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I need help with significant figures 3.414s 10.02s 58.325s 0.00098s

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There are 4 sig figs (sfs) in 3.414.

  • 4 sfs in 10.02
  • 5 sfs in 58.325
  • 2 sfs in 0.00098

The rule I use is the "dot right-moving arrow" rule.
I know it seems weird, but it is a very powerful rule, always reliable!

Here is what you do:
If the number has a dot in it (that is, if it has a decimal in it), imagine an arrow swooshing from left to right through the number. Start counting sig figs as soon as the imaginary arrow strikes a non-zero digit. Every digit the arrow goes through after it hits that first non-zero digit, is a significant digit (sig fig). The total number of sig figs is the sum of the first non-zero digit + all the following digits the arrow goes through after that. Very simple, right?

As an example, in 0.00098, the arrow sweeps through the leading zeros without counting until it stikes the first nonzero digit, 9. (BONK!!) So you must count it and the following digit (8). So the total number of sfs is only 2 for this number. Try it on the other numbers for practice.

For a better closure, I guess I should explain the other related rule for sig figs:
The "no-dot left arrow" rule. You can use this rule when a number does not have a decimal in it. For example, the number 500 s. (I am using the same unit you gave in your quantities. As you can see, no decimal is shown. So you can not be sure the number has 3 sfs or not. It would only have 3 sig figs if you were informed it was an exact number. An exact number is a number which has been obtained by counting every object it represents. As in a classroom filled with 200 students, each one counted by their teacher during roll call.

To apply the no-dot left-moving arrow rule, simply imagine an arrow moving left until it hits the first non-zero digit. In this case, that digit is the 5, which is only one digit. Therefore, there is only 1 sig fig in 500 s.

Suggestion: Google up "sig figs" and get some more examples of quantities to practice counting sig figs. Also pay attention to the important related topic of proper rounding off of calculated quantities which have different numbers of sig figs. You will find this skill invaluable when you take a lab based chemistry or physics course!

Good luck!


Posted on Jan 05, 2011


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