Significant Figures

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DEFINITION:

It is to make sure that the answers you get isn't more precise than the numbers you started with.

The significant figures of a number are digits that cary meaningful contributions to its measurement resolution. This includes all digitexcept: all leading zeros. It is to round some numbers/ digits for them to become smaller or less precise.

EXAMPLES:

1. 62,881/ 97= 648.257732 We use the lowest number and then all the rest numbers are zero.

5 2 - 650 / = division

2. 5,621 x 893 - 5,019,553

4 3 - 5,020,000

3. 218 / 26 - 8.3846154

3 2 - 8.4

4. 59,411 x 2 - 118,22

5 1 - 100,000

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Zeros sandwiched between non-zero digits are always significant: (Decimal points do not matter)

Examples:

3,091 ( 4 significant digits)

82,024 (5 significant digits)

109,003 (6 significant digits)

500603 ( 6 significant digits)

Zeros that come before all non-zero digits are never significant

Examples.

0.000491(3 significant digits)

0.0132 (3 significant digits)

0.0000000000000062 (2 significant digits)

Zeros that come after non-zero digits: are significant just because the decimal point.

Eamples:

83,000 (2 significant digits)

83,000. (5 significant digits)

83.000 (5 significant digits)

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RULES FOR SIGNIFICANT FIGURES

All non-zero numbers ARE significant.

Zeros between two non-zero digits ARE significant.

Trailing zeros to the right of the decimal ARE significant.

Trailing zeros in a whole number with the decimal shown ARE significant.

Trailing zeros in a whole number with no decimal shown are NOT significant.

Exact numbers have an INFINITE number of significant figures.

For a number in scientific notation: N x 10x, all digits comprising N ARE significant by the first 6 rules; "10" and "x" are NOT significant.

SOURCE:

https://ccnmtl.columbia.edu/projects/mmt/frontiers/web/chapter_5/6665.html

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EXCERCISE:

530.0010000

Significant figures: 10