Question

What conclusions can be drawn about finding the quotient in scientific notation? Check all that apply. StartFraction (9. 6 times 10 Superscript negative 8 Baseline) Over (3. 2 times 10 Superscript 4 Baseline) EndFraction The coefficient of the solution is 6. 4, the difference of the original coefficients. The exponent of the solution is –12, the difference of the original exponents. The coefficient of the solution must be greater than or equal to one but less than 10. The quotient is 3. 0 × 10-12 The solution is a very large number.

Answer 1

As to divide the number with power of same base subtract their power keeping the base same.

The quotient of the given number is $3\times 10^{-12}$. Thus, The following conclusion with solution can be made-

• B) The exponent of the solution is –12, the difference of the original exponents.
• C) The coefficient of the solution must be greater than or equal to one but less than 10, which is 3.
• D) The quotient is $3\times 10^{-12}$

What is the exponent power with base 10?

To write the big number in short form, we write them in the positive power of 10.

To write the very small number, we write them in the negative power of 10.

How to divide number with different power?

When the two number has different power but the base is same, then to divide them subtract their power keeping the base same.

Given information-

The expression given in the problem (let $n$) is,

$n=\dfrac{9.6\times10^{-8}}{3.2\times10^4}$

The above equation can be written as,

$n=\dfrac{9.6}{3.2}\times\dfrac{10^{-8}}{10^4}$

As to divide the number with power of same base subtract their power keeping the base same.

Thus,

$n=\dfrac{9.6}{3.2}\times{10^{(-8-4)}}\\n=3\times{10^{-12}}$

Hence the quotient of the given number is $3\times 10^{-12}$. Thus, The following conclusion with solution can be made-

• B) The exponent of the solution is –12, the difference of the original exponents.
• C) The coefficient of the solution must be greater than or equal to one but less than 10, which is 3.
• D) The quotient is $3\times 10^{-12}$

Learn more about the exponent power with base 10 here;

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