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! Digits from 1-9 are always significant. Zeros between two other significant digits are always significant Zeros at the beginning of a number are never significant. Zeros at the end of a number are only significant IF there is a decimal place.

Example: Number of sig figs Why? 453kg 3 All non-zero digits are always significant. 5057L 4 Zeros between 2 sig. dig. are significant. 5.00 Additional zeros to the right of decimal and a sig. dig. are significant. 0.007 1 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 5.8746 = ___________ 8008= _____________ 24.567= _________ 100.04= __________ 5634.3999= ____________ 1.675 x 103= ____________

5.8746 = __5.87_________ 8008= ___8010__________ 24.567= __24.6_______ 100.04= ___100._______ 5634.3999= __5630__________ 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 Practice 1. 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 g 3.76 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 Practice 1. 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 Practice 0.0826 _______________ 2 630 000 _______________ 945 000 _______________ 1 760 000 _______________ 0.00507 _______________ 1.23 x 10-4 _______________ 7.51 x 105 _______________ 3.09 x 10-3 _______________ 2.91 x 102 _______________ 9.6 x 104 _______________

0.0826 __8.26 x 10-2___ 2 630 000 __2.63 x 106___ 945 000 __9.45 x 105___ 1 760 000 __1.76 x 106___ 0.00507 __5.07 x 10-3___ 1.23 x 10-4 __0.000123_____ 7.51 x 105 __751000______ 3.09 x 10-3 __0.00309_____ 2.91 x 102 __291_________ 9.6 x 104 __96000_______