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Write as a fraction or mixed number. Simplify the answer if possible.
ⓐ ⓑ ⓒ
Write as a fraction or mixed number. Simplify the answer if possible.
ⓐ ⓑ ⓒ
Since decimals are forms of fractions, locating decimals on the number line is similar to locating fractions on the number line.
Locate on a number line.
The decimal is equivalent to so is located between and On a number line, divide the interval between and into equal parts and place marks to separate the parts.
Label the marks
We write
as
and
as
so that the numbers are consistently in tenths. Finally, mark
on the number line.
Locate on a number line.
The decimal
is equivalent to
so it is located between
and
On a number line, mark off and label the hundredths in the interval between
and
(
,
, etc.) and mark
between
and
a little closer to
.
Which is larger, or
If you think of this as money, you know that (forty cents) is greater than (four cents). So,
In previous chapters, we used the number line to order numbers.
Where are and located on the number line?
We see that is to the right of So we know
How does compare to This doesn’t translate into money to make the comparison easy. But if we convert and to fractions, we can tell which is larger.
| Convert to fractions. | ||
| We need a common denominator to compare them. |
 |
|
Because we know that Therefore,
Notice what we did in converting to a fraction—we started with the fraction and ended with the equivalent fraction Converting back to a decimal gives So is equivalent to Writing zeros at the end of a decimal does not change its value.
If two decimals have the same value, they are said to be equivalent decimals.
We say and are equivalent decimals.
Two decimals are equivalent decimals if they convert to equivalent fractions.
Remember, writing zeros at the end of a decimal does not change its value.
Order the following decimals using
ⓐ
ⓑ
| ⓐ | |
| Check to see if both numbers have the same number of decimal places. They do not, so write one zero at the right of 0.6. | |
| Compare the numbers to the right of the decimal point as if they were whole numbers. | |
| Order the numbers using the appropriate inequality sign. |
|
| ⓑ | |
| Check to see if both numbers have the same number of decimal places. They do not, so write one zero at the right of 0.83. | |
| Compare the numbers to the right of the decimal point as if they were whole numbers. | |
| Order the numbers using the appropriate inequality sign. |
|
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