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Place Value and Comparing Decimals

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Place Value for Decimals

Just as "ones," "tens," and "hundreds" are used to describe place
value for whole numbers, there are terms that
describe place value for decimals: tenths, hundredths, thousandths, ten
thousandths, hundred thousandths, millionths, etc. These terms are used from
left to right, starting with the first numeral after the decimal point. For
example, the number 0.1234 has a "1" in the tenths place, a "2" in the
hundredths place, a "3" in the thousandths place, and a "4" in the ten
thousandths place. The number 78.304 has a "7" in the tens place, an "8" in the
ones place, a "3" in the tenths place, a "0" in the hundredths place, and a "4"
in the thousandths place.

Because our system is base ten, a value of 10
in one place is equal to a value of 1 in the place to the left: 10 thousandths
is equivalent to 1 hundredth, 10 hundredths is equivalent to 1 tenth, 10 tenths
is equivalent to 1 one, and so on.

*Example 1.* What are the place values for 67.0534?

67.0534 has a **6** in the **tens** place, a **7** in the **ones**
place, a in the tenths place, a **5** in the **hundredths**
place, a **3** in the **thousandths** place, and a **4** in the **ten
thousandths** place.

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A Fact about Decimals

A decimal does not change when zeros are added at the end. For example, 3.45 is
equal to 3.450 is equal to 3.4500, and so on.

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Comparing Decimals

It is sometimes tricky to determine which decimal is the larger of two decimals.
Upon first glance, it appears that 0.304 is larger than 0.62, because 304 is
larger than 62. However, this is **not** the case. In order to determine
which decimal is larger, we must compare the two place-by-place, starting from
the tenths place, until the decimals differ. 0.304 has a "3" in the tenths
place, and 0.62 has a "6" in the tenths place. Since 6 is greater than 3, 0.62
is greater than 0.304--it is not necessary to look to further decimal places.

*Example 2.* Compare 0.4531 and 0.4507. Which is greater?

0.4531 and 0.4507 both have a "4" in the tenths place.

0.4531 and 0.4507 both have a "5" in the hundredths place.

0.4531 has a "3" in the thousandths place and 0.4507 has a "0" in the
thousandths place.

3 is greater than 0, so 0.4531 is greater than 0.4507.