8Significant

Figures

Significant figuresThe number of meaningful digits in a measurement including the uncertain digit.

“sig figs”

0.5200.00255000.02300120035500.2.0 x 105

3 do not count zeros at the beginning21 do not count end zeros if no decimal 4 count all other zeros632 do not expand

Significant figuresThe number of meaningful digits in a measurement including the uncertain digit.

“sig figs”2.50020.0065050010.02003000.02010200200.2.0 x 102

2. x 102

534641321

Significant figuresExact numbers that are counted or defined and not measured have zero uncertainty and infinite “sig figs”.

“sig figs”

2.50 cm3 girls62.33 kJ1 cm = 10 mm 12.3 oC200 lb1 cm3 = 1 mL $75.00

3infinite4infinite31infiniteinfinite

Adding and Subtraction with Significant Figures

When adding or subtracting numbers round the answer to the largest decimal place found in the uncertain digits of any of the numbers used.

1.21.036

+ 22.1

Adding and Subtraction with Significant Figures

When adding or subtracting numbers round the answer to the largest decimal place found in the uncertain digits of any of the numbers used

1.21.036

+ 22.1??

Adding and Subtraction with Significant Figures

When adding or subtracting numbers round the answer to the largest decimal place found in the uncertain digits of any of the numbers used.

1.21.036

+ 22.1??= 43.1 the largest decimal place is the first

Adding and Subtraction with Significant Figures

When adding or subtracting numbers round the answer to the largest decimal place found in the uncertain digits of any of the numbers used

2.25.654

- 22.1??=

Adding and Subtraction with Significant Figures

When adding or subtracting numbers round the answer to the largest decimal place found in the uncertain digits of any of the numbers used

2.25.654

- 22.1??= 3.6 the largest decimal place is the first

Adding and Subtraction with Significant Figures

When adding or subtracting numbers round the answer to the largest decimal place found in the uncertain digits of any of the numbers used

3.301.2256

- 0.36

Adding and Subtraction with Significant Figures

When adding or subtracting numbers round the answer to the largest decimal place found in the uncertain digits of any of the numbers used

3.301.2256

- 0.36300.87 the largest decimal is the second

Adding and Subtraction with Significant Figures

When adding or subtracting numbers round the answer to the largest decimal place found in the uncertain digits of any of the numbers used

4. 8.053 x 107

+ 2.3 x 104

Adding and Subtraction with Significant Figures

When adding or subtracting numbers round the answer to the largest decimal place found in the uncertain digits of any of the numbers used.

4. ↓ largest decimal place8.053 x 107 80530000.

+ 2.3 x 104 23000.

Adding and Subtraction with Significant Figures

When adding or subtracting numbers round the answer to the largest decimal place found in the uncertain digits of any of the numbers used.

4. ↓ largest decimal place8.053 x 107 80530000.

+ 2.3 x 104 23000.8.055 x 107 80550000.

Adding and Subtraction with Significant Figures

When adding or subtracting numbers round the answer to the largest decimal place found in the uncertain digits of any of the numbers used.

5.2.463 x 10-5

+ 5.006 x 10-2

Adding and Subtraction with Significant Figures

When adding or subtracting numbers round the answer to the largest decimal place found in the uncertain digits of any of the numbers used.

5.2.463 x 10-5 0.00002463

+ 5.006 x 10-2 0.05006 ↑ largest decimal place

Adding and Subtraction with Significant Figures

When adding or subtracting numbers round the answer to the largest decimal place found in the uncertain digits of any of the numbers used.

5.2.463 x 10-5 0.00002463

+ 5.006 x 10-2 0.050065.008 x 10-2 0.05008 largest decimal place

Adding and Subtraction with Significant Figures

When adding or subtracting numbers round the answer to the largest decimal place found in the uncertain digits of any of the numbers used.

6. 5.331 x 10-4

- 2.126 x 10-5

Adding and Subtraction with Significant Figures

When adding or subtracting numbers round the answer to the largest decimal place found in the uncertain digits of any of the numbers used.

6. ↓ largest decimal place5.331 x 10-4 0.0005331

- 2.126 x 10-5 0.00002126

Adding and Subtraction with Significant Figures

When adding or subtracting numbers round the answer to the largest decimal place found in the uncertain digits of any of the numbers used.

6. ↓ largest decimal place5.331 x 10-4 0.0005331

- 2.126 x 10-5 0.000021265.118 x 10-4 0.0005118

7. Add the two numbers- another way to do it

2.657 x 10-12

2.684 x 10-12

2.657 x 10-14

Change the lower exponent to the higher and write it directly underneath.You are making the exponent larger so make the number smaller.

0.02657 x 10-12

0.027 x 10-12

8. Subtract the two numbers- another way to do it

8.9967 x 1018

8.9914 x 1018

- 5.222 x 1015

Change the lower exponent to the higher and write it directly underneath.You are making the exponent larger so make the number smaller.

0.005292 x 1018

- 0.0053 x 1018