In a calculation, a scientist obtained the number 0.0008367070 on a calculator. If the number actually had five (5) significant figures, how should it be written?

Question

In a calculation, a scientist obtained the number 0.0008367070 on a calculator.  If the number actually had five (5) significant figures, how should it be written?

BlackTom AI · Accepted Answer

To determine how to report a number with a specific significant figure requirement, we first identify how many significant figures are requested and which digits are significant in the given value.
The original value is 0.0008367070. In scientific and engineering practice, leading zeros are not significant; the significant figures start at the first nonzero digit, which here is 8. Therefore the sequence of significant digits in the given number is 8-3-6-7-0-7-0, making seven significant figures total.
We are told the number actually had five significant figures. That means we should round the value to five significant digits. The five most significant digits are 8, 3, 6, 7, and the next digit is 0? Wait, when counting the five most significant digits, the digits are 8-3-6-7-0 (i.e., 83670). The next digit after these five is 7, which is greater than or equal to 5, so we round the last kept digit (the 0 in 83670) up by 1, turning 83670 into 83671.
Thus, the properly rounded value with five significant figures is 0.00083671.
Now evaluate the answer choices:
- 0.0008367: This has only four significant digits (8, 3, 6, 7), so it does not meet the five-significant-figure requirement.
- 0.00084: This number has only two significant digits (8 and 4) and also rounds the value in a way that does not reflect five significant figures.
- 0.0008: This contains a single significant figure, far fewer than five, so it is not correct.
- 0.000836707: This presents seven significant figures, not five, so it overstates the precision compared to the instruction.
- 0.00083671: This is the value rounded to five significant figures, matching the required precision and the original magnitude.

In a calculation, a scientist obtained the number 0.0008367070 on a calculator. If the number actually had five (5) significant figures, how should it be written?

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