lesson 5

Question 1

scientific notation

Answer 1

a number written as the product of a decimal number multiplied by a power of 10

Question 2

standard notation

Answer 2

a number as we usually write it (e.g., 3, 5.1, −115)

Question 3

Example

Answer 3

a. The number 2.09 could be the lead number in scientific notation because The whole number portion is 2.
b. The number 10.23 could not be the lead number in scientific notation because . The whole number portion is 10.
c. The number 0.678 could not be the lead number in scientific notation because The whole number portion is 0.

Writing a number in scientific notation is fairly simple.

1 –The lead number part will be a number greater than or equal to 1 and less than 10, written in decimal format.

2 –The lead number part is multiplied by the second part, which is a power of 10 that has an integer exponent.

Question 4

Example 1

Answer 4

Change 1,300 from standard form to scientific notation.

Remember, any whole number that doesn’t show a decimal point has an unwritten point at the end.

1 –In order to make the lead number part be a number from 1 to 9, move the decimal point 3 places to the left. Since the zeros are at the end of the number, we can cross them out and still have the same value.

2 –Because we moved the decimal point 3 places to the left, the second part will be multiplied by 10 with a positive exponent of 3.

3 –You can check your work on paper or with a calculator.

Question 5

Example 2

Answer 5

Change 0.023 from standard form to scientific notation.

1 – Any leading zeros may be crossed out.

2 –Because we moved the decimal point 2 places to the right, the second part will be multiplied by 10 with a negative exponent of

A positive exponent goes with numbers greater than or equal to 1.

A negative exponent goes with numbers less than 1 but greater than zero.

Question 6

Example 4

Answer 6

Which numbers are in scientific notation?

a. This is scientific notation, because 1.5 is larger than 1 but less than 10.
b. This is not a scientific notation, because 0.4 is less than 1.
c. This is not a scientific notation, because the exponent is not an integer.

Question 7

A normal number is written in

Answer 7

standard notation

Question 8

A number written as the product of a decimal number multiplied by a power of 10 is in the form of

Answer 8

scientific notation

Question 9

Choose the correct scientific notation for the given number.

1543

Answer 9

15.45 x 10 by the power of two

Question 10

Choose the correct scientific notation for the given number.

0.0026

Answer 10

2.6 x 10 to the power of negative three.

Question 11

Choose the correct scientific notation for the given number.

10.69

Answer 11

1.069 x 10 to the power of one