Scientific Notation

Twenty-five thousandths can be written as 2.5 x 10^-2 in scientific notation.

The scientific notation of 0.000332 is 3.32 × 10-4

A million is 1.0 x 106. Then, 97.4 million is 97.4 x 106. Move one more decimal place to the left to get 9.74 x 107.

47.784 expressed in scientific notation is 4.7784 × 10^1.

3.125 × 10-1

or

3.125E-1

Addition:

1) Change the lower exponent to match (by dividing its number by 10 successively)

2) Add the numbers.

3) Keep the biger exponent (then adjust if necessary)

Example 1:

4x10^6 + 9x10^4

1) 9x10^4=0.9x10^5=0.09x10^6

2) 4+0.09=4.09

3) 4.09x10^6

Example 2: 6x10^7 + 5.5x10^7

1) No change needed (same exponent)

2) 6+5.5=11.5

3)11.5x10^7

Subtraction:

1) Change the lowe exponent to match (by dividing its number by 10 successively)

2) Subtract the numbers

3)keep the bigger exponent (adjust if necessary)

Example 1:

4x10^6 - 9x10^4

1)9x10^4= 0.9x10^5=0.09x10^6

2) 4 - 0.09 = 3.91

3) 3.91x10^6

Example 2:

6x10^7 - 5.5x10^7

1) No change needed (same exponent)

2) 6 - .5 = 0.5

3) 0.5x10^7 = 5x10^6

Notice that in exmaple 1 we didn't change the exponent in step 3, but in example 2 we did.

Multiplucation:

1) Multiply the numbers

2) Add the exponents

3) If necessary, adjus the exponent

Wxample:

3x10^8 x 5x10^4

1) 3x5= 13

2) 8+4= 12

3) 15x10^12=1.3x10^13

Division:

1) Divide the numbers.

2) Subtract the exponents.

3) If necessary, adjust the exponent.

Example:

2x10^9 / 5x10^4

1) 2/5= 0.4

2) 9-4=5

3) 0.4x10^5= 4x10^4

5.2x10 to the power of 2

The number 5,000,000,000 can be written as 5.0 x 10^9.

The exponential notation of 72 is: 7.2 × 101 or 7.2E1

In scientific notation, 92900000 can be written as 9.29 x 10^7.

The scientific notation for 6.55 million is 6.55 x 10^6.

0.000796 can be written in scientific notation as 7.96 x 10^-4.

It is: 1.72*10^4

The scientific notation of 0.000002505 is 2.505 x 10^-6.

It is: 7.18*10^-4

The weight of one eagle feather is approximately 2.85×10^(-2) kilograms in scientific notation.

0.000750 = 7.5 x 10^-4

It is 1.23453*10^5 in scientific notation

The number 64960000 in scientific notation is 6.496 x 10^7.

To write 0.00083 in scientific notation, move the decimal point to the right until there is one non-zero digit to its left. In this case, the decimal point would need to be moved 4 places to the right. Therefore, 0.00083 in scientific notation would be 8.3 x 10^-4.

51200 in scientific notation is 5.12 x 10^4

68.5 can be written in scientific notation as 6.85 x 10^1.

Usually number under 1,000 are not written in scientific notation, however 60 would be written as 6.0 x 101.

There is only one scientific notation and it is a way of representing numbers, usually very large or very small, in the form a*10^b where 1 <= |a| < 10 is a decimal number and b is an integer (negative or positive). ais called the mantissa and b is called the exponent.