Significant Figures SPH 3 U Precision How well

Significant Figures SPH 3 U

• 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: 453 kg 5057 L Number of Why? sig figs 3 All non-zero digits are always significant. 4 Zeros between 2 sig. dig. are significant. 5. 00 3 0. 007 1 Additional zeros to the right of decimal and a sig. dig. are significant. Placeholders are not sig.

Problems: Indicate the number of significant figures. . . 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 1. 235 2. 90 0. 0987 0. 450 5. 00 230 230. 0 9870345 1. 00000 ______ ______ ______

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 1. 235 2. 90 0. 0987 0. 450 5. 00 230 230. 0 9870345 1. 00000 ___4___ ___3___ ___2___ ___4___ ___7___ ___6___

Round these numbers to 3 significant figures 1) 2) 3) 4) 5) 6) 5. 8746 = ______ 8008= _______ 24. 567= _____ 100. 04= _____ 5634. 3999= ______ 1. 675 x 103= ______

1) 2) 3) 4) 5) 6) 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. 2. 3. 4. 5. 6. 7. 8. 9. 10. 42. 3 x 2. 61 32. 99 x 0. 23 46. 1 ÷ 1. 21 23. 3 ÷ 4. 1 0. 61 x 42. 1 47. 2 x 0. 02 47. 2 ÷ 0. 023 100 x 23 124 ÷ 0. 12 120 x 12 ÷ 12. 5 ______ ______ ______

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 42. 3 x 2. 61 32. 99 x 0. 23 46. 1 ÷ 1. 21 23. 3 ÷ 4. 1 0. 61 x 42. 1 47. 2 x 0. 02 47. 2 ÷ 0. 023 100 x 23 124 ÷ 0. 12 120 x 12 ÷ 12. 5 __110. ____ __7. 6____ __38. 1____ __5. 7____ __26____ __0. 9____ __2100____ __2000____ __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. 3. 4. 5. 6. 7. 8. 9. 10. 2. 634 + 0. 02 2. 634 - 0. 02 230 + 50. 034 + 1. 00 4. 56 - 0. 34 3. 09 - 2. 0 349 + 34. 09 234 - 0. 98 238 + 0. 98 123. 98 + 0. 54 - 2. 3 ______ ______ ______

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 2. 634 + 0. 02 2. 634 - 0. 02 230 + 50. 034 + 1. 00 4. 56 - 0. 34 3. 09 - 2. 0 349 + 34. 09 234 - 0. 98 238 + 0. 98 123. 98 + 0. 54 - 2. 3 __2. 65____ __2. 61____ __280____ __1. 03____ __4. 22____ __1. 1____ __383____ __239____ __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 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 a) b) c) d) e) 0. 0826 2 630 000 945 000 1 760 000 0. 00507 _______________ ________ a) b) c) d) e) 1. 23 x 10 -4 7. 51 x 105 3. 09 x 10 -3 2. 91 x 102 9. 6 x 104 _______________ ________

a) b) c) d) e) 0. 0826 2 630 000 945 000 1 760 000 0. 00507 __8. 26 x 10 -2___ __2. 63 x 106___ __9. 45 x 105___ __1. 76 x 106___ __5. 07 x 10 -3___ a) b) c) d) e) 1. 23 x 10 -4 7. 51 x 105 3. 09 x 10 -3 2. 91 x 102 9. 6 x 104 __0. 000123_____ __751000______ __0. 00309_____ __291_____ __96000_______