Math Problem Statement

1.    CONVERT THE FOLLOWING DECIMAL NUMBER TO BINARY

226

Solution

To convert the decimal number 226 to binary, we need to repeatedly divide the number by 2 and record the remainders.

Let's go through the process step by step:

  1. Divide 226 by 2:
    226÷2=113226 \div 2 = 113 with a remainder of 0.

  2. Divide 113 by 2:
    113÷2=56113 \div 2 = 56 with a remainder of 1.

  3. Divide 56 by 2:
    56÷2=2856 \div 2 = 28 with a remainder of 0.

  4. Divide 28 by 2:
    28÷2=1428 \div 2 = 14 with a remainder of 0.

  5. Divide 14 by 2:
    14÷2=714 \div 2 = 7 with a remainder of 0.

  6. Divide 7 by 2:
    7÷2=37 \div 2 = 3 with a remainder of 1.

  7. Divide 3 by 2:
    3÷2=13 \div 2 = 1 with a remainder of 1.

  8. Divide 1 by 2:
    1÷2=01 \div 2 = 0 with a remainder of 1.

Now, we read the remainders from bottom to top:
226 in decimal is equal to 11100010 in binary.

Answer: 11100010

Would you like more details on the conversion process, or have any questions? Here are some related questions for further exploration:

  1. What is the binary representation of 150?
  2. How do you convert a binary number back to decimal?
  3. What is the largest binary number that can be represented in 8 bits?
  4. How do you add two binary numbers together?
  5. What is the significance of binary numbers in computer systems?

Tip: Always keep track of the remainders when dividing by 2, as they determine the binary digits in reverse order.

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Math Problem Analysis

Mathematical Concepts

Number Systems
Binary Numbers
Decimal to Binary Conversion

Formulas

Divide the decimal number by 2 and record the remainders until the quotient is 0

Theorems

Division by 2 method for converting decimal to binary

Suitable Grade Level

Grades 5-7