significant figures examples with answers

To decide the number of giant figures in quite a number use the subsequent three rules:

1. Non-0 digits are usually giant
2. Any zeros among giant digits are giant
3. A very last 0 or trailing zeros withinside the decimal element ONLY are giant

Example:  .500 or .632000 the zeros are giant

                .006  or .000968 the zeros are NOT giant

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 For addition and subtraction using the subsequent rules:

1. Count the number of giant figures withinside the decimal element ONLY of every quantity withinside the hassle
2. Add or subtract withinside the regular fashion
3. Your very last solution might also additionally haven't any extra giant figures to the proper of the decimal than the LEAST quantity of giant figures in any quantity withinside the hassle.

 

 

For multiplication and department use the subsequent rule:

 

1. The LEAST quantity of giant figures in any quantity of the hassle determines the number of giant figures withinside the solution. (You are actually searching at the complete quantity, now no longer simply the decimal element)

*This approach you've got in order to apprehend giant figures so that it will use this rule*

      Example: 5.26 has three giant figures

                      6.1 has 2 giant figures

Rules for counting widespread figures are summarized below.

Zeros within more than a few are constantly widespread. Both 4308 and 40.05 incorporate 4 widespread figures.

Zeros that do not anything however set the decimal factor aren't widespread. Thus, 470,000 has widespread figures.

Trailing zeros that are not had to keep the decimal factor are widespread. For example, 4.00 has 3 widespread figures.

If you aren't positive whether or not a digit is widespread, anticipate that it isn't. For example, if the guidelines for a test read: "Add the pattern to four hundred mL of water," anticipate the extent of water is understood to 1 widespread figure.

Multiplication and Division With Significant Figures

The equal precept governs using widespread figures in multiplication and division: the very last end result may be no extra correct than the least correct measurement. In this case, however, we rely the widespread figures in every measurement, now no longer the variety of decimal places: When measurements are accelerated or divided, the solution can incorporate no extra widespread figures than the least correct measurement.

Example: To illustrate this rule, let's calculate the price of the copper in an antique penny this is natural copper. Let's anticipate that the penny has a mass of 2.531 grams, that it is largely natural copper, and that the rate of copper is sixty-seven cents in line with the pound. We can begin through from grams to pounds.

There are 4 widespread figures in each the mass of the penny (2.531) and the variety of grams in a pound (453.6). But there are simplest widespread figures withinside the rate of copper, so the very last solution can simplest have widespread figures.

Rounding Off

When the solution to a calculation consists of too many widespread figures, it has to be rounded off.

There are 10 digits that can arise withinside the remaining decimal area in a calculation. One manner of rounding off involves underestimating the solution for 5 of those digits (0, 1, 2, 3, and 4) and overestimating the solution for the opposite 5 (five, 6, 7, 8, and 9). This technique to rounding off is summarized as follows.

If the digit is smaller than five, drop this digit and go away the last variety unchanged. Thus, 1.684 turns into 1.68.

If the digit is five or larger, drop this digit and upload 1 to the previous digit. Thus, 1.247 turns into 1.25.