Question

For each of the following numbers, if the number is rewritten in scientific notation, will the exponent of the power of 10 be positive, negative, or zero? a. \(1 / 10^{3}\) b. 0.00045 c. 52,550 d. 7.21 e. \(1 / 3\)

Short answer

a. Negative b. Negative c. Positive d. Zero e. Negative

Step-by-step solution

Analysing Number \(1 / 10^{3}\)

We are given the number \(1 / 10^{3}\). As the inverse of a positive power of 10, we know that the exponent will be negative. In this case, it would be -3 since there are three powers of 10 in the denominator. b.

Analysing Number 0.00045

We have the number 0.00045. To convert this number into scientific notation, we can rewrite it as \(4.5 \times 10^{-4}\). So, the exponent is -4, which means it's negative. c.

Analysing Number 52,550

We have the number 52,550. In scientific notation, this number can be expressed as \(5.255 \times 10^{4}\). The exponent in this case is 4, which is positive. d.

Analysing Number 7.21

We have the number 7.21. As this number is already between 1 and 10, it can be written as \(7.21 \times 10^{0}\). The exponent is 0 in this case. e.

Analysing Number \(1 / 3\)

We have the number \(1 / 3\), which is approximately equal to 0.333. In scientific notation, we can rewrite this as \(3.33 \times 10^{-1}\). The exponent is -1, which means it's negative. In summary: a. The exponent of the power of 10 is negative; b. The exponent of the power of 10 is negative; c. The exponent of the power of 10 is positive; d. The exponent of the power of 10 is zero; e. The exponent of the power of 10 is negative.