Solved on Jan 24, 2024

Determine the correct product of $(-4 \times 10^{2})$ and $(2 \times 10^{-8})$ . The coefficient may be rounded.

STEP 1

Assumptions
1. We are multiplying two numbers in scientific notation.
2. The base of the scientific notation is 10.
3. The coefficients of the numbers are -4 and 2, respectively.
4. The exponents of the numbers are 2 and -8, respectively.

STEP 2

To multiply two numbers in scientific notation, we multiply their coefficients and add their exponents.
$\left(a \times 10^{m}\right)\left(b \times 10^{n}\right) = (a \cdot b) \times 10^{m+n}$

STEP 3

Now, plug in the given values for the coefficients and exponents to calculate the product.
$\left(-4 \times 10^{2}\right)\left(2 \times 10^{-8}\right) = (-4 \cdot 2) \times 10^{2+(-8)}$

STEP 4

Multiply the coefficients.
$-4 \cdot 2 = -8$

STEP 5

Add the exponents.
$2 + (-8) = -6$

STEP 6

Combine the results to get the product in scientific notation.
$(-8) \times 10^{-6}$
The correct product is $-8 \times 10^{-6}$ .

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Determine the correct product of $(-4 \times 10^{2})$ and $(2 \times 10^{-8})$ . The coefficient may be rounded.

STEP 1

Assumptions
1. We are multiplying two numbers in scientific notation.
2. The base of the scientific notation is 10.
3. The coefficients of the numbers are -4 and 2, respectively.
4. The exponents of the numbers are 2 and -8, respectively.

STEP 2

To multiply two numbers in scientific notation, we multiply their coefficients and add their exponents.
$\left(a \times 10^{m}\right)\left(b \times 10^{n}\right) = (a \cdot b) \times 10^{m+n}$

STEP 3

Now, plug in the given values for the coefficients and exponents to calculate the product.
$\left(-4 \times 10^{2}\right)\left(2 \times 10^{-8}\right) = (-4 \cdot 2) \times 10^{2+(-8)}$

STEP 4

Multiply the coefficients.
$-4 \cdot 2 = -8$

STEP 5

Add the exponents.
$2 + (-8) = -6$

STEP 6

Combine the results to get the product in scientific notation.
$(-8) \times 10^{-6}$
The correct product is $-8 \times 10^{-6}$ .

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Determine the correct product of (−4×102)(-4 \times 10^{2})(−4×102) and (2×10−8)(2 \times 10^{-8})(2×10−8). The coefficient may be rounded.

STEP 1

Assumptions1. We are multiplying two numbers in scientific notation.2. The base of the scientific notation is 10.3. The coefficients of the numbers are -4 and 2, respectively.4. The exponents of the numbers are 2 and -8, respectively.

STEP 2

To multiply two numbers in scientific notation, we multiply their coefficients and add their exponents.(a×10m)(b×10n)=(a⋅b)×10m+n \left(a \times 10^{m}\right)\left(b \times 10^{n}\right) = (a \cdot b) \times 10^{m+n} (a×10m)(b×10n)=(a⋅b)×10m+n

STEP 3

Now, plug in the given values for the coefficients and exponents to calculate the product.(−4×102)(2×10−8)=(−4⋅2)×102+(−8) \left(-4 \times 10^{2}\right)\left(2 \times 10^{-8}\right) = (-4 \cdot 2) \times 10^{2+(-8)} (−4×102)(2×10−8)=(−4⋅2)×102+(−8)

STEP 4

Multiply the coefficients.−4⋅2=−8 -4 \cdot 2 = -8 −4⋅2=−8

STEP 5

Add the exponents.2+(−8)=−6 2 + (-8) = -6 2+(−8)=−6

STEP 6

Combine the results to get the product in scientific notation.(−8)×10−6 (-8) \times 10^{-6} (−8)×10−6The correct product is −8×10−6-8 \times 10^{-6}−8×10−6.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Determine the correct product of $(-4 \times 10^{2})$ and $(2 \times 10^{-8})$ . The coefficient may be rounded.

Assumptions
1. We are multiplying two numbers in scientific notation.
2. The base of the scientific notation is 10.
3. The coefficients of the numbers are -4 and 2, respectively.
4. The exponents of the numbers are 2 and -8, respectively.

To multiply two numbers in scientific notation, we multiply their coefficients and add their exponents.
$\left(a \times 10^{m}\right)\left(b \times 10^{n}\right) = (a \cdot b) \times 10^{m+n}$

Now, plug in the given values for the coefficients and exponents to calculate the product.
$\left(-4 \times 10^{2}\right)\left(2 \times 10^{-8}\right) = (-4 \cdot 2) \times 10^{2+(-8)}$

Multiply the coefficients.
$-4 \cdot 2 = -8$

Add the exponents.
$2 + (-8) = -6$

Combine the results to get the product in scientific notation.
$(-8) \times 10^{-6}$
The correct product is $-8 \times 10^{-6}$ .