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Express (9 × 10⁶)(11 × 10⁴) in scientific notation.
Express nine times 10 to the sixth power times 11 times 10 to the fourth power in scientific notation.
To solve this problem, I’m gonna use the communitive property of multiplication. The communitive property of multiplication tells me that I can multiply numbers in any order to produce the same outcome. So let’s re-group this multiplication.
Let’s group the nine times 11 together and then group 10 to the sixth power times 10 to the fourth power. Nine times 11 is 99. 10 to the sixth power times 10 to the fourth power equals 10 to the six plus four. We add those exponents together. So this number is 99 times 10 to the tenth power. Unfortunately, this is not scientific notation. It looks like it’s almost in scientific notation, 𝑎 times 10 to the 𝑏.
For scientific notation, we need our 𝑎 to be greater than or equal to one but less than 10. Our 99 is larger than 10, so it doesn’t qualify. So I’m gonna add a decimal at the end of the 99 and I’ll move the decimal one place to the left.
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. We can multiply that by 10 to the tenth power. We add the one and the 10 to give us nine and nine tenths times 10 to the 11th power. This is the product of the above multiplication problem in scientific notation, nine and nine tenths times 10 to the 11th power.
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