Solved on Oct 24, 2023

Find the quotient of $\frac{4.5576 \times 10^{-15}}{7.2 \times 10^{-12}}$

STEP 1

Assumptions1. We are asked to find the quotient of $\frac{4.5576 \times10^{-15}}{7. \times10^{-12}}$ . We are dealing with numbers in scientific notation, where a number is written as the product of two numbers a coefficient and10 raised to a power.

STEP 2

The quotient of two numbers in scientific notation can be found by dividing the coefficients and subtracting the exponents.
$\frac{a \times10^m}{b \times10^n} = \frac{a}{b} \times10^{m-n}$

STEP 3

Now, plug in the given values for a, b, m, and n to calculate the quotient.
$\frac{.5576 \times10^{-15}}{7.2 \times10^{-12}} = \frac{.5576}{7.2} \times10^{-15-(-12)}$

STEP 4

Calculate the division of the coefficients and the subtraction of the exponents.
$\frac{4.5576}{7.2} =0.6324444444444444$ $-15 - (-12) = -3$

STEP 5

Now, plug in the calculated values to get the quotient in scientific notation.
$Quotient =0.6324444444444444 \times10^{-3}$

STEP 6

We can round the coefficient to two decimal places to match the format of the options given in the problem.
$Quotient =0.63 \times10^{-3}$

STEP 7

Finally, we can rewrite $0.63 \times10^{-3}$ as $6.3 \times10^{-4}$ to match the standard form of scientific notation, where the coefficient is between1 and10.
$Quotient =6.3 \times10^{-4}$ The quotient of $\frac{4.5576 \times10^{-15}}{7.2 \times10^{-12}}$ is $6.3 \times10^{-4}$ .

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Find the quotient of $\frac{4.5576 \times 10^{-15}}{7.2 \times 10^{-12}}$

STEP 1

Assumptions1. We are asked to find the quotient of $\frac{4.5576 \times10^{-15}}{7. \times10^{-12}}$ . We are dealing with numbers in scientific notation, where a number is written as the product of two numbers a coefficient and10 raised to a power.

STEP 2

The quotient of two numbers in scientific notation can be found by dividing the coefficients and subtracting the exponents.
$\frac{a \times10^m}{b \times10^n} = \frac{a}{b} \times10^{m-n}$

STEP 3

Now, plug in the given values for a, b, m, and n to calculate the quotient.
$\frac{.5576 \times10^{-15}}{7.2 \times10^{-12}} = \frac{.5576}{7.2} \times10^{-15-(-12)}$

STEP 4

Calculate the division of the coefficients and the subtraction of the exponents.
$\frac{4.5576}{7.2} =0.6324444444444444$ $-15 - (-12) = -3$

STEP 5

Now, plug in the calculated values to get the quotient in scientific notation.
$Quotient =0.6324444444444444 \times10^{-3}$

STEP 6

We can round the coefficient to two decimal places to match the format of the options given in the problem.
$Quotient =0.63 \times10^{-3}$

STEP 7

Finally, we can rewrite $0.63 \times10^{-3}$ as $6.3 \times10^{-4}$ to match the standard form of scientific notation, where the coefficient is between1 and10.
$Quotient =6.3 \times10^{-4}$ The quotient of $\frac{4.5576 \times10^{-15}}{7.2 \times10^{-12}}$ is $6.3 \times10^{-4}$ .

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Find the quotient of 4.5576×10−157.2×10−12\frac{4.5576 \times 10^{-15}}{7.2 \times 10^{-12}}7.2×10−124.5576×10−15​

STEP 1

STEP 2

The quotient of two numbers in scientific notation can be found by dividing the coefficients and subtracting the exponents.a×10mb×10n=ab×10m−n\frac{a \times10^m}{b \times10^n} = \frac{a}{b} \times10^{m-n}b×10na×10m​=ba​×10m−n

STEP 3

Now, plug in the given values for a, b, m, and n to calculate the quotient..5576×10−157.2×10−12=.55767.2×10−15−(−12)\frac{.5576 \times10^{-15}}{7.2 \times10^{-12}} = \frac{.5576}{7.2} \times10^{-15-(-12)}7.2×10−12.5576×10−15​=7.2.5576​×10−15−(−12)

STEP 4

Calculate the division of the coefficients and the subtraction of the exponents.4.55767.2=0.6324444444444444\frac{4.5576}{7.2} =0.63244444444444447.24.5576​=0.6324444444444444−15−(−12)=−3-15 - (-12) = -3−15−(−12)=−3

STEP 5

Now, plug in the calculated values to get the quotient in scientific notation.Quotient=0.6324444444444444×10−3Quotient =0.6324444444444444 \times10^{-3}Quotient=0.6324444444444444×10−3

STEP 6

We can round the coefficient to two decimal places to match the format of the options given in the problem.Quotient=0.63×10−3Quotient =0.63 \times10^{-3}Quotient=0.63×10−3

STEP 7

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Find the quotient of $\frac{4.5576 \times 10^{-15}}{7.2 \times 10^{-12}}$

The quotient of two numbers in scientific notation can be found by dividing the coefficients and subtracting the exponents.
$\frac{a \times10^m}{b \times10^n} = \frac{a}{b} \times10^{m-n}$

Now, plug in the given values for a, b, m, and n to calculate the quotient.
$\frac{.5576 \times10^{-15}}{7.2 \times10^{-12}} = \frac{.5576}{7.2} \times10^{-15-(-12)}$

Calculate the division of the coefficients and the subtraction of the exponents.
$\frac{4.5576}{7.2} =0.6324444444444444$ $-15 - (-12) = -3$

Now, plug in the calculated values to get the quotient in scientific notation.
$Quotient =0.6324444444444444 \times10^{-3}$

We can round the coefficient to two decimal places to match the format of the options given in the problem.
$Quotient =0.63 \times10^{-3}$