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Fill in the boxes to show how the value 4.75 can be represented in binary scientific notation:

Question

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Solution

Binary scientific notation represents numbers as a binary decimal and an exponent of two.

Here's how to convert 4.75 into binary scientific notation:

  1. Convert the whole number part (4) to binary: 4 in binary is 100.

  2. Convert the decimal part (0.75) to binary: 0.75 in binary is 0.11.

  3. Combine the two parts: 4.75 in binary is 100.11.

  4. Normalize the binary number: Move the binary point two places to the left to get 1.0011. This is the mantissa.

  5. The exponent is the number of places you moved the binary point. Since we moved it two places to the right, the exponent is 2.

  6. Write the exponent in binary: 2 in binary is 10.

So, 4.75 in binary scientific notation is 1.0011 x 2^10.

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