scientific notationA value written as the product of two numbers: a coefficient and 10 raised to a power. Ex: 602,000,000,000,000,000,000,000

is 6.02 × 1023

The coefficient in this number is 6.02. (It is always a number equal to or greater than 1, and less than 10.) The power of 10, or exponent, is 23.

Entering scientific notation correctly in a calculator is important.

Here is the procedure for our classroom calculators:

6.02 × 1023 is entered as 6 . 0 2 EE 23

Some calculators may require you to press “2nd EE”, or EXP instead of EE

• Write 843,000 in as many different powers of 10 as you can:

• 8430000 x 10-1

• 843000 x 100

• 84300 x 101

• 8430 x 102

• 843 x 103

• 84.3 x 104

• 8.43 x 105

• 0.843 x 106

• 0.0843 x 107

Calculations with Scientific Notation:

Adding: convert all numbers to the same power of 10, then add coefficients.6.02 X 1023 + 3.01 x 1024 =0.602 x 10 24 + 3.01 x 10 24 = 3.61 x 10 24

Subtracting: convert all numbers to the same power of 10, then subtract coefficients.6.02 X 1024 - 3.01 x 1023 =6.02 x 10 24 - 0.301 x 10 24 = 5.72 x 10 24

Calculations with Scientific Notation:

Multiplying: multiply coefficients and add exponents.

6.02 X 1023 x 3.01 x 1024 = 18.1 x 10 47

Dividing: divide coefficients and subtract exponents.6.02 X 1024 ÷ 3.01 x 1023 = 2.00 x 101

3.1

Accuracy, Precision, and Error

–Accuracy and Precision–Accuracy is a measure of how close a

measurement comes to the actual or true value of whatever is measured.

–Precision is a measure of how close a series of measurements are to one another.

3.1

Accuracy, Precision, and Error

–To evaluate the accuracy of a measurement, the measured value must be compared to the correct value.

–To evaluate the precision of a measurement, you must compare the values of two or more repeated measurements.

3.1

Accuracy, Precision, and Error

3.1

Accuracy, Precision, and Error–Determining Error

–The accepted value is the correct value based on reliable references.

–The experimental value is the value measured in the lab.

–The difference between the experimental value and the accepted value is called the error.

3.1

Accuracy, Precision, and Error

•The percent error is the absolute value of the error divided by the accepted value, multiplied by 100%.

SIGNIFICANT FIGURES• What are they good for?

– They tell us how precise a measurement is. The more significant figures, the more precise the measurement.

• How do you know how many you have?– All known digits that you can read from the

ruler, graduated cylinder, etc, plus one estimated digit.

When is a digit significant? (red ones ARE)

1. Every nonzero digit is significant. 24.7 m, 0.743 m, and 714 m

2. Zeros between nonzero digits are significant. 7003 m, 40.79 m

3. Leftmost zeros appearing in front of nonzero digits are not significant. They are placeholders. 0.000099 meter

4. Zeros at the end and to the right of a decimal point are significant43.00 m, 1.010 m , 9.000 m

5. Zeros at the rightmost end, left of an understood decimal point are not significant if they serve as placeholders. 300 m, 7000 m, and 27,210 m

(If they ARE known measured values, however, then they would be significant. Writing the value 300m in scientific notation as 3.00 x 102 m makes it clear that these zeros are significant.)

6. Counting values & exactly defined quantities have an unlimited number of significant figures;. 23 students, 60 min = 1 hr

When calculating with measurements, how do you know the correct number of significant figures for your answer?

An answer cannot be more precise than the least precise measurement from which it was calculated. The answer must be rounded to make it consistent with the measurements from which it was calculated.

Density = mass/volume 11.2 g / 2.1 ml = 5.333333333333333 g/ml

= 5.3 g/ml

How do you round the answers?

Once you know the number of significant figures your answer should have, round to that many digits, counting from the left.

* If the digit immediately to the right of the last significant digit is less than 5, drop it and the last

significant digit stays the same.

* If the digit in question is 5 or greater, the last significant digit is increased by 1.

Adding / Subtracting measurements:

The answer to an addition or subtraction calculation should be rounded to the same number of decimal places (not digits) as the measurement with the least number of decimal places.

12.52 meters349.0 meters+ 8.24 meters

369.76 meters369.8 meters

Multiplication and DivisionRound the answer to the same number of significant figures as the measurement with the least number of significant figures.

7.55 m x 0.34 m = 2.567 m2

= 2.6 m2

(0.34 meter has the least number of significant figures: two.)

prefix symbol value expanded value English name

yotta Y 1024 1 000 000 000 000 000 000 000 000 U.S. septillion; U.K. quadrillion

zetta Z 1021 1 000 000 000 000 000 000 000 U.S. sextillion

exa E 1018 1 000 000 000 000 000 000 U.S. quintillion; U.K. trillion

peta P 1015 1 000 000 000 000 000 U.S. quadrillion

tera T 1012 1 000 000 000 000 U.S. trillion; U.K. billion

giga G 109 1 000 000 000 U.S. billion

mega M 106 1 000 000 million

kilo k 103 1 000 thousand

hecto h 102 100 hundred

deca da 101 10 ten

100 1 one

deci d 10-1 0.1 tenth

centi c 10-2 0.01 hundredth

milli m 10-3 0.001 thousandth

micro u 10-6 0.000 001 millionth

nano n 10-9 0.000 000 001 U.S. billionth

pico p 10-12 0.000 000 000 001 U.S. trillionth; U.K. billionth

femto f 10-15 0.000 000 000 000 001 U.S. quadrillionth

atto a 10-18 0.000 000 000 000 000 001 U.S. quintillionth; U.K. trillionth

zepto z 10-21 0.000 000 000 000 000 000 001 U.S. sextillionth

yocto y 10-24 0.000 000 000 000 000 000 000 001

U.S. septillionth; U.K. quadrillionth