Question Video: Number Operations in Scientific Notation

Work out the value of (3 × 10⁴) × (1.2 × 10⁷), giving your answer in scientific notation.

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Video Transcript

Work out the value of three times 10 to the four times 1.2 times 10 to the power of seven, giving your answer in scientific notation.

Well, with multiplication, it doesn’t actually matter what order we multiply these things together in, so I can get rid of those parentheses straight away. So, that’s the same as three times 10 to the four times 1.2 times 10 to the power of seven. Now, we can multiply the 10 to the four and the 10 to the seven together, and we can multiply the three by the 1.2. Now, three times 1.2 is 3.6. And if I multiply by 10 four times and then another seven times, I’ve multiplied by 10 11 times. That’s 10 to the power of 11. So, that’s equal to 3.6 times 10 to the power of 11.

Now, remember, to be in proper scientific notation, the number must be in this format, 𝑎 times 10 to the power of 𝑏, where 𝑎 is a number between one and 10. It can be equal to one, but it can’t be equal to 10. And 𝑏 is a positive or negative power or exponent of 10. Now, in our case, the 𝑎 value, this 3.6, that is in the right range. It’s bigger than or equal to one, but it’s less than 10. And we have, in this case, a positive power, or exponent, of 10. So, our answer is 3.6 times 10 to the power of 11.

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