Calculating with Scientific Notation Learn it…

Did You Know? mass of a hydrogen atom = 0.000000000000000000000000001673 kg speed of light = 299,792,458 m / s distance light travels in one year(1 light year) 9, 461, 000, 000, 000 km.

To do this conveniently, they Scientists need to express small measurements, such as the mass of the proton at the center of a hydrogen atom 0.000 000 000 000 000 000 000 000 001 673 kg, and large measurements, such as the temperature at the center of the Sun (15 000 000 K). To do this conveniently, they express the numerical values of small and large measurements in scientific notation.

Scientific notation allows us to reduce the number of zeros that we see while still keeping track of them for us. For example the age of the Earth (see above) can be written as 4.6 X 109 years. This means that this number has 9 places after the decimal place - filled with zeros unless a number comes after the decimal when writing scientific notation. So 4.6 X 109 years represents 4600000000 years.

Very small numbers use the same type of notation only the exponent on the 10 is usually a negative number. For example, 0.00000000000000000000000000166 kg (the weight of one atomic mass unit (a.m.u.)) would be written 1.66 x 10-27 using scientific notation. A negative number after the 10 means that we count places before the decimal point in the scientific notation. You can count how many numbers are between the decimal point in the first number and the second number and it should equal 27.

Let’s Get To Work…

5.67 x 105 coefficient base exponent This is the scientific notation for the standard number, 567,000.  Now look at the number again, with the three parts labeled. 5.67 x 105  coefficient      base        exponent

In order for a number to be in correct scientific notation, the following conditions must be true: 1. The coefficient must be greater than 0 and less than 10. (When placing the decimal in the coefficient, be sure to remember this)

2. The base must be 10. ALWAYS.

3. The exponent shows the number of decimal places that the decimal needs to be moved. A NEGATIVE exponent means that the decimal is moved to the LEFT when changing to standard notation. (thus making the number is standard form very SMALL) A POSITIVE exponent means that the decimal is moved to the RIGHT when changing to standard notation. (thus making the number is standard form very LARGE)

Changing numbers from scientific notation to standard notation. Example #1 Change 6.03 x 107 to standard notation remember,  107 = 10 x 10 x 10 x 10 x 10 x 10 x 10 = 10,000,000 so,    6.03 x 107 = 6.03 x 10,000,000 = 60,300,000 (or move the decimal to the RIGHT 7 times) answer = _____________________

Example #2 Change 5.3 x 10-4 to standard notation. The exponent tells us the # in standard form will be quite small… 5.3 x 10-4 = __________________

Changing numbers from standard notation to scientific notation Example #3   Change 56,760,000,000 to scientific notation Remember, the decimal is at the end of the final zero. be sure to follow the coefficient rule! Answer: __________________________

Example #4 Change 0.000000902 to scientific notation be sure to follow the coefficient rule! Answer: ___________________________

Next Step: When you have finished the for examples, show Ms. Wilson to ensure accuracy and then move on to the Calculating with Scientific Notation: Use It! station.

6.5240 X 105 2.9945 X 10-7 8.0184 X 107 2.1476 X 10-9

27,743 0.00000008882 523,680,000 0.0000000018247