1. Scientific Notation with Positive Powers of 10

2. Warm Up Write each number in scientific notation.
1. 58, ,304,000,000
6,730, ,300
Write each number in standard notation.
4 x x 109
x x 107

3. You can use scientific notation to express very large quantities by writing the large quantity as the product of a number greater than or equal to 1 and less than 10 and a power of 10.

4. When you write 9 × 107 in standard notation, how many zeros do you write?
If you were to write 9 × 102 in standard notation, how many zeros would you write?
The standard notation for 9.3 × 107 is 93,000,000. Why are there 6 zeros instead of 7 zeros in the standard notation?

5. The average distance from Earth to Mars is about 140,000,000 miles
The average distance from Earth to Mars is about 140,000,000 miles. Write this distance in scientific notation.

6. Scientific notation is used to represent very large numbers.
One very large named number is a googol – the number 1 followed by 100 zeros.
An even larger named number is the googolplex – the number 1 followed by a googol (10100) of zeros.
This massive number can be represented as 10googol.
This idea has been extended even further to name a googolplexian, which is the number 1 followed by a googolplex of zeros.
The googol (also spelled google) was named by the nine-year-old nephew of the American mathematician Edward Kasner.

7. Write 7.8 × 109 in standard notation.

8. What is the value of 100? Any number to the zero power is equal to 1.

9. How can we compare the values 7. 034 × 109 and 2
How can we compare the values × 109 and 2.36 × 105 when they are expressed in scientific notation.
We can compare the exponents of 10.
Because 109 has a greater exponent than 105, × 109 is greater than 2.36 × 105.
When comparing two numbers written in scientific notation, compare the power of 10 first.
When the power of 10 is the same, compare the coefficients.
When the power of 10 is different, you do not need to compare the coefficient.

10. Cognitive Strategies Visualize how the final number will look before you write anything down.
If the question says “Write in scientific notation,” realize that the answer will be the product of a number greater than or equal to 1 and less than 10, and a power of 10.
If the question says “Write in standard notation,” be aware that an answer may have zeros as placeholders to show the number’s size.

11. Which of the following numbers are written in scientific notation?
0.641 x 103
9.999 x 104
2 x 101
4.38 x 510

12. Which measurement would be least likely to be written in scientific notation: number of stars in a galaxy, number of grains of sand on a beach, speed of a car, or population of a country? Explain your reasoning.

13. Compare the two numbers to find which is greater
Compare the two numbers to find which is greater. Explain how you can compare them without writing them in standard notation first. 4.5 × × 108

14. Exit Ticket
The approximate mass of Mars is 6.42 × 1023 kilograms. Write this mass in standard notation.
An adult blue whale can eat about 40,000,000 krill a day. Write this number in scientific notation.
Write 9 in scientific notation.
Write 1.0 × 105 in standard notation and in words.
Is 10.2 × 105 written in scientific notation? Explain.