Locating and Ordering Decimals With a Number Line
Learning Outcomes
- Locate decimals on a number line
- Order decimals using inequality notation
Since decimals are forms of fractions, locating decimals on the number line is similar to locating fractions on the number line.
Exercises
Locate on a number line. Solution 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.
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[ohm_question]146228[/ohm_question] Locate on a number line.Answer:
example
Locate on a number line.Answer:
Solution
The decimal is equivalent to , so it is located between and . On a number line, mark off and label the multiples of in the interval between and ( , , etc.) and mark between and , a little closer to .
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[ohm_question]146577[/ohm_question] [ohm_question]146578[/ohm_question]Order Decimals
Which is larger, or If you think of this as money, you know that $0.40 (forty cents) is greater than $0.04 (four cents). So, In previous chapters, we used the number line to order numbers. Where are and located on the number line?
Convert to fractions. | ||
We need a common denominator to compare them. | ||
Equivalent Decimals
Two decimals are equivalent decimals if they convert to equivalent fractions.Order decimals
- Check to see if both numbers have the same number of decimal places. If not, write zeros at the end of the one with fewer digits to make them match.
- Compare the numbers to the right of the decimal point as if they were whole numbers.
- Order the numbers using the appropriate inequality sign.
example
Order the following decimals using ⓐ 0.64__0.6 ⓑ 0.83__0.803Answer: Solution
ⓐ | |
0.64__0.6 | |
Check to see if both numbers have the same number of decimal places. They do not, so write one zero at the right of . | 0.64__0.60 |
Compare the numbers to the right of the decimal point as if they were whole numbers. | |
Order the numbers using the appropriate inequality sign. |
ⓑ | |
0.83__0.803 | |
Check to see if both numbers have the same number of decimal places. They do not, so write one zero at the right of . | 0.830__0.803 |
Compare the numbers to the right of the decimal point as if they were whole numbers. | |
Order the numbers using the appropriate inequality sign. |
try it
[ohm_question]146232[/ohm_question] [ohm_question]146237[/ohm_question] [ohm_question]146238[/ohm_question]
example
Use ; to order. -0.1__ - 0.8.Answer: Solution
-0.1__ - 0.8 | |
Write the numbers one under the other, lining up the decimal points. | |
They have the same number of digits. | |
Since tenth is greater than tenths. |