Question

Work out (5*10^3)*(9*10^7).

Give your answer in standard form.

Work out (7*10^5) / (2*10^2).
Give your answer in standard form.

Answer 1

(5*10^3)*(9*10^7) = 4.5*10^11

(7*10^5) / (2*10^2) = 3.5*10^3

Explanation:

calculate 5 multiply by 9

5*9=45

the multiple of the power in the same base of number is calculated by using addition(+)

(10^3)*(10^7) = 10^(3+7)

= 10^10

in standard form, it should be written as x*10^n, and x is only allowed from 1-9, so

45*(10^10)

= (4.5*10^1) * (10^10)

= 4.5*10^(1+10)

= 4.5*10^11

calculate 7 divide by 2

7/2=3.5

the dividing of the power in the same base of number is calculated by using subtraction(-)

(10^5)/(10^2)

= 10^(5-2)

= 10^3

in standard form, it should be written as x*10^n, and x is only allowed from 1-9, so

3.5*10^3

Answer 2

→ (5×10³)×(9×10⁷) = 4.5 × 10¹¹

→ (7×10⁵) / (2×10²) = 3.5 × 10³

Explanation:

(5×10³)×(9×10⁷)

= 5×10³×9×10⁷

= 5×9×10³×10⁷ (commutative property)

= (5×9)×(10³×10⁷) (associative property)

= 45 × 10³⁺⁷

= 45 × 10¹⁰. (Exponent property)

= 4.5 × 10¹¹

…………………………………………

(7×10⁵) / (2×10²)

= (7/2) × (10⁵/10²)

= 3.5 × 10⁵⁻²

= 3.5 × 10³