Significant Figures

•Precision: How well a group of measurements made of the same object, under the same conditions, actually agree with one another.

•These points are precise with one another but not “accurate”.

•Accuracy: represents the closeness of a measurement to the true value.

•Ex: the bulls-eye would be the true value, so these points are accurate.

Why Significant Figures?•Precision is determined by the instrument

we use to take measurements. So, our calculations must be only as precise as the measurements.

•NOTE: The last digit of any measurement is always a “guess” therefore it is uncertain.

Measuring: precision

Other instruments…

Rounding

•You will need to round off sig. figs when you multiply, divide, add or subtract.

•When rounding off to a certain place value, you need to look one place farther.

•If the next digit is a 5 or higher, you round the digit before it UP.

•If the next digit is a 4 or lower, you DON”T round up.

Using sig figs: The Rules!

1. Digits from 1-9 are always significant.

2. Zeros between two other significant digits are always significant

3. Zeros at the beginning of a number are never significant.

4. Zeros at the end of a number are only significant IF there is a decimal place.

Example:Example: Number Number of sig of sig figsfigs

Why?Why?

453kg453kg 33 All non-zero digits are All non-zero digits are always significant. always significant.

5057L5057L 44 Zeros between 2 sig. Zeros between 2 sig. dig. are significant. dig. are significant.

5.005.00 33 Additional zeros to the Additional zeros to the right of decimal and a right of decimal and a sig. dig. are significant. sig. dig. are significant.

0.0070.007 11 Placeholders are not sig. Placeholders are not sig.

Problems: Indicate the number of significant figures...

1. 1.235 ______2. 2.90 ______3. 0.0987 ______4. 0.450 ______5. 5.00 ______6. 2300 ______7. 230 ______8. 230.0 ______9. 9870345 ______10. 1.00000 ______

1. 1.235 ___4___2. 2.90 ___3___3. 0.0987 ___3___4. 0.450 ___3___5. 5.00 ___3___6. 2300 ___2___7. 230 ___2___8. 230.0 ___4___9. 9870345 ___7___10. 1.00000 ___6___

Round these numbers to 3 significant figures

1) 5.8746 = ___________2) 8008= _____________3) 24.567= _________4) 100.04= __________5) 5634.3999= ____________6) 1.675 x 103= ____________

1) 5.8746 = __5.87_________2) 8008= ___8010__________3) 24.567= __24.6_______4) 100.04= ___100._______5) 5634.3999= __5630__________6) 1.675 x 103= ___1.68 x 103 _____

Multiplying and Dividing

•RULE: your answer may only show as many significant figures as the multiplied or divided measurement showing the least number of significant digits.

•Example: 22.37 cm x 3.10 cm = 69.3 (only 3 sig figs allowed)

Multiplying and Dividing Practice1. 42.3 x 2.61 ______2. 32.99 x 0.23 ______3. 46.1 ÷ 1.21 ______4. 23.3 ÷ 4.1 ______5. 0.61 x 42.1 ______6. 47.2 x 0.02 ______7. 47.2 ÷ 0.023 ______8. 100 x 23 ______9. 124 ÷ 0.12 ______10. 120 x 12 ÷ 12.5 ______

1. 42.3 x 2.61 __110.____2. 32.99 x 0.23 __7.6____3. 46.1 ÷ 1.21 __38.1____4. 23.3 ÷ 4.1 __5.7____5. 0.61 x 42.1 __26____6. 47.2 x 0.02 __0.9____7. 47.2 ÷ 0.023 __2100____8. 100 x 23 __2000____9. 124 ÷ 0.12 __1000____10. 120 x 12 ÷ 12.5 __110____

Adding and Subtracting:•RULE: your answer can only show as

many place values as the measurement having the fewest number of decimal places.

•Example: 3.76 g + 14.83 g + 2.1 g = 20.7 g3.76 is precise to the hundredths place,

14.83 is precise to the hundredths place, 2.1 is only precise to the tenths place, so we round off the final answer to the tenths place.

Adding and Subtracting Practice1. 2.634 + 0.02 ______2. 2.634 - 0.02 ______3. 230 + 50.0 ______4. 0.034 + 1.00 ______5. 4.56 - 0.34 ______6. 3.09 - 2.0 ______7. 349 + 34.09 ______8. 234 - 0.98 ______9. 238 + 0.98 ______10. 123.98 + 0.54 - 2.3 ______

1. 2.634 + 0.02 __2.65____2. 2.634 - 0.02 __2.61____3. 230 + 50.0

__280____4. 0.034 + 1.00 __1.03____5. 4.56 - 0.34 __4.22____6. 3.09 - 2.0 __1.1____7. 349 + 34.09 __383____8. 234 - 0.98 __233____9. 238 + 0.98

__239____10. 123.98 + 0.54 - 2.3 __122.2____

Scientific Notation

Scientific Notation•Scientists have developed a shorter

method to express very large numbers. •Scientific Notation is based on powers of

the base number 10.

•123,000,000,000 in s.n. is 1.23 x 1011

•The first number 1.23 is called the coefficient. It must be between 1 - 9.99

•The second number is called the base . The base number 10 is always written in exponent form. In the number 1.23 x 1011 the number 11 is referred to as the exponent or power of ten.

To write a small number in s.n.ex: 0.00064•First move the decimal after the first real

number and drop the zeroes. Ex: 6.4•Next, count the number of places moved

from the original decimal spot to the new decimal spot. Ex: 4

•Numbers less than 1 will have a negative exponent. Ex: -4

•Finally, put it together. Ex: 6.4 x 10-4

Scientific Notation Practicea) 0.0826 _______________b) 2 630 000 _______________c) 945 000 _______________d) 1 760 000 _______________e) 0.00507 _______________

a) 1.23 x 10-4 _______________b) 7.51 x 105 _______________c) 3.09 x 10-3 _______________d) 2.91 x 102 _______________e) 9.6 x 104 _______________

a) 0.0826 __8.26 x 10-2___b) 2 630 000 __2.63 x 106___c) 945 000 __9.45 x 105___d) 1 760 000 __1.76 x 106___e) 0.00507 __5.07 x 10-3___

a) 1.23 x 10-4 __0.000123_____b) 7.51 x 105 __751000______c) 3.09 x 10-3 __0.00309_____d) 2.91 x 102 __291_________e) 9.6 x 104 __96000_______