Question #6232

estimate the order of magnitude of the answer for each of the following calculations:
a) (6.2 x 10^20) x (3.8 x 10^-18) b) (600) x (10 x 10^8)
c) 5.4 x 10^-12 divide by 3.1 x 10^-15
the answers are: a) 10^3 or 10^4 if converted to OM first. b) 10^12
c) 10^3 or 10^4 if converted to OM first.

Expert's answer

a) (6.2×10∧20)×(3.8×10∧−18)=6.2×3.8×10∧(20+(−18))=6.2×3.8×10∧2=23.56×10∧2=2.356×10∧3(6.2 \times 10^{\wedge}20) \times (3.8 \times 10^{\wedge} - 18) = 6.2 \times 3.8 \times 10^{\wedge}(20 + (-18)) = 6.2 \times 3.8 \times 10^{\wedge}2 = 23.56 \times 10^{\wedge}2 = 2.356 \times 10^{\wedge}3

b) (600)×(10×10∧8)=600×10×10∧8=6000×10∧8=6×10∧3×10∧8=6×10∧(8+3)=6×10∧11(600) \times (10 \times 10^{\wedge}8) = 600 \times 10 \times 10^{\wedge}8 = 6000 \times 10^{\wedge}8 = 6 \times 10^{\wedge}3 \times 10^{\wedge}8 = 6 \times 10^{\wedge}(8 + 3) = 6 \times 10^{\wedge}11

c) 5.4×10∧−125.4 \times 10^{\wedge} - 12 divide by 3.1×10∧−15=(5.4/3.1)×10∧(−12−(−15))=1.741935484×10∧33.1 \times 10^{\wedge} - 15 = (5.4 / 3.1) \times 10^{\wedge}(-12 - (-15)) = 1.741935484 \times 10^{\wedge}3

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Canada #340153 on Dec 2023