Express each measure in standard form.

(One more thing by the way you need this few prefixes)

Tera= 10 to the 12th power
Giga= 10 to the 9th power
Mega= 10 to the 6th power
Kilo= 10 to the 3rd power
Pico= 10 to the -12th power
Nano= 10 to the -9th power
Micro= 10 to the -6th power
Milli= 10 to the -3rd power

1. 4 Megahertz
Answer: 4*10 (To the 6th power)
Which equals 4000000

2. 82 Kilobytes
Answer: 82*10 (to the 3rd power)
Which equals 82000

3. 2.3 Micrograms
Answer: .0000023

Express each number in scientific notation
1. 24000
Answer: 2.4*10 (to the 3rd power)

2. 25000000
Answer: 2.5* 10 (to the 6th power)

3. 0.08
Answer: 8*10 (to the -2nd power)

4. 15.9
Answer: 5.9*10 (to the -1st power)

5. 1000000
Answer: 1.0*10 (to the 6th power)

6. 0.0000946
Answer: 9.46*10 (to the 4th power)

Evaluate each expression. Express each result in scientific notation and standard form.

1. (4 * 10(to the 2nd power)(1.5 * 10(to the 6th power)
Answer: 6*10(to the 8th power)

2. (7.8 * 10(to the -6 power)(1* 10(to the -2 power)
Answer: 8.8*10(to the -8 power)

Evaluate each expression. Express each result in scientific and standard notation.

1. 8* 10(to the 2nd power)
--------------------------
2* 10(to the -3rd power)
Answer: 800000

2. Find the product of (1.2 * 10(to the 5th power) and (5 * 10(to the -4th power) mentally.
Answer: 60

3. The mass of an orchid seed is 3.5 * 10 (to the -6th power) grams. Express 3.5 * 10(to the -6th power)
Answer: 0.0000035

4. Engineering notation is similar to scientific notation. However, in engineering notaioin, the powers of ten are always mulitiples of 3, such as 10(to the 3rd power), 10(to the 6th power), 10(to the -9th power), and 10 ( to the -12th power. For example: 240000 is expressed as 240 * 10(to the 3rd power). Express 15000 ohms in scientific notation and engineering notation.
Answer: SN: 1.5 * 10(to the 4th power)
EN: 1.5* 10(to the 3rd power)

5a.

32 * 10(to the fifth power)
Answer: 3200000

5B

284 * 10(to the third power)
Answer: 284000

5C

0.76* 10(to the -2 power)
Answer: 0.0076

5D

0.09 * 10(to the -3rd power)
Answer: 0.0009

4. 15.9

Answer: 5.9*10 (to the -1st power)
I think
1.59 * 10^1

6. 0.0000946

Answer: 9.46*10 (to the 4th power)
I think
9.46*10^-5

2. (7.8 * 10(to the -6 power)(1* 10(to the -2 power)

Answer: 8.8*10(to the -8 power)
I think
7.8 * 10^-8

On the engineering notation, you did not do them to powers of three.

Take 5c for example: 7.6*10^-3

There is another way to express powers, often used on ascii keyboards, or else where powers are difficult.

1.4*10^5 would be written as 1.4E5. In older times it was 1.4Exp5, and you see some older calculators around with an Exp or E key. This notation cameabout in the early days of IBM computers (and Fortran Language).

1. 8* 10(to the 2nd power)

--------------------------
2* 10(to the -3rd power)
Answer: 800000

.9*10^5 = 9 *10^4 = 90,000

7.8*1o ^5 in standard notation

78

780,000

yygyggygg

To express each measure in standard form, you need to convert the given value to a number multiplied by a power of 10.

1. 4 Megahertz = 4 * 10^6 = 4000000
You multiply 4 by 10 raised to the power of 6.

2. 82 Kilobytes = 82 * 10^3 = 82000
You multiply 82 by 10 raised to the power of 3.

3. 2.3 Micrograms = 2.3 * 10^-6
You simply write the number as it is, and the 10 is raised to the power of -6.

To express each number in scientific notation, you need to write the number in the form of a multiplied value between 1 and 10, multiplied by a power of 10.

1. 24000 = 2.4 * 10^3
You divide 24000 by 10000 to get 2.4 and raise 10 to the power of 3.

2. 25000000 = 2.5 * 10^6
You divide 25000000 by 10000000 to get 2.5 and raise 10 to the power of 6.

3. 0.08 = 8 * 10^-2
You divide 0.08 by 10 to get 8 and raise 10 to the power of -2.

4. 15.9 = 1.59 * 10^1
You divide 15.9 by 10 to get 1.59 and raise 10 to the power of 1.

5. 1000000 = 1.0 * 10^6
The number is already in the correct form, so you just raise 10 to the power of 6.

6. 0.0000946 = 9.46 * 10^-5
You divide 0.0000946 by 10000 to get 9.46 and raise 10 to the power of -5.

To evaluate each expression, express the result in scientific notation and standard form.

1. (4 * 10^2) * (1.5 * 10^6) = 6 * 10^8
You multiply 4 by 1.5 to get 6 and add the exponents 2 and 6 to get 8.

2. (7.8 * 10^-6) * (1 * 10^-2) = 8.8 * 10^-8
You multiply 7.8 by 1 to get 7.8 and add the exponents -6 and -2 to get -8.

To evaluate each expression and express the result in scientific and standard notation:

1. (8 * 10^2) / (2 * 10^-3) = 4 * 10^5
You divide 8 by 2 to get 4 and subtract the exponent -3 from 2 to get 5.

2. (1.2 * 10^5) * (5 * 10^-4) = 6 * 10^1
You multiply 1.2 by 5 to get 6 and add the exponents 5 and -4 to get 1.

3. 3.5 * 10^-6 grams can be expressed as 0.0000035 grams in standard notation.

4. 15000 ohms = 1.5 * 10^4 in scientific notation and 1.5 * 10^3 in engineering notation.

5a. 32 * 10^5 = 3200000 in standard notation.

5b. 284 * 10^3 = 284000 in standard notation.

5c. 0.76 * 10^-2 = 0.0076 in standard notation.

5d. 0.09 * 10^-3 = 0.0009 in standard notation.