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 Dependent Variable

 Number of inequalities to solve: 23456789
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Scientific Notation

After studying this lesson, you will be able to:

• Convert standard notation to scientific notation.
• Convert scientific notation to standard notation

Standard Notation is the "normal" way of writing a number.

Example: 45,800

Example: 0.034

Scientific Notation is the way of writing a number as the product of a power of 10 and a number between 1 and 10. Scientific notation is often used to express very large numbers (using positive exponents) or very small numbers (using negative exponents.)

Example: 4.58 Ã— 10 4

Example: 3.4 Ã— 10 -2

Example 1

Write 1.25 Ã— 10 3 in standard notation.

To convert we move the decimal the same number of places as the exponent. Since multiplying by 10 3 is the same as multiplying by 1000, we can just move the decimal three places to the right. (Hint: if we have positive exponents, we move the decimal to the right because we are multiplying.)

1.25 Ã— 10 3 will be 1250 (we moved the decimal 3 places to the right)

Example 2

Write 7 Ã— 10 5 in standard notation.

To convert we move the decimal the same number of places as the exponent. Since multiplying by 10 5 is the same as multiplying by 100,000, we can just move the decimal five places to the right.

7 Ã— 10 5 will be 700,000 (we moved the decimal 5 places to the right)

Example 3

Write 4.8 x 10 -3 in standard notation.

To convert we move the decimal the same number of places as the exponent. Multiplying by a negative power of 10 is the same as dividing by that power of ten. Since multiplying by 10 -3 is the same as dividing by 1000, we can just move the decimal five places to the left. (Hint: if we have negative exponents, we move the decimal to the left because we are dividing.)

4.8 Ã— 10 -3 will be .0048 (we moved the decimal 3 places to the left)

Example 4

Write 1.8 Ã— 10 -4 in standard notation.

To convert we move the decimal the same number of places as the exponent. Multiplying by a negative power of 10 is the same as dividing by that power of ten. Since multiplying by 10 -4 is the same as dividing by 10000, we can just move the decimal four places to the left. (Hint: if we have negative exponents, we move the decimal to the left because we are dividing.)

1.8 Ã— 10 -4 will be .00018 (we moved the decimal 4 places to the left)

Example 5

Write 12,450 in scientific notation. When converting from standard notation to scientific notation, the first thing we do is to move the decimal in 12,450 to a point that the new number will be between 1 and 10. That means we need to move the decimal to where it is between the 1 and the 2. That means we moved the decimal 4 places to the left. Now, we write the product of 1.245 and a power of 10. Our power of 10 will be 3 since we moved the decimal 3 places . (Hint: when we are converting numbers greater than 1 we use positive exponents. Numbers less than 1 use negative exponents.)

12,450 will be 1.245 Ã— 10 3 (we moved the decimal 3 places to the left)

Example 6

Write 139,000 in scientific notation. When converting from standard notation to scientific notation, the first thing we do is to move the decimal in 139,000 to a point that the new number will be between 1 and 10. That means we need to move the decimal to where it is between the 1 and the 3. That means we moved the decimal 5 places to the left. Now, we write the product of 1.39 and a power of 10. Our power of 10 will be 5 since we moved the decimal 5 places .

139,000 will be 1.39 Ã— 10 5 (we moved the decimal 5 places to the left)

Example 7

Write 0.2362 in scientific notation. When converting from standard notation to scientific notation, the first thing we do is to move the decimal in 0.2362 to a point that the new number will be between 1 and 10. That means we need to move the decimal to where it is between the 2 and the 3. That means we moved the decimal 1 place to the right. Now, we write the product of 2.362 and a power of 10. Our power of 10 will be -1 since we moved the decimal 1 place . (Hint: when we are converting numbers less than 1 we use negative exponents.)

0.2362 will be 2.362 Ã— 10 -1 (we moved the decimal 1 place to the right) ?

Example 8

Write 0.02004 in scientific notation. When converting from standard notation to scientific notation, the first thing we do is to move the decimal in 0.02004 to a point that the new number will be between 1 and 10. That means we need to move the decimal to where it is between the 2 and the 0. That means we moved the decimal 2 places to the right. Now, we write the product of 2.004 and a power of 10. Our power of 10 will be -2 since we moved the decimal 2 places . (Hint: when we are converting numbers less than 1 we use negative exponents.)

0.02004 will be 2.004 Ã— 10 -2 (we moved the decimal 2 places to the right)