Sovi.AI - AI Math Tutor

Scan to solve math questions

QUESTION IMAGE

7) scientific notation is a way to express extremely big and extremely …

Question

  1. scientific notation is a way to express extremely big and extremely small numbers using exponents. for example, the water surface area of the earth is 1.4 x 10^8. how would this number be written in standard form? 8) extremely small numbers are expressed with negative exponents. for example, the mass of a dust particle is 7.53 x 10^-10. this means the same thing as 7.53 ÷ 10^10. how would this number be written in standard form?

Explanation:

Step1: Convert \(1.4\times10^{8}\) to standard form

When converting \(a\times10^{n}\) (\(n>0\)) to standard form, we move the decimal point \(n\) places to the right. For \(1.4\times10^{8}\), \(n = 8\).

$$1.4\times10^{8}=140000000$$

Step2: Convert \(7.53\times10^{- 10}\) to standard form

When converting \(a\times10^{-n}\) (\(n>0\)) to standard form, we move the decimal point \(n\) places to the left. For \(7.53\times10^{-10}\), \(n = 10\).

$$7.53\times10^{-10}=0.000000000753$$

Answer:

  1. \(140000000\)
  2. \(0.000000000753\)