Video Transcript
Express 3.06707 times 10 raised to the 10th power in normal form.
In this question, we are asked to convert a number given in scientific notation back into normal form.
To do this, we note that we are multiplying a decimal number by an integer power of 10. And we can recall that each multiple of 10 will move the decimal point. If the exponent is positive, we move the decimal point to the right. If it is negative, we move it to the left. For instance, 3.0 times 10 raised to the first power is equal to 30. Similarly, 3.06 times 10 squared will be equal to 306.
The same method works regardless of how high or low the exponent of 10 is, as long as it is an integer. And it also works for any number of decimal places. For instance, 3.06707 times 10 squared is 306.707. We want to use this idea to rewrite 3.06707 times 10 raised to the 10th power in normal form. This means that we want to move the decimal point 10 places to the right.
To help us calculate this, we first note that if we multiply the decimal by 10 raised to the fifth power, then we remove all of the decimal places in our answer, and we’re left with an integer. We need to multiply by another five factors of 10, so we need to add five extra digits of zero onto this value, as shown. Finally, we can improve the readability of the value in normal form by adding commas. We obtain 30,670,700,000.
