Video Transcript
Which of the following is closest to one million? Option (A) 1.8 times 10 raised to the fifth power. Option (B) 1.8 times 10 raised to the sixth power. Option (C) 18 million. Option (D) 1.8 times 10 raised to the eighth power. Or is it option (E) 1.8 times 10 raised to the ninth power?
In this question, we are asked to determine which of five given numbers is closest to one million. And we can see that four of these numbers are given in scientific notation.
There are a few different ways of answering this question. For instance, we could rewrite all of the options to be in normal form to see which is closest to one million. However, we are going to start by comparing the sizes of all of the options and one million. We can first note that one million is equal to one times 10 raised to the sixth power.
We can also rewrite option (C) into scientific notation. Remember, each time we multiply by 10, we move the decimal point one place to the right. We can see that moving the decimal point in 1.8 seven places to the right gives us 18 million. So 18 million is equal to 1.8 times 10 raised to the seventh power.
We can now compare the sizes of the numbers in the options with one million. First, we note that all of the numbers are positive and that the power of 10 in option (A) is the smallest. So option (A) is the smallest number.
Next, we note that option (B) and one million both have 10 raised to the sixth power. Therefore, to compare these numbers, we need to compare the sizes of the first factor. We note that one is smaller than 1.8. Hence, one million is smaller than the value in option (B).
Although it is not necessary, we can order the rest of the options by ordering the powers of 10. We see that (C) is smaller than (D) is smaller than (E). This means that we only need to check which of values (A) and (B) is closest to one million. We can do this by writing both numbers in normal form.
Let’s start by rewriting 1.8 times 10 raised to the fifth power. We need to move the decimal point five places to the right. Doing this gives us 180,000. We can follow the same process for 1.8 times 10 raised to the sixth power. We move the decimal point six places to the right to obtain 1,800,000.
We can then find the number closer to one million by considering their differences with one million. We first calculate that one million minus 180,000 is 820,000. Similarly, we calculate that one million minus 1,800,000 is equal to negative 800,000. Therefore, we can see that option (B) is 800,000 away from one million. But option (A) is 820,000 away from one million. So option (B), 1.8 times 10 raised to the sixth power, is the closest to one million.
