Final answer:
When dividing whole numbers to get a decimal, it's critical to use signficant figures correctly. A calculator may provide a decimal with too many places, so the user needs to round the answer to the appropriate number of significant figures after performing the division.
Step-by-step explanation:
When dividing whole numbers to get a decimal, calculators will often provide a result with more decimal places than is appropriate based on the significant figures of the numbers involved. It is essential to apply the rules of significant figures after performing the division to ensure that the answer reported is as accurate as the original measurements. In division, the resulting decimal should have as many significant figures as the original number with the fewest significant figures. For instance, if you divide 125 by 307, although the calculator gives a long decimal, both numbers have three significant figures, so the result should be rounded to three significant figures as well, which would be 0.407.
Let's consider the example of dividing 1.9436 by powers of 10:
- 1.9436 ÷ 10 = 0.19436
- 1.9436 ÷ 100 = 0.019436
- 1.9436 ÷ 1000 = 0.0019436
The number of significant figures remains the same after division, but the decimal point moves.
Understanding the concept of units is also important when dividing numbers as dividing the units can create a new unit that was not initially present.