12.7 2 cm

12.72 cm12.71 cm

12.73 cm

7.58 cm7.57 cm

7.59 cm

12.72 cmx 7.58 cm

96. 4176 cm2

7.6 cm

12.7 cm

96. 418 cm2

96. 42 cm2

96. 4 cm2

96. cm2

x 7.6 cm12.7 cm

96.52 cm2

What is wrong with these measurements and calculation?

Missing Estimate ± Estimate

3 S.F.

REVIEW: How many Sig Figs?1. 2.832. 36.773. 14.04. 0.00335. 0.026. 0.24107. 2.350 x 10

–

2

8. 1.000099. 310. 0.0056040

3 4 3 214461 (Infinite if counting) 5

Practice Rounding with Sig FigsMake (round) the following into a 3 Sig Fig number

a) 1.5587

b) 0.0037421

c) 1367

d) 128,522

e) 1.6683 106

1.56

0.00374

1370

129,000

1.67 106

d) Your Final number must be of the same value as the number you started with, 129,000 and not 129.

Is $129,000 the same as $129 ???

a) 4965.03

b) 780,582

c) 1999.5

4965

780,600 NOT 7,806

2000. or 2.000 x 103

Practice Rounding with Sig FigsMake (round) the following into a 4 Sig Fig number

Decimal is Present (from the left)

Remember : in scientific notation all digits are significant : 2.000 = 4 s.f.

RULE 1. In carrying out a multiplication or division, the answer cannot have more significant figures than either of the original numbers.

The product is limited to 3 sig figs

Calculating Sig Figs for MULTIPLICATION and DIVISION:

Multiplication & Division = LEAST number of sig figs


1) 47.37 cm x 0.24 cm = 11.3688 cm2

4 s.f. 2 s.f.11 cm2

2) 126.46 m x 2.750 m = 347.765 m2

5 s.f. 4 s.f.347.8 m2

3) 51.3 m x 200 m = 10,260 m2

3 s.f. 1 s.f.10,000 m2

4) 61.00 km x 120 km = 7,320 km2

4 s.f. 2 s.f.7,300 km2

1.1 x 101 cm2

3.478 x 102 m2

1 x 104 m2

7.3 x 103 km2

32.27 1.54 = 49.6958

3.68 .07925 = 46.4353312

1.750 .0342000 = 0.05985

3.2650106 4.858 = 1.586137 107

6.0221023 1.66110-24 = 1.000252

49.7

46.4

.05985

1.586 107

1.000


a)

b)

c)

d)

e)

Practice Problems: Round to the correct number of sig figs

•RULE 2. In carrying out an addition or subtraction, the answer cannot have more digits after the decimal point than either of the original numbers.

Calculating Sig Figs for ADDITION and SUBTRACTION:

Addition & Subtraction = LEAST number of decimal places

25.5 32.72 320

+34.270 ‑ 0.0049 + 12.5

59.770 32.7151 332.5

59.8 32.72 330


Look for the last important digit (with highest value)

Round to the correct number of sig figs.

.56 + .153 = .713

82000 + 5.32 = 82005.32

10.0 - 9.8742 = .12580

10 – 9.8742 = .12580

.71 (hundredths place)

82000 (Thousands place)

.1

0

Round to the correct number of sig figs. HINT: Look for the last important digit (with highest value)

What is the difference between these two values?


a)

b)

c)

d)

c) 10.0 - 9.8742 0.12580

d) 10 - 9.8742 0.12580

Mixed Order of Operation

8.52 + 4.1586 18.73 + 153.2 =

(8.52 + 4.1586) (18.73 + 153.2) =

239.6

2180.

= 8.52 + 77.89 + 153.2 = 239.61 =

= 12.68 171.9 = 2179.692 =



4 s.f.

4 s.f.

4 s.f. 4 s.f. 4 s.f.

Tenths place

What is Density? Density = mass/volumeDensity is the amount of matter (mass)

within a given space (volume)

What is Kelvin? Kelvin = °Celsius + 273

Kelvin is SI unit for temperature. The Kelvin temperature scale takes “absolute zero” into account

Mass = 4.62 gVolume = 2.0 cm3

Density = mass/volumeDensity = 4.62 g / 2.0 cm3

Density = 2.3 g/cm3

Temp = 22.4 °C Kelvin = °Celsius + 273Kelvin = 22.4 °C + 273Kelvin = 295 °C

_1

_.4

.15

12.72 cm12.71 cm

12.73 cm

7.58 cm7.57 cm

7.59 cm

12.72 cmx 7.58 cm

96. 4176 cm2

7.6 cm

12.7 cm

96. 418 cm2

96. 41 cm2

96. 4 cm2

96. cm2

x 7.6 cm12.7 cm

96.52 cm2

What is wrong with these measurements and calculation?

Missing Estimate ± Estimate

3 S.F.

AREA = 96.2, 96.3, 96.4, 96.5, 96.6

12.71 cm 12.72 cm 12.73 cm

7.57 cm 7.57 cm 7.57 cm

96.2147 cm2 96.2904 cm2 96.3661 cm2

12.71 cm 12.72 cm 12.73 cm

7.58 cm 7.58 cm 7.58 cm

96.3418 cm2 96.4176 cm2 96.4934 cm2

12.71 cm 12.72 cm 12.73 cm

7.59 cm 7.59 cm 7.59 cm

96.4689 cm2 96.5448 cm2 96.6207 cm2

96.2 cm2 96.3 cm2 96.4 cm2

96.3 cm2 96.4 cm2 96.5 cm2

96.5 cm2 96.5 cm2 96.6 cm2

4 s.f.3 s.f.


12.7 2 cm

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