Video Transcript
Complete 5.91 times 10 what 591 divided by 100 using the symbol for is less than, is equal to, or is greater than.
In this problem, we have two calculations. The first is a multiplication, 5.91 times 10. The second calculation involves some similar digits. This time it’s a division, 591 divided by 100. Now, in between our two calculations, there’s a space. And we need to choose the correct symbol to go in between these two statements. Should we say that 5.91 times 10 is less than 591 divided by 100, is equal to 591 divided by 100? Or should we say that it’s greater than 591 divided by 100?
To answer this question correctly, we need to think about how the digits in numbers behave when they’re multiplied or divided by numbers like 10, 100, 1000, and so on. Let’s sketch a place value grid to help us do this. Now, to begin with, let’s look at the multiplication part of our statement. We need to multiply 5.91 by 10. So let’s begin by writing the digits 5.91 in the correct places on our grid. And when our number is multiplied by 10, its digits become 10 times greater.
Now, we know that each column to the left of another column is 10 times greater. So, for example, 10 times greater than the ones column is the tens column. So instead of five ones, the five digit shifts to be now worth five tens. Instead of nine tenths, the nine digit shifts one place to now be worth nine ones. And instead of one hundredth, the one digit shifts to now become worth one tenth. The whole number has shifted one place to the left. This is what multiplying by 10 does. And so, the value of the first expression, which is 5.91 times 10, is 59.1.
Now, let’s think about the division part of our expression, 591 divided by 100. We can start by writing the number 591 in our place value grid. Because when a number is divided by 10, 100, 1000, and so on, its digits shift again. This time they shift to the right. Now, as we’ve already said, if we shift the digits one place, this is the same as dividing or multiplying by 10. Well, 100 is 10 times 10. So we need to shift our digits two places to the right. And so, one whole divided by 100 now becomes worth one hundredth. And if we shift nine tens, they now become worth nine tenths. And finally, if we shift the digit five, which is worth five hundreds, and we divide by 100, it’s now going to be worth five ones. 591 divided by 100 has a value of 5.91. We can see that the number on the left, 59.1, is greater than the number on the right, 5.91.
Remember, when we’re using comparison symbols and we’re not sure which one to write. We always write the part with the widest opening towards the greater value. So this symbol means is greater than. We looked at how digits in numbers move when they’re multiplied or divided by 10 and 100 to find out the value of each statement. 5.91 times 10 is greater than 591 divided by 100. The correct symbol is: is greater than.
