Math/Calc. Set 1 – Significant Figures in Numbers

The following number is a measurement or estimate.  Indicate how many sigificant figures are in the number, and then write the number in scientific (exponential) notation in standard form (with the number to the left of the decimal point being between 1 and 10).  Use only the correct number of significant figures.

0.000 000 002 030 40

0.000 000 002 030 40

Only the numbers shown in green are significant.

 6 SF;  2.03040 ? 10–9


Zeroes to the left of the first non-zero digit are not significant because they just keep the decimal place.  If there are any trailing zeroes at the end (at the right), they are always significant.

 

 

The number

4.560 ? 10-11

 is written in scientific (exponential) notation.  How many significant figures are in this number?  Write this number as an ordinary number, using the proper number of significant figures.

4 SF

0.000 000 000 045 60

Numbers written in green are significant.

We know that

1 foot  =  12 inches

 

How many significant figures are in the number “12” as it is used above?

The number “12” is an exact number that has an infinite number of significant figures.  The foot has been defined so that it is exactly equal to twelve inches.  In other words:

1.000000000… ft  =  12.00000000… in

The following number is a measurement or estimate. Indicate how many sigificant figures are in the number, and then write the number in scientific (exponential) notation in standard form (with the number to the left of the decimal point being between 1 and 10). Use only the correct number of significant figures.

0.000 000 600 780

 

0.000 000 600 780

Only the numbers shown in green are significant.

6 SF;  6.00780 ? 10–7


Zeroes to the left of the first non-zero digit are not significant because they just keep the decimal place. If there are any trailing zeroes at the end (at the right), they are always significant.

We know that

1 pound (lb)  =  453.6 grams (g)

How many significant figures are in the number “453.6” as it is used above?

4 SF

Lecture handout #3 explains that the pound is defined in the USA so that

1 lb  =  453.59237000.. g  (exactly)

Virtually nobody ever uses (or even knows) this exact conversion factor.  It is generall rounded either to

1 lb = 434 g  (3 SF)

or  1 lb = 453.6 g (4 SF)

The following number is a measurement or estimate. Indicate how many sigificant figures are in the number, and then write the number in scientific (exponential) notation in standard form (with the number to the left of the decimal point being between 1 and 10). Use only the correct number of significant figures.

0.000 500 60

0.000 500 60

Only the numbers shown in green are significant.

5 SF; 5.0060 ? 10–4


Zeroes to the left of the first non-zero digit are not significant because they just keep the decimal place. If there are any trailing zeroes at the end (at the right), they are always significant.

We know that

1 inch (in) = 2.54 centimeters (cm)

How many significant figures are in the number “2.54” as it is used above?

The number 2.54 actually has an infinite number of significant figures.  Inches and centimeters have been defined so that there are exactly 2.54000000… centimeters in one inch.  The word “exactly” means that the number of significant figures is infinite.

The following number is a measurement or estimate. Indicate how many sigificant figures are in the number, and then write the number in scientific (exponential) notation in standard form (with the number to the left of the decimal point being between 1 and 10). Use only the correct number of significant figures.

0.000 000 004 050 30

0.000 000 004 050 30

Only the numbers shown in green are significant.

6 SF;  4.05030 ? 10–9


Zeroes to the left of the first non-zero digit are not significant because they just keep the decimal place. If there are any trailing zeroes at the end (at the right), they are always significant.

The following number is a measurement or estimate. Indicate how many sigificant figures are in the number, and then write the number in scientific (exponential) notation in standard form (with the number to the left of the decimal point being between 1 and 10). Use only the correct number of significant figures.

600

Either 1 SF, 2 SF, or 3 SF.

Some YouTube videos mislead you and incorrectly state that a number such as 600 has only 1 SF, because trailing zeroes (here at the right of the number 6) are never significant.  This oversimplification is not really correct.  Actually, there are three possibilities, depending on the possible error (uncertainty) in the measurement.  The possibilities are:

600 ± 100  has  1 SF:  6 ? 102

600 ± 100   has 2 SF:  6.0 ? 102

600 ± 100   3 SF:  6.00 ? 102

 

We know that

1 mile (mi)  =  5,280 feet (ft)

How many significant figures are in the number “5,280” as it is used above?

The number 5,280 actually has an infinite number of significant figures.  Miles and feet have been defined so that there are exactly 5,280.0000000… feet in one mile.  The word “exactly” means that the number of significant figures is infinite.

The number

6.8310 ? 103

is written in scientific (exponential) notation. How many significant figures are in this number? Write this number as an ordinary number, using the proper number of significant figures.

6831.0

 

We know that

1 liter (L)  =  1,000 milliliters (mL)

How many significant figures are in the number “1,000” as it is used above?

The number 1,000 actually has an infinite number of significant figures.  Whenever you use any metric system prefixes (centi-, milli-, kilo-, micro-, deci-, etc.) in connection with basic metric system units (gram, liter, meter, etc.), the resulting equalities are always exact and have an infinite number of significant figures in them.  Similarly, there are exactly 100.0000… centimeters in one meter.

The following number is a measurement or estimate. Indicate how many sigificant figures are in the number, and then write the number in scientific (exponential) notation in standard form (with the number to the left of the decimal point being between 1 and 10). Use only the correct number of significant figures.

902.00

The answer is 5 SF.  The zero between the 9 and the 2, as well as the two trailing zeroes at the end, are all significant.  When the number is written in scientific notation in standard form, the result is

9.0200 x 102   (also 5 SF)

How many significant figures are there in the number 5000. ?  Write this number in scientific (exponential) notation in standard form (with the number to the left of the decimal point being between 1 and 10).  Use only the correct number of significant figures.

This one is a little tricky.  Whever a decimal point is used in a number like this, all of the zeroes to the left of the decimal point are automatically significant.  (This is why we used the decimal point in the first place!)  For this reason, that number definitely has 4 SF and it must be written as

5.000 ? 104

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