Question

How do you write \[{10^{ - 7}}\] in decimal form?

Answer 1

Hint: Here we have to write the number in the form of decimal, the number in the question is in the form of exponential. The exponent of the number is having negative sign; it can be written in the form of fraction and then by the division we can find the value in decimal form.

Complete step by step solution:
Consider the given question, the number is in the form of exponential form. The exponential number is defined as the number of times the number is multiplied by itself. If we see the number in the question the exponent is a negative value. If the exponent is a negative value it can be written in the form of fraction. therefore, the number \[{10^{ - 7}}\] is written as \[\dfrac{1}{{{{10}^7}}}\] . The number which is in the denominator is a multiple of 10. So we have to multiply the number 10 to 7 times. Therefore \[{10^7}\] is written as \[10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10\] . On multiplying we get \[10000000\] . The given number is written as \[\dfrac{1}{{10000000}}\] . When we divide the number 1 by 10000000.
We cancel the one zero in the denominator and add a decimal point before the number 1. so we have \[\dfrac{{0.1}}{{1000000}}\]
Now we move the decimal point to the left side in the numerator and we cancel one zero in the denominator. the number is written as \[\dfrac{{0.01}}{{100000}}\]
Now we move the decimal point to the left side in the numerator and we cancel one zero in the denominator. the number is written as \[\dfrac{{0.001}}{{10000}}\]
Now we move the decimal point to the left side in the numerator and we cancel one zero in the denominator. the number is written as \[\dfrac{{0.0001}}{{1000}}\]
Now we move the decimal point to the left side in the numerator and we cancel one zero in the denominator. the number is written as \[\dfrac{{0.00001}}{{100}}\]
Now we move the decimal point to the left side in the numerator and we cancel one zero in the denominator. the number is written as \[\dfrac{{0.000001}}{{10}}\]
Now we move the decimal point to the left side in the numerator and we cancel one zero in the denominator. the number is written as \[\dfrac{{0.0000001}}{1}\]
Hence there is no greater number in the denominator. We have 1 in the denominator. So we need not shift the decimal number further.
Therefore, the decimal number of \[{10^{ - 7}}\] is 0.0000001.
So, the correct answer is “0.0000001”.

Note: The decimal point is shifted based on the number of zeros present in the denominator. The fraction number can be converted into the decimal number. To convert we have a specific rule. By applying the rule we determine the value for the given solution and we obtain the solution.