# Scientific notation A 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.

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scientific notation A 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 × is entered as EE 23 Some calculators may require you to press “2nd EE”, or EXP instead of EE

Calculations with Scientific Notation:
Adding: convert all numbers to the same power of 10, then add coefficients. 6.02 X x 1024 = 0.602 x x = 3.61 x 10 24 Subtracting: convert all numbers to the same power of 10, then subtract coefficients. 6.02 X x 1023 = 6.02 x x = 5.72 x 10 24

Calculations with Scientific Notation:
Multiplying: multiply coefficients and add exponents. 6.02 X x x = x 10 47 Dividing: divide coefficients and subtract exponents. 6.02 X ÷ x 1023 = x 101

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 m, m, and 714 m 2. Zeros between nonzero digits are significant m, m 3. Leftmost zeros appearing in front of nonzero digits are not significant. They are placeholders meter 4. Zeros at the end and to the right of a decimal point are significant m, m , m 5. Zeros at the rightmost end, left of an understood decimal point are not significant if they serve as placeholders 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 g / 2.1 ml = 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.

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 meters meters meters 369.8 meters meters

Multiplication and Division
Round the answer to the same number of significant figures as the measurement with the least number of significant figures. 7.55 m x m = m2 = m2 (0.34 meter has the least number of significant figures: two.)

Factor Factor prefix symbol value expanded value English name yotta Y
Table 5.  SI prefixes Table 5.  SI prefixes Factor Factor prefix symbol value expanded value English name yotta Y 1024 U.S. septillion; U.K. quadrillion zetta Z 1021 U.S. sextillion exa E 1018 U.S. quintillion; U.K. trillion peta P 1015 U.S. quadrillion tera T 1012 U.S. trillion; U.K. billion giga G 109 U.S. billion mega M 106 million kilo k 103 1 000 thousand hecto h 102 100 hundred deca da 101 10 ten 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 millionth nano n 10-9 U.S. billionth pico p 10-12 U.S. trillionth; U.K. billionth femto f 10-15 U.S. quadrillionth atto a 10-18 U.S. quintillionth; U.K. trillionth zepto z 10-21 U.S. sextillionth yocto y 10-24 U.S. septillionth; U.K. quadrillionth

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