Math Problem Statement

Convert the following numbers to base 10 using positional value method.

Solution

From the uploaded images, I can see a few conversion problems involving different number systems. Let’s break them down:


First Image:

  1. 3758=N10375_{8} = N_{10}
    Convert the octal number 3758375_8 to decimal (base 10).

  2. 84216=N10842_{16} = N_{10}
    Convert the hexadecimal number 84216842_{16} to decimal (base 10).


Second Image:

  1. 6548=N10654_8 = N_{10}
    Convert the octal number 6548654_8 to decimal (base 10).

  2. C4D16=N10C4D_{16} = N_{10}
    Convert the hexadecimal number C4D16C4D_{16} to decimal (base 10).

  3. 111100012=N1011110001_2 = N_{10}
    Convert the binary number 11110001211110001_2 to decimal (base 10).


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Math Problem Analysis

Mathematical Concepts

Number Systems
Base Conversion

Formulas

Positional value formula: N_b = d_n*b^n + d_(n-1)*b^(n-1) + ... + d_1*b^1 + d_0*b^0
Octal to Decimal: Use base 8
Hexadecimal to Decimal: Use base 16
Binary to Decimal: Use base 2

Theorems

Positional Numeral System Theorem

Suitable Grade Level

Grades 9-12