Question

What is the product of (5.1 × 103) • (3.2 × 103)? A. 16.32 × 106 B. 1.632 × 107 C. 16.32 × 109 D. 1.632 × 1010

Answer 1

Since multiplication is commutative, you can change the order of the factors:

$5.1 \times 10^3 \cdot 3.2 \times 10^3 = 5.1 \cdot 3.2 \times 10^3 \cdot 10^3$

So, the numeric parti is simply

$5.1 \cdot 3.2 = 16.32$

For the powers of ten, use the rule $a^b\cdot a^c=a^{b+c}$ to write

$10^3 \cdot 10^3 = 10^{3+3} = 10^6$

So, the answer is

$16.32 \times 10^6$

To write the answer is proper scientific notation, you can write it as

$1.623 \times 10^7$

So, answers A and B represent the same number, and they are both correct. If you need the answer to be written in rigorous scientific notation, then answer is B.

Answer 2

$(5.1\cdot10^3)\cdot(3.2\cdot10^3)=5.1\cdot10^3\cdot3.2\cdot10^3\\\\\text{use commutative property}\ a \cdot b=b\cdot a\\\\=5.1\cdot3.2\cdot10^3\cdot10^3\\\\\text{use associative property}\ (a\cdot b)\cdot c=a\cdot(b\cdot c)\\\\=(5.1\cdot3.2)\cdot(10^3\cdot10^3)\\\\\text{use}\ a^n\cdot a^m=a^{n+m}\\\\=16.32\cdot10^{3+3}=\boxed{16.32\cdot10^6}\to\boxed{A.}$