Video: Comparing Large Numbers

Which of the following numbers could complete the expression 51416427958 < _ < 51614427958? [A] 51426427958 [B] 51415427958 [C] 51316427958 [D] 51714427958.

03:02

Video Transcript

Which of the following numbers could complete the expression 51416427958 is less than some number which is less than 51614427958?

One key here is noticing that we’re dealing with two less than symbols. This means we’re working from the least to the greatest and we need a value between these two outer numbers. Both of the outer numbers have 51 billions. That means that our number in the middle will need 51 billion. All four of our answer choices have 51 billion.

So we can move to our hundred millions. So we’ll move to the hundred millions. Our least value — our number on the left — has a four in the hundred millions place. Our greatest value has a six in the hundred millions place. This means that our value in the middle, we’ll have a number between 400 million and 600 million.

Our first answer choice has a four in the hundred millions, so does our second answer choice. The third answer choice has a three in the hundred millions place. This value is too small. Our fourth answer choice has a seven in the hundred millions place. This value is too large.

Now, let’s take a closer look at the millions place all together. Our smallest number has 416 million and our largest number has 614 million. Which of our answer choices fall between 416 million and 614 million? 426 is larger than 416 and it’s smaller than 614. 415 million is smaller than 416 million. Answer choice b does not fall between our smallest and largest value.

Here’s what we found: 51426427958 completes our expression. It is between the two values we were given.

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