Question

Write each number in decimal notation.

1. $3.19\times {10}^5$
2. $2.721\times {10}^8$
3. $2.670\times {10}^{-8}$
4. $9.999\times {10}^{-9}$

Short answer

1. $319,000$
2. $272,100,000$
3. $0.00000002670$
4. $0.000000009999$

Step-by-step solution

a.Step 1. Scientific Notation.

A positive number x is said to be written in scientific notation if it is expressed as follows:

$x=a\times {10}^n\text{where}1\le a<10$ and n is an integer.

Step-2. Determine the exponent.

Consider the given number $3.19\times {10}^5$.

The exponent on the factor 10 is 5.

Since the exponent is positive, we move decimal point right.

Step 3. Write the decimal notation.

Move the decimal point 5 place right to create a new number, add zeros if needed.

$3.19\times {10}^5=319,000$

b.Step 1. Scientific Notation.

A positive number x is said to be written in scientific notation if it is expressed as follows:

$x=a\times {10}^n\text{where}1\le a<10$ and n is an integer.

Step 2. Determine the exponent.

Consider the given number $2.721\times {10}^8$.

The exponent on the factor 10 is 8.

Since the exponent is positive, we move decimal point right.

Step 3. Write the decimal notation.

Move the decimal point 8 place right to create a new number, add zeros if needed.

$2.721\times {10}^8=272,100,000$

c.Step 1. Scientific Notation.

A positive number x is said to be written in scientific notation if it is expressed as follows:

$x=a\times {10}^n\text{where}1\le a<10$ and n is an integer.

Step 2. Determine the exponent.

Consider the given number $2.670\times {10}^{-8}$.

The exponent on the factor 10 is negative 8.

Since the exponent is negative, we move decimal point left.

Step 3. Write the decimal notation.

Move the decimal point 8 place left to create a new number, add zeros if needed.

$2.670\times {10}^{-8}=0.00000002670$

d.Step 1. Scientific Notation.

A positive number x is said to be written in scientific notation if it is expressed as follows:

$x=a\times {10}^n\text{where}1\le a<10$ and n is an integer.

Step 2. Determine the exponent.

Consider the given number $9.999\times {10}^{-9}$.

The exponent on the factor 10 is negative 9.

Since the exponent is negative, we move decimal point left.

Step 3. Write the decimal notation.

Move the decimal point 9 place left to create a new number, add zeros if needed.

$9.999\times {10}^{-9}=0.000000009999$