Video Transcript
Write three plus seven multiplied by 10 plus eight multiplied by 10 squared plus six multiplied by 10 cubed plus six multiplied by 10 to the power of four plus two multiplied by 10 to the power of five in standard form.
We begin by recalling that a number is written in standard form, also called scientific notation, if it is in the form 𝑎 multiplied by 10 to the power of 𝑛, where the absolute value of 𝑎 must be greater than or equal to one and less than 10 and 𝑛 is an integer.
Whilst we could begin by writing all the individual products with the same power of 10, in this question it is easier to write them all as ordinary numbers first. Seven multiplied by 10 is equal to 70. Eight multiplied by 10 squared is equal to eight multiplied by 100, which is 800. Six multiplied by 10 cubed equals 6,000. Continuing this process, six multiplied by 10 to the power of four is equal to 60,000. And two multiplied by 10 to the power of five is 200,000. Substituting these values into our original expression, we have three plus 70 plus 800 plus 6,000 plus 60,000 plus 200,000, which is equal to 266,873.
We now need to write this number in standard form. Since our value of 𝑎 must be greater than or equal to one and less than 10, we have 2.66873 multiplied by 10 to the power of five, which is the value of the original expression in standard form.
Whilst it is not required in this question, we often round the value of 𝑎 to a given degree of accuracy. For example, to one decimal place, our answer in standard form or scientific notation would be 2.7 multiplied by 10 to the power of five.
