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Express nine times 10 to the sixth power times 11 times 10 to the fourth power in scientific notation.
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To solve this problem, I’m gonna use the communitive property of multiplication.
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The communitive property of multiplication tells me that I can multiply numbers in any order to produce the same outcome.
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So let’s re-group this multiplication.
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Let’s group the nine times 11 together and then group 10 to the sixth power times 10 to the fourth power.
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Nine times 11 is 99.
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10 to the sixth power times 10 to the fourth power equals 10 to the six plus four.
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We add those exponents together.
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So this number is 99 times 10 to the tenth power.
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Unfortunately, this is not scientific notation.
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It looks like it’s almost in scientific notation, 𝑎 times 10 to the 𝑏.
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For scientific notation, we need our 𝑎 to be greater than or equal to one but less than 10.
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Our 99 is larger than 10, so it doesn’t qualify.
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So I’m gonna add a decimal at the end of the 99 and I’ll move the decimal one place to the left.
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Since I moved the decimal one point to the left, I’ll have 99 equal to nine point nine times 10 to the first power.
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We can multiply that by 10 to the tenth power.
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We add the one and the 10 to give us nine and nine tenths times 10 to the 11th power.
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This is the product of the above multiplication problem in scientific notation, nine and nine tenths times 10 to the 11th power.