Question

Expand by expressing powers of 10 in the exponential form: 56,439

Answer 1

Hint: We will use the concept of place values to expand the given number as powers of 10 in the exponential form. We will write the place values of all digits in the given number. Then we will write these in terms of powers of 10. After that, we can write the expansion of the given number as powers of 10 in the exponential form.

Complete step-by-step solution
The given number is 56,439. Now we will write the place value of all the digits. The digit 9 is at the unit’s place. So, its place value is 9. We can write 9 as $9\times {{10}^{0}}$, since ${{10}^{0}}=1$. Next is the digit 3 at the ten’s place. So its place value is 30 and it can be written as $3\times {{10}^{1}}$. Then, we have the digit 4 at the hundred’s place. Its place value is 400 and it can be written as $4\times {{10}^{2}}$. After that is the digit 6 at the thousand’s place. The place value of 6 is 6,000 and it can be written as $6\times {{10}^{3}}$. Next is the digit 5 at ten thousand’s places. Its place value is 50,000 and we can write it as $5\times {{10}^{4}}$.
Now, we can expand the given number as powers of 10 in the exponential form in the following manner,
$56,439=5\times {{10}^{4}}+6\times {{10}^{3}}+4\times {{10}^{2}}+3\times {{10}^{1}}+9\times {{10}^{0}}$

Note: It is essential that we are familiar with the concept of place values for such type of questions. This process can also be used in a reverse manner, which means we can form any number by adding the place values of each digit we need in the number. We generally use the decimal number system and hence, we associate powers of 10 to the place values of digits in numbers. There are other number systems like binary or hexadecimal number systems where we can expand a number in powers of 2 or 16 respectively.