OMS-KD-Scientific Notation

Definition/Rules

100

What is the purpose of scientific notation?

To represent really big or small numbers in more convenient way.

200

What numbers must the coefficient always be between?

What is 1 and 10?

300

What does a positive exponent tell us about the number in scientific notation?

-Big number

-Multiplying by powers of 10

-Decimal point moves to the right

400

What does a negative exponent tell us about the number in scientific notation?

-Small number

-Dividing by powers of 10

-Decimal point moves to the left

500

Why is the base always 10 for a number written in scientific notation?

Because our number system is base 10.

Converting

100

Convert the following number into scientific notation:

0.0002829

What is 

2.829*10^-4?

200

Convert the following number into standard form:

4.37*10^6

What is 

4,370,000?

300

Convert the following number into scientific notation:

980,100

What is 

9.801*10^5?

400

Convert the following number into standard form:

8.2*10^-7

What is 

0.00000082?

500

Convert the following number into scientific notation:

0.00065300

What is 

6.53*10^-4?

Multiplying/Dividing

100

Perform the indicated operation:

(3.2*10^8)*(2.56*10^-2)

What is 

8.192*10^6?

200

Perform the indicated operation:

(9.282*10^4)/(2.21*10^-1

What is 

4.2*10^5?

300

Perform the indicated operation:

(9.1*10^-6)*(8.62*10^-4)

What is 

7.8442*10^-9?

400

Perform the indicated operation:

(1.5616*10^8)/(6.1*10^2)

What is 

2.56*10^5?

500

The population of the United States in 1922 was about 1.1*10⁸ people. The current population in the United States is about 3.3*10⁸ people. How many times bigger is the population of the United States today compared to 100 years ago?

What is 3 times bigger?

Adding/Subtracting

100

Perform the indicated operation:

(9.845*10^-11)-(6.25*10^-11)

What is 

3.604*10^-11?

200

Perform the indicated operation:

(6.72*10^8)+(8.9*10^8)

What is 

1.562*10^9?

300

Perform the indicated operation:

(7.2*10^4)+(8.54*10^7)

What is 

8.5472*10^7?

400

Perform the indicated operation:

(1.26*10^5)-(3.82*10^4)

What is 

8.78*10^4?

500

Company A made 9.451*10⁸ dollars in 2021, and Company B made 1.12*10⁹ dollars in 2021. How much more money did Company B make than Company A in 2021? Write your answer in both standard form and scientific notation.

Standard form: 1,749,00,000

Scientific Notation: 

1.749*10^8