Regrouping decimal numbers
Regrouping with decimals: 86.93
We're asked to fill in the blanks to complete the equation. So they have 86.93 is equal to 5 tens plus blank ones plus 9 tenths plus 3 hundredths. So let me expand out 86.93 and just think about how I could regroup the value in the different places so that I get something more close or exactly what we have on the right-hand side. So the 8 in 86.93, that's in the tens place. So it literally represents 8 tens. So I can write that down as 80. The 6 in 86 represents 6 ones. So I can write that down as 6. Then the 9 in 86.93, that's 9 tenths. So I could write that down. I could write this 9. That's right of the decimal place. This is plus 9 tenths. And then the 3 in 86.93, that is in the hundredths place. It represents 3 hundredths. So this is plus 3 over 100. So I've expanded out the number that I have on the left. Now let me write out what they have on the right again. So this is going to be equal to-- they have 5 tens here. So I'll write all the tens places in this red color. Then they have blank ones. So I'm just going to literally write out a blank plus 9 tenths. So the 9 tenths is still 9 tenths plus 3 hundredths. So let me make sure that we color code this. So that's the 9 tenths. This is the 5 tens. That's the 50. We have the blank ones. That's this right over here, 9 tenths. And then finally we have the 3 hundredths, so plus 3 over 100. So how do we get the right-hand side to be the exact same thing as the left-hand side by adjusting this blank? Well, both sides have a 3/100 on it, both sides have a 9/10 on it. And so what's really different about the two sides is on the left-hand side-- let me do this in a color we can actually see. On the left-hand side you have an 80 plus a 6. On the right-hand side you have a 50 plus a blank. So 80 plus 6 is clearly 86. Well, what has to be added to 50 to get to 86? Well, you have to add 36. So now both sides add up to the same thing. 80 plus 6 is 86. 50 plus 36 is 86. Then you have 9/10, 9/10, 3/100, 3/100. Now, you might be saying, hey wait, you wrote a 36 here. Does this literally means 36 ones? And I will say yes, it literally represents 36 ones. This is the same thing as 36 times 1. So we can fill in the blank here. 86.93 is equal to 5 tens plus 36 ones plus 9 tenths plus 3 hundredths. And I encourage you to add this up. You will get 86.93. Now, what have we essentially done here? What we essentially did, if you compare the 8 and the 5 right over here, you see that we took 3 from the tens place. But taking 3 from the tens place is essentially taking 30 from the value that it represents. So we took 30 from the tens place, and we gave that 30 to the ones place. So you had 86. You take 30 away, you have 50 in the tens place, represented by this 5. And then you give that 30 to the ones place, you have 36. You have 36 ones.