Ex: Measure Lengths in Centimeters – Decimal Notation and Mixed Numbers
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We’re determining the length of each bar. First thing we should
notice is that the units are centimeters, and
whenever expressing a length it is important to include the units. Next, notice how each
centimeter is partitioned or cut into smaller equal pieces. Notice there are 10 tick
marks between each centimeter and therefore each tick mark represents 1/10 of a centimeter. And we’ll express our lengths
both in decimal notation as well as using fractions
just to make a connection. It is normally common to express a length in centimeters using decimal notation. So starting here we can count the number of whole centimeters here, one, two, three, four, five, six, seven, eight, nine, 10. You’ll notice how the length is longer than 10 centimeters. So from here we can count
the number of tick marks, which again, each tick mark represents 1/10 of a centimeter. So we have one, two, three,
four, 5/10 of a centimeter longer than 10 centimeters,
so the total length would be 10 5/10 of a
centimeter, which we can write as 10.5 centimeters using decimal notation, or in fraction notation we
could say 10 5/10 centimeters. We normally don’t express
a mixed number in this form because this fraction can be simplified, meaning we can use larger
partitions than 10ths to express this length as a mixed number. So going back to the ruler,
we know from 10 centimeters to 11 centimeters is one centimeter. So if we partition this
length into smaller lengths, let’s say half centimeters
here, we can see this length is exactly 10 1/2 centimeters. So instead of 10 5/10 it would
be better to express this as 10 1/2 centimeters. And again, normally when
expressing length in centimeters we do only express it
using decimal notation or this notation here. Let’s take a look at our second example. Starting here, again
we’ll count the number of complete centimeters. So one, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13, 14, and again, then length is longer than 14 centimeters. So let’s count the number of tick marks. It might be hard to see on the screen, but we have 1/10, 2/10, 3/10, 4/10 of a centimeter longer
than 14 centimeters. So we have 14 4/10 centimeters, which we can write using decimal notation as 14.4 centimeters, or using mixed numbers
we could say 14 4/10. And again, we can simplify
4/10 or express this using larger partitions. If you look at the centimeter
from 14 centimeters to 15 centimeters you
know it’s already divided into 10 equal pieces. So if we partition this one centimeter into five equal partitions,
each partition consisting of 2/10 of a centimeter,
we’d have a partition here, here, here, and here. It’s probably hard to see. That would be 2/5 of a centimeter, so it’s better to express 4/10 as 2/5. Another way to do this
would be to start with 4/10 and divide out the common factor of two. Four divided by two is two,
10 divided by two is five. So 4/10 is equivalent to 2/5, but 2/5 is a simplified fraction and therefore the best way to
write this as a mixed number. But once again when expressing
a length using centimeters, we’re mainly only concerned
about the decimal notation. I hope you found this explanation helpful.

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