Question

a. write 5.3 as a product of a whole number times a power of 10.
5.3 = ____ × 10—
b. write 0.87 as a product of a whole number times a power of 10.
0.87 = ____ × 10—
c. find the product of the two expressions above.
(__ × 10—) × ( × 10—) = ( × ) × (10— × 10—) = __ × 10—
d. rewrite the product from part c as a decimal.

Explanation:

Step1: Rewrite 5.3 in scientific notation

To get a whole number, use 53, and since we move the decimal left 1 place, the exponent is -1.
$5.3 = 53 \times 10^{-1}$

Step2: Rewrite 0.87 in scientific notation

To get a whole number, use 87, and since we move the decimal right 2 places, the exponent is -2.
$0.87 = 87 \times 10^{-2}$

Step3: Multiply the two expressions

Group whole numbers and powers of 10. Use exponent rule $10^a \times 10^b = 10^{a+b}$.
$(53 \times 10^{-1}) \times (87 \times 10^{-2}) = (53 \times 87) \times (10^{-1} \times 10^{-2}) = 4611 \times 10^{-3}$

Step4: Convert product to decimal

$10^{-3}$ means divide by 1000, so move decimal left 3 places.
$4611 \times 10^{-3} = 4.611$

Answer:

a. $53 \times 10^{-1}$
b. $87 \times 10^{-2}$
c. $(53 \times 10^{-1}) \times (87 \times 10^{-2}) = (53 \times 87) \times (10^{-1} \times 10^{-2}) = 4611 \times 10^{-3}$
d. $4.611$