Expressing Numbers in Scientific Notation (Standard Form)

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Expressing Numbers in Scientific Notation (Standard Form) Suppose we have two numbers 59760000 & 528000000 How do we compare them? Comparing them becomes difficult when the number are large. So, we write both number in standard form 59760000 So, our two numbers are 5.976 × 10^7 5.28 × 10^8 = 5976 × 10^4 = (5.976 × 10^3) × 10^4 = 5.976 × 10^3 × 10^4 Using 𝑎^𝑚 × 𝑎^𝑛 = 𝑎^(𝑚 + 𝑛) = 5.976 × 10^(3 + 4) = 5.976 × 10^7 Higher Power 528000000 = 528 × 10^6 = (5.28 × 10^2) × 10^6 = 5.28 × 10^2 × 10^6 Using 𝑎^𝑚 × 𝑎^𝑛 = 𝑎^(𝑚 + 𝑛) = 5.28 × 10^(2 + 6) = 5.28 × 10^8 So, 5.28 × 10^8 > 5.976 × 10^7 Here, Standard form is In standard form We write number as power of 10 There is only 1 digit before decimal point Let’s take some more examples Write 28488 in standard form 28488 = 2.8488 × 10^4 Write 8680 in standard form 8680 = 868 × 10^1 = 8.68 × 10^2 × 10^1 = 8.68 × 10^(2 + 1) = 8.68 × 10^3 Write 35.89 in standard form 35.89 = 3589/100 = 3589 × 1/100 = 3589 × 1/10^2 = (3.589 × 103) × 1/10^2 = 3.589 × 10^3/10^2 = 3.589 × 10^(3 − 2) = 3.589 × 10^1 ("Using " 𝑎^𝑚/𝑎^𝑛 " = " 𝑎^(𝑚 − 𝑛) " " ) Write 2.008 in standard form 2.008 = 2.008 × 10^0 Write 0.00008 in standard form 0.00008 = 8/100000 = 8/10^5 = 8 × 10^(−5) Write 0.0092 in standard form 0.0092 = 92/10000 = 92 × 1/10000 = 9.2 × 10 × 1/10000 = 9.2 × 1/1000 = 9.2 × 1/10^3 = 9.2 × 10^(−3)