Star X emits 4.8 \times 10^{22} Joules of energy per second, which is 16 times the energy … — ACT

Star X emits $4.8 \times 10^{22}$ Joules of energy per second, which is 16 times the energy emitted per second by Star Y. What is the energy, in Joules, emitted per second by Star Y, expressed in scientific notation?

A
$7.68 \times 10^{23}$
B
$3.0 \times 10^{23}$
C
$3.0 \times 10^{22}$
$3.0 \times 10^{21}$ Answer
E
$3.0 \times 10^{20}$

Answer

3.0 \times 10^{21}

The energy emitted by Star Y is found by dividing Star X's energy output (

4.8 \times 10^{22}

) by 16. Dividing

4.8

by 16 yields

0.3

. To put

0.3 \times 10^{22}

in standard scientific notation, move the decimal point one place to the right, which reduces the exponent from 22 to 21, resulting in

3.0 \times 10^{21}

Step-by-Step Solution

Translate the relationship into an equation.

\text{Energy}_X = 16 \times \text{Energy}_Y

, so

\text{Energy}_Y = \frac{\text{Energy}_X}{16} = \frac{4.8 \times 10^{22}}{16}

Since Star X emits 16 times as much energy as Star Y, dividing Star X's energy output by 16 gives Star Y's energy output.

Divide the numerical coefficient by 16.

\frac{4.8}{16} \times 10^{22} = 0.3 \times 10^{22}

Perform the division on the non-exponent part of the scientific notation expression.

Convert

0.3 \times 10^{22}

into standard scientific notation.

0.3 \times 10^{22} = (3.0 \times 10^{-1}) \times 10^{22} = 3.0 \times 10^{21}

Standard scientific notation requires the coefficient

a

to satisfy

1 \le |a| < 10

. Moving the decimal point one place to the right decreases the exponent of 10 by 1.

Key Concept

Division of Numbers in Scientific Notation

Question

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