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QuestionCalculate the significant figures for the result of 4.5×1014/8.3×108.4.5 \times 10^{14} / 8.3 \times 10^{8}.

Studdy Solution

STEP 1

Assumptions1. The operation to be performed is division. . The numbers are in scientific notation.
3. The answer should be reported to the correct number of significant figures.

STEP 2

First, divide the two numbers without considering the powers of10.
4.58.\frac{4.5}{8.}

STEP 3

Calculate the result of the division.
.58.3≈0.5421686746987951\frac{.5}{8.3} \approx0.5421686746987951

STEP 4

Now, subtract the powers of10 in the denominator from the power of10 in the numerator.
1014/108=1014−8=10610^{14} /10^{8} =10^{14-8} =10^{6}

STEP 5

Multiply the result of the division by the result of the subtraction of the powers of10.
0.5421686746987951×100.5421686746987951 \times10^{}

STEP 6

The result is approximately542168.6746987951, but we need to report the answer to the correct number of significant figures. The number with the least number of significant figures in the problem is4.5, which has two significant figures.

STEP 7

Therefore, we round the result to two significant figures.
542168.6746987951≈540000542168.6746987951 \approx540000So, the answer to the problem is approximately 5.4×1055.4 \times10^{5} to the correct number of significant figures.

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