In the number shown, which of the following is the value of the underlined digit?

Rationale

9 X 10 ^ - 2

The underlined digit represents the value of 9 when expressed in scientific notation, specifically indicating that it is multiplied by 10 raised to the power of -2. This notation effectively conveys the number's scale and magnitude in a compact form.

A (9 X 1 ^ - 2) YOUR ANSWER

This choice incorrectly suggests that the value is multiplied by 1 raised to the power of -2, which is equal to 1 regardless of the exponent. Therefore, the expression simplifies to just 9, failing to account for the correct scaling of the number by a power of 10.

B (9 X 10 ^ - 2) CORRECT

This choice accurately reflects the value of the underlined digit as it indicates that 9 is multiplied by 10 raised to the power of -2, representing a decimal point shift two places to the left (0.09). This expression correctly captures the scientific notation format for the number.

C (9 X100^ 2) YOUR ANSWER

This option misrepresents the value by suggesting that 9 is multiplied by 100 raised to the power of 2, which equals 9 multiplied by 10,000. This results in a vastly larger number (90,000), which is not reflective of the original underlined digit.

D (9X1.000^ - 2) YOUR ANSWER

This choice incorrectly implies that the digit is multiplied by 1.000 raised to the power of -2. Since 1.000 raised to any power remains 1, this would simply reduce to 9, overlooking the necessary scaling factor of 10 that indicates the actual size of the number.

Conclusion

In scientific notation, the expression 9 X 10 ^ - 2 accurately conveys the value represented by the underlined digit, indicating a decimal shift by two places. Other choices fail to reflect the correct exponent and scaling, leading to misinterpretations of the number's true value. Understanding scientific notation is crucial for accurately representing and manipulating numbers in mathematical and scientific contexts.

In the number shown, which of the following is the value of the underlined digit?

9 X 10 ^ - 2

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