks for taking the time to read Convert 71 to a number in base tex f tex A 1078 B 1068 C 718 D 178. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada