Question

Write each number in decimal notation.

1. $7.1\times {10}^{14}$
2. $6\times {10}^{12}$
3. $8.55\times {10}^{-3}$
4. $6.257\times {10}^{-10}$

Short answer

1. $710,000,000,000,000$
2. $6,000,000,000,000$
3. $0.00855$
4. $0.0000000006257$

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 $7.1\times {10}^{14}$.

The exponent on the factor 10 is 14.

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

Step 3. Write the decimal notation.

Move the decimal point 14 place right to create a new number, add zeros if needed.

$7.1\times {10}^{14}=710,000,000,000,000$

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 $6\times {10}^{12}$.

The exponent on the factor 10 is 12.

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

Step 3. Write the decimal notation.

Move the decimal point 12 place right to create a new number, add zeros if needed.

$6\times {10}^{12}=6,000,000,000,000$

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 $8.55\times {10}^{-3}$.

The exponent on the factor 10 is negative 3.

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

Step 3. Write the decimal notation.

Move the decimal point 3 place left to create a new number, add zeros if needed.

$8.55\times {10}^{-3}=0.00855$

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 $6.257\times {10}^{-10}$.

The exponent on the factor 10 is negative 10.

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

Step 3. Write the decimal notation.

Move the decimal point 10 place left to create a new number, add zeros if needed.

$6.257\times {10}^{-10}=0.0000000006257$