Rounding and Calculations with Significant Digits

Do Now

Oral Drill

9.00 metersHow many significant figures?

900 metersHow many significant figures?

900 golf clubsHow many significant figures?

0.0009 metersHow many significant figures?

0.0090 metersHow many significant figures?

900.00 metersHow many significant figures?

90 milesHow many significant figures?

24 hours/1 dayHow many significant figures?

4.5 m4.6 m4.7 m4.5 m

(True value = 1.5 m)

Describe this data with respect to accuracy and precision

4.5 L4.6 L4.7 L4.5 L

(True value = 4.5L)

Describe this data with respect to accuracy and precision

If leftmost digit to be dropped is:◦ Less than 5 (1, 2, 3, or 4):

◦ More than 5 (6, 7, 8 or 9) :

◦ Equal to 5 AND there are no numbers or all zeros after it:

If ODD:

If EVEN:

AND there are non-zeros after it: :

Reviewing Rounding Rules

Practice: 6.8001 (round to three s.f)

Practice: 6.8060 (round to three s.f)

Practice: 6.8050 (round to three s.f)

Practice: 6.8051 (round to three s.f)

90,050

8,994

73,555

73,500

73,515

Practice: Round to 3 s.d.

Number Stated Number of Significant Digits Answer

1)350,000 2 350,0002) 23.11 3 23.13) 23.10 3 23.14) 23.15 3 23.25) 22.50 2 226) 22.51 2 237) 0.007955 2 0.00808) 0.006855 2 0.0069

Your answer should use the same number of s.f. as the least number of significant digits after the decimal in your measurements

Rule for adding and subtracting with Significant Figures

4.5m + 7m = 11.5mExample:

15.000m – 1.00m= 14mExample

1)    357.89 + 0.002 = 

357.892  357.89

2)   17.95 + 32.42 + 50 

  100.37  100

3)   5.5 + 3.7 + 2.97 

12.17  12.2

4) 84.675 - 3 =

81.675 82

5) 75 - 2.55 =

72.45 72

6) 10 - 9.9 =

0.1 0

Your answer should use the same number of s.f. as the least number of significant digits in your measurements

Rule for multiplying and dividing with Significant Figures

9.0m x 0.5400m = 4.86m2

Example:

1)     12.8 x 1.0 =

12.8  132)    100 x 8.57 =

857  9003)    0.00005 x 520 =

0.026  0.034) 6000 / 30 =

2005) 72 / 9.000 =

8 8.0

6) 600.0 / 20.0 =

3030.0

Complete Significant Digits HW II (I will pass it back to you)

Complete WiRe

Independent Practice