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 answer:
 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.

	0.0000001
10000000	10
	-0
	100
	-0
	1000
	-0
	10000
	-0
	100000
	-0
	1000000
	-0
	10000000
	-10000000
	0

when we place a decimal point in the quotient, then in every step we can add the zero to the number which we obtained as remainder.
On applying the division to the number. We divide the number until and unless we get a remainder as 0.
Therefore, the decimal number of ${10^{ - 7}}$ is 0.0000001.
So, the correct answer is “0.0000001”.

Note: We should know the rule of division when we use the decimal point. When we place a decimal point in the quotient when we are dividing the number then to the number the place value of the number will change and we insert zero in the unit place.