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Why does multiplying by 10 shift each digit one place to the left? (A) Each digit represents 10 less. (B) Each digit represents 10 more. (C) Each digit represents 10 times its original value. (D) Each digit represents (1)/(10) of its original value.

Why does multiplying by 1010 shift each digit one place to the left?\newline(A) Each digit represents 1010 less.\newline(B) Each digit represents 1010 more.\newline(C) Each digit represents 1010 times its original value.\newline(D) Each digit represents 110 \frac{1}{10} of its original value.

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Full solution

Q. Why does multiplying by 1010 shift each digit one place to the left?\newline(A) Each digit represents 1010 less.\newline(B) Each digit represents 1010 more.\newline(C) Each digit represents 1010 times its original value.\newline(D) Each digit represents 110 \frac{1}{10} of its original value.
  1. Understand Base−10-10 Number System: Understand the base−10-10 number system.\newlineIn the base−10-10 number system, each digit in a number has a place value that is ten times the place value of the digit to its right. This means that as we move from right to left, each digit represents a value that is 1010 times greater than the digit to its right.
  2. Effect of Multiplying by 1010: Analyze the effect of multiplying by 1010. When we multiply a number by 1010, we are essentially increasing the place value of each digit by a factor of ten. This results in each digit moving one place to the left to accommodate the new place value, and a zero is added at the end (rightmost position) of the number.
  3. Determine Correct Answer: Determine the correct answer based on the analysis.\newlineBased on the understanding of the base-1010 number system and the effect of multiplying by 1010, we can conclude that each digit represents 1010 times its original value after the multiplication. This is why the digits shift one place to the left.

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