Video: Expressing Numbers in Scientific Notation

Write 782 million in scientific notation.

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Video Transcript

Write 782 million in scientific notation.

As one million is written as one with six zeros following it, 782 million will be 782 followed by six zeros. A number can be written in scientific notation in the form 𝑎 multiplied by 10 to the power of 𝑏 where 𝑎 is greater than or equal to one and less than 10 and 𝑏 is an integer value, positive or negative.

In this case, our value for 𝑎 will be 7.82 as we must place the decimal point between the seven and eight so that our value of 𝑎 is between one and 10. In order to work out the exponent, 𝑏, we look at how many places we have to move the decimal point. In this case we have to move the decimal point eight places to the left.

Therefore, our exponent or power is eight. This means that 782 million can be written in scientific notation as 7.82 multiplied by 10 to the power of eight. In order to check our answer, we can multiply 7.82 by 10 to the power of eight.

This would involve moving the decimal point eight places to the right and would return us to the number in our question, 782 million. Scientific notation is a really useful way of writing very large or very small numbers.

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