Significant Digits

Uncertainty of Measurement

Three Rules

• Non-zero digits are significant • Zeros

between

two significant digits are significant • Zeros at the right end of a number, after a decimal point, are significant

Non-zero digits are significant

• Number 455.6

7.98

0.6224

5.2

• Significant Digits 4 3 4 2

Zero to left of decimal point •

0

.78895

5 significant digits • The zero to the left of the decimal point is there to communicate that the decimal point

is a decimal point

convention

• Numbers like 308.5

0.000811

5000

Problems!

Zeros between non-zero digits are significant • Number 28.09

1008.91

3.005

2.03

• Significant Digits 4 6 4 3

Space Holding zeros on numbers less than one • •

0.00

678

0.0

30086 3 significant digits 5 significant digits

Trailing Zeros

• 200 is considered to have only

one

significant digit • 38,000 has

two

significant digits

Problem area

• 5000 might really have four significant digits - an exact count or measurement • write number as 5000

.

• Scientific notation used to indicate significant digits

• 78002.1

• 0.00006003

• 34.61

• 8.81

• 42,300 Review • 6 • 4 • 4 • 3 • 3

Multiplication & Division

• An answer cannot have more significant digits than the measurement with the

least

number of significant digits used in the operation.

(3.006) X (0.0067) = 0.0201402

= 0.020

only 2 sig. Digits

Addition & Subtraction • The answer is

rounded

to the

least

number of places in the

decimal

portion of any number in the operation 134.008

89.70

57.9 281.608 = 281.6