Scientific Notation

Objectives and Vocabulary Be able to write a number in scientific notation when given the decimal form of the number. Be able to write a number in decimal form when given the number in scientific notation. Perform mathematical calculations involving scientific notation. Solve problems using scientific notation. Decimal form – A number written with place values corresponding to powers of ten such as 152, 9.5, 0.08. Scientific notation – a number expressed in the form c x 10n where n is an integer and 1 c  10.

Writing in Decimal Form Write the following number in decimal form. This expression can be rewritten as Furthermore

Positive Powers of 10 Positive powers of 10 – When the exponent (n) is positive, move the decimal point to the right the same number of places as the exponent. Add zeros when digits are not present. Write the following numbers in decimal form: Solutions

Dividing by 10 Write the following number in decimal form. This expression can be rewritten as: Furthermore,

Negative Powers of 10 Negative powers of 10 – When the exponent (n) is negative, move the decimal point to the left the same number of places as the absolute value exponent. Add zeros when digits are not present. Write the following numbers in decimal form: Solutions

Writing in Scientific Notation Move the decimal point to the right or left until you have a number that is greater than or equal to 1, but less than 10. Count how many places you moved the decimal point. This number will become the absolute value of the exponent. If you moved the decimal point to the left, the exponent will be positive. If you moved the decimal point to the right, make the exponent negative.

Examples Write the following numbers in scientific notation. Solutions The decimal is to the right of the 3. Move it left 3 places. This number is already greater than or equal to one and less than 10. Therefore, the decimal doesn’t have to be moved and the exponent will be 0 Move the decimal right 4 places.

Using a calculator Use a calculator to perform the indicated operation. Write your result in correct scientific notation. Enter 9.1 in your calculator. Press the key marked EXP or EE on your calculator. If this is written above another key, then you will have to press SHIFT or 2nd before pressing the EXP or EE key. Enter the value of the exponent. Press the times key. Enter 4.2 Repeat steps 2 and 3. Press Enter or =. You should get 3.822x10-1

You Try It Decide whether the number is in scientific notation. If not, tell why the number is not in correct scientific notation Write the following numbers using scientific notation: Write the following numbers in decimal form: Atoms are composed of protons, neutrons and electrons. If the mass of protons and neutrons are each 1.67 x 10-24 grams and an electron has a mass of 9.11 x 10-28 gram. Find the mass of an atom of silver which has 47 protons, 47 electrons, and 60 neutrons.

Problem 1 This number is not written correctly in scientific notation. The value of c is supposed to be greater than or equal to 1and less than 10. Here, the value of c is less than 1. This number is not correctly written using scientific notation because the power of 10 is supposed to be an integer. Thus, it can’t be a fraction. This number is correctly written using scientific notation

Problem 2 The decimal had to be moved left three places so the power of ten is positive 3. The decimal had to be moved to the right two places, so the power of ten is negative two. The decimal does not need to be moved. Therefore, the power of ten is zero.

Problem 3 The decimal point had to be moved two places to the left because the power of ten was negative two. The decimal point had to be moved six places to the right because the power of ten was positive six

Problem 4 Find the mass of the protons. Find the mass of the neutrons. Find the mass of the electrons. Add the values together from steps 1-3 to get the final answer.