Question

Write each number in scientific notation.

1. $129,540,000$
2. $7,259,000,000$
3. $0.0000000014$
4. $0.0007029$

Short answer

1. $1.2954\times {10}^8$
2. $7.259\times {10}^9$
3. $1.4\times {10}^{-9}$
4. $7.029\times {10}^{-4}$

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. Number of place decimal point move.

Consider the given number $129,540,000$.

Move the decimal point 8 place left to create a new number from 1 up to 10.

Step 3. Write the scientific notation.

We move decimal 8 times; also, because we moved decimal to the left, the exponent is positive.

$129,540,000=1.2954\times {10}^8$

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. Number of place decimal point move.

Consider the given number $7,259,000,000$.

Move the decimal point 9 place left to create a new number from 1 up to 10.

Step 3. Write the scientific notation.

We move decimal 9 times; also, because we moved decimal to the left, the exponent is positive.

$7,259,000,000=7.259\times {10}^9$

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. Number of place decimal point move.

Consider the given number $0.0000000014$.

Move the decimal point 9 place right to create a new number from 1 up to 10.

Step 3. Write the scientific notation.

We move decimal 9 times; also, because we moved decimal to the right, the exponent is negative.

$0.0000000014=1.4\times {10}^{-9}$

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. Number of place decimal point move.

Consider the given number $0.0007029$.

Move the decimal point 4 place right to create a new number from 1 up to 10.

Step 3. Write the scientific notation.

We move decimal 4 times; also, because we moved decimal to the right, the exponent is negative.

$0.0007029=7.029\times {10}^{-4}$