Chapter 5.4, Problem 1P

Write the following numbers as powers of 10:

1. 0.000001
2. 10,000,000
3. the number whose decimal representation is a 1 followed by 50 zeros
4. the number whose decimal representation is a decimal point followed by 10 zeros, followed by a 1
5. the number whose decimal representation is a decimal point followed by 50 zeros, followed by a 1

To determine

To write:

The given numbers as a power of 10.

Answer to Problem 1P

  $0.000001$ as a power of 10 would be ${10}^{-6}$

Explanation of Solution

Given:

A number: $0.000001$ .

Calculation:

First of all, we will write $0.000001$ as a fraction as shown below:

  $0.000001=\frac{0.000001\times 1,000,000}{1,000,000}=\frac{1}{1,000,000}$

Now, we will write $1,000,000$ as a power of 10:

  $0.000001=\frac{1}{1,000,000}=\frac{1}{{10}^6}$

Using property $\frac{1}{m^n}=m^{-n}$ , we will get:

  $0.000001=\frac{1}{{10}^6}={10}^{-6}$

Therefore, $0.000001$ as a power of 10 would be ${10}^{-6}$ .

To determine

To write:

The given numbers as a power of 10.

Answer to Problem 1P

  $10,000,000$ as a power of 10 would be ${10}^7$

Explanation of Solution

Given:

A number: $10,000,000$ .

Calculation:

We can see that there are 7 zeros after 1, this means that 10 is multiplied to itself by 7 times.

We can write $10,000,000$ as a power of 10 as shown below:

  $10,000,000={10}^7$

Therefore, $10,000,000$ as a power of 10 would be ${10}^7$ .

To determine

To write:

The given numbers as a power of 10.

Answer to Problem 1P

1 followed by 50 zeros as a power of 10 would be ${10}^{50}$

Explanation of Solution

Given:

A number, whose decimal representation is a 1 followed by 50 zeros.

Calculation:

1 followed by 50 zerosmeans that 1 followed by 50 zeros that is 10 multiplied to itself by 50 times.

We can write 1 followed by 50 zeros as a power of 10 by raising 10 to 50^th power as:

  $\underset{(50\text{ zeros)}}{\underbrace{1,000,0000,\mathrm{........},000}}={10}^{50}$

Therefore,1 followed by 50 zerosas a power of 10 would be ${10}^{50}$ .

To determine

To write:

The given numbers as a power of 10.

Answer to Problem 1P

A decimal point followed by 10 zeros, followed by a1 as a power of 10 would be ${10}^{-11}$

Explanation of Solution

Given:

A number, whose decimal representation is a decimal point followed by 10 zeros, followed by a1.

Calculation:

A decimal point followed by 10 zeros, followed by a 1 would be $0.00000000001$ .

We will write $0.00000000001$ as a fraction as shown below:

  $0.00000000001=\frac{0.00000000001\times {10}^{11}}{{10}^{11}}=\frac{1}{{10}^{11}}$

Using property $\frac{1}{m^n}=m^{-n}$ , we will get:

  $0.00000000001=\frac{1}{{10}^{11}}={10}^{-11}$

Therefore, $0.00000000001$ as a power of 10 would be ${10}^{-11}$ .

To determine

To write:

The given numbers as a power of 10.

Answer to Problem 1P

A decimal point followed by 50 zeros, followed by a 1as a power of 10 would be ${10}^{-51}$

Explanation of Solution

Given:

A number, whose decimal representation is a decimal point followed by 50 zeros, followed by a 1.

Calculation:

A decimal point followed by 150 zeros, followed by a 1 would be $\underset{50\text{ zeros}}{\underbrace{0.000,\mathrm{.....},0001}}$ .

To write $\underset{50\text{ zeros}}{\underbrace{0.000,\mathrm{.....},0001}}$ as a power of 10, we will raise 10 to negative 51 power as it has 51 digits after decimal.

  $\underset{50\text{ zeros}}{\underbrace{0.000,\mathrm{.....},0001}}={10}^{-51}$

Therefore, $\underset{50\text{ zeros}}{\underbrace{0.000,\mathrm{.....},0001}}$ as a power of 10 would be ${10}^{-51}$ .