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### Course: 5th grade (Eureka Math/EngageNY) > Unit 1

Lesson 2: Topic B: Decimal fractions and place value patterns- Write decimals in expanded form
- Decimals in expanded form
- Decimals in expanded form review
- Decimals in written form (hundredths)
- Decimals in written form (thousandths)
- Decimals in written form
- Decimals in written form review
- Expressing decimals in multiple forms
- Decimals in written and expanded form
- Visual understanding of regrouping decimals
- Write common fractions as decimals
- Comparing decimals: 9.97 and 9.798
- Comparing decimals: 156.378 and 156.348
- Compare decimals through thousandths
- Comparing decimals in different representations
- Compare decimals in different forms
- Order decimals
- Comparing decimals word problems
- Compare decimals word problems
- Regroup decimals
- Ordering decimals
- Ordering decimals through thousandths

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# Comparing decimals word problems

Explore the concept of comparing decimals. Learn the importance of aligning place values and starting from the largest place value when comparing. The video also demonstrates that more digits doesn't necessarily mean a larger number.

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## Video transcript

- [Lecturer] Al is comparing
two recipes for homemade bread. The recipe for white bread calls for 4/10 of a kilogram of flour. The recipe for whole wheat bread calls for 385/1000 of a kilogram of flour. Which bread takes less flour? So the white bread calls
for 4/10 of a kilogram, while the recipe of whole
wheat bread calls for 0.385 kilograms, or
385/1000 of a kilogram. Now the way I wrote it is important. You always want to line up the decimals when you are comparing,
because you want to compare numbers in the same place value. And this is an interesting
example of even though the number down here has
more digits it doesn't mean that it's necessarily a larger number. What we want to do when we compare numbers and this is true whether we're
dealing with decimals or not, is we start in the largest place value. We could start in the ones place, 'cause both of these have zero ones. Then we go one place value
down, we go to the tenths place. The white bread, it requires 4/10 of flour while in the whole wheat bread
we only have 3/10 of flour. So we can stop right there. This has more tenths than this does. It doesn't matter that this has more hundredths and thousandths. Those are less significant. They don't add up to as much
as what we're dealing with when we look just at the tenths place. So because four is greater than three, and we're in the tenths place
we know that white bread takes more flour, but we
have to be very careful. They said which bread takes less flour? So it's going to be whole wheat bread. Three is less than four. Let's do another one of these. A group of fifth graders kept track of the number of hours they spent working on their science project right? Put the students in order from the least to greatest amount of time spent. The student with the least amount of time should be at the top of the list. So pause this video and
see if you can do this. And this is actually a screenshot from the Khan Academy exercise. If you're doing the Khan Academy exercise you'd actually be able to click on these and move them around. But let's compare them. So as I mentioned in the last example, when you're comparing numbers it's good to line up the place
values, so let's do that. So Adam is 5.5. Aviv is five, and Jenny is 5.17. So once again, start at
the largest place value. Start at the ones. They all have exactly five ones, so then we move to the next place value. In this case, we're going
to go to the tenths place. So when we look at the tenths place, interesting things are going on. Aviv has no tenths. It's a blank here, but
you could do this as 5.0. So Aviv has the fewest tenths, then comes Jenny with only 1/10
and then Adam has 5/10. So that tells us enough so
that we can order the three. We don't even have to look
at the hundredths place because the tenths here are different. So the least number of tenths is Aviv, so that's going to be Aviv is the least. They all have the same number of ones, but Aviv has the least tenths. Then comes Jenny. Jenny, once again, they all
have the same number of ones but then Jenny has less tenths than Adam, and then comes Adam. Adam has the most tenths. It doesn't matter that
Jenny also has 7/100. Notice you could view this as 17/100 which is going to be less than 5/10 which could also be viewed as 50/100. So the general way to think about it, start at the most significant, the largest place value, compare. If things are equal, go
to the next place value. When things are different, then you have enough information to start ordering them.