SIGNIFICANTFIGURES

AMOLE2015

WHAT & WHY?

Refer to them as “Sig Figs” for short Used to communicate the degree of

precision measured Example - Scientists records: 50 mL

Does that mean… 50 mL exact?Could he only measure to the ones place?

Did he round up from 49.8?Is it really 50.12 mL?

RULE #1: NON ZEROS Every nonzero digit is

significant. If it’s not a zero, it will count Examples:

24 = 2 sig figs 3.56 = 3 sig figs 7 = 1 sig figs

COUNT!

RULE #2: CAPTURED ZEROS

Also called “trapped” or “sandwiched” zeros

Zeros between non-zeros are significant

Examples: 7003 = 4 sig figs 40.9 = 3 sig figs 60.09 = ?

COUNT!

RULE #3: LEADING ZEROS Zeros appearing in front of non-

zero digits are not significantAct as placeholdersCan’t be dropped, show magnitude

Examples: 0.00024 = 2 sig figs 0.453 = 3 sig figs 0.003 = ?

DON’T COUNT

RULE #4: TRAILING ZEROS Zeros at the end of a number with a decimal point are significant.

At the end and to the right of a decimal point

Examples: 43.00 = 4 sig figs 1.010 = 4 sig figs 1.50 = ?COUNT!

RULE #5: TRAILING ZEROS Zeros at the end of a number without a decimal point are not significant.

At the end and to the right of a decimal point

Examples: 300 = 1 sig figs 27,300 = 3 sig figs 120 = ?DON’T COUNT

All non-zero digits DO count. Leading zeros DON’T count.

(zeros in front of numbers)

Captive Zeros DO count.(zeros between non-zero numbers)

Trailing Zeros DO count IF the number contains a DECIMAL.(zeros at the end of numbers)

TRY THESE!

4.012

87,900

91.0005

500,001

0.005

0.6010

7,040, 100

2.100

= 4 sig. figs.= 3 sig. figs.= 6 sig. figs.= 6 sig. figs.= 1 sig. figs.= 4 sig. figs.= 5 sig. figs.= 4 sig. figs.

ADDING & SUBTRACTING The answer cannot be more precise than

the values in the calculation The answer is rounded off so it contains

the same decimal places as the number in the problem with the fewest .

Example: 12.11 + 18.0 = 30.1112.11 = 2 decimal places18.0 = 1 decimal place

12.11 + 18.0 = 30.1

YOU TRY: 2.140 + 0.023 = ?

2.140 = 3 decimal places0.023 = 3 decimal places

Answer unrounded: 2.163 Answer with appropriate sig figs:

2.163

MULTIPLYING & DIVIDING The answer cannot be more precise than

the values in the calculation Answer should contain the same number

of sig figs as the number with the least sig figs in the problem: Example: 4.56 x 1.4 = 6.38

4.56 = 31.4 = 2

4.56 x 1.4 = 6.4

YOU TRY:1.20 x 0.51 = ?

1.20 = 30.51 = 2

Answer unrounded: 0.612

Answer with appropriate sig figs: 0.61

TRY THESE!

4.01 + 0.03

87.957 – 85.1

4.13 x 1.2

500 / 5.5

= 4.04 = 4.04

= 2.857 = 2.9

= 4.956 = 5.0

= 90.90909 = 90

PUTTING IT ALL TOGETHER(1.2 x 103) x (3 x 104) = ?

(3.6 x 107) / (4.0 x 105) = ?

(1.2 x 10-3) x (3 x 104) = ?

(3.6 x 107) / (4.0 x 10-5) = ?