If (5.0 \times 10^{-4}) \times (4.0 \times 10^{7}) = 2.0 \times 10^n, what is the value of… — GRE General Test

If $(5.0 \times 10^{-4}) \times (4.0 \times 10^{7}) = 2.0 \times 10^n$ , what is the value of $n$ ?

Answer: 4

The value of

n

is 4.

Multiplying the coefficients yields

5.0 \times 4.0 = 20.0

, and multiplying the powers of ten yields

10^{-4} \times 10^7 = 10^3

. Combining these gives

20.0 \times 10^3

. Rewriting

20.0 \times 10^3

into standard scientific notation gives

2.0 \times 10^4

. Therefore,

n = 4

Multiply the numerical coefficients

5.0 \times 4.0 = 20.0

When multiplying numbers in scientific notation, separate the coefficients from the exponential terms.

Add the exponents of the base 10 terms

10^{-4} \times 10^{7} = 10^{3}

By exponent rules,

10^a \times 10^b = 10^{a+b}

Adjust the product to standard scientific notation form

20.0 \times 10^3 = 2.0 \times 10^4

Shift the decimal point one place to the left to obtain a coefficient

2.0

(

1 \le a < 10

), which increases the power of 10 by 1.

Determine the exponent value

n

n = 4

Comparing

2.0 \times 10^4

2.0 \times 10^n

gives

n = 4

Scientific notation multiplication and place value rules

Question