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 [latex]0.4[/latex] on a number line. Solution The decimal [latex]0.4[/latex] is equivalent to [latex]\frac{4}{10}[/latex], so [latex]0.4[/latex] is located between [latex]0[/latex] and [latex]1[/latex]. On a number line, divide the interval between [latex]0[/latex] and [latex]1[/latex] into [latex]10[/latex] equal parts and place marks to separate the parts. Label the marks [latex]0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0[/latex]. We write [latex]0[/latex] as [latex]0.0[/latex] and [latex]1[/latex] as [latex]1.0[/latex], so that the numbers are consistently in tenths. Finally, mark [latex]0.4[/latex] on the number line.try it
[ohm_question]146228[/ohm_question] Locate [latex]0.6[/latex] on a number line.Answer:
example
Locate [latex]-0.74[/latex] on a number line.Answer: Solution The decimal [latex]-0.74[/latex] is equivalent to [latex]-\frac{74}{100}[/latex], so it is located between [latex]0[/latex] and [latex]-1[/latex]. On a number line, mark off and label the multiples of [latex]-0.10[/latex] in the interval between [latex]0[/latex] and [latex]-1[/latex] ( [latex]-0.10[/latex] , [latex]-0.20[/latex] , etc.) and mark [latex]-0.74[/latex] between [latex]-0.70[/latex] and [latex]-0.80[/latex], a little closer to [latex]-0.70[/latex] .
try it
[ohm_question]146577[/ohm_question] [ohm_question]146578[/ohm_question]Order Decimals
Which is larger, [latex]0.04[/latex] or [latex]0.40?[/latex] If you think of this as money, you know that [latex]$0.40[/latex] (forty cents) is greater than [latex]$0.04[/latex] (four cents). So, [latex-display]0.40>0.04[/latex-display] In previous chapters, we used the number line to order numbers. [latex-display]\begin{array}{}\\ a<b\text{ }a\text{ is less than }b\text{ when }a\text{ is to the left of }b\text{ on the number line}\hfill \\ a>b\text{ }a\text{ is greater than }b\text{ when }a\text{ is to the right of }b\text{ on the number line}\hfill \end{array}[/latex-display] Where are [latex]0.04[/latex] and [latex]0.40[/latex] located on the number line? We see that [latex]0.40[/latex] is to the right of [latex]0.04[/latex]. So we know [latex]0.40>0.04[/latex]. How does [latex]0.31[/latex] compare to [latex]0.308?[/latex] This doesn’t translate into money to make the comparison easy. But if we convert [latex]0.31[/latex] and [latex]0.308[/latex] to fractions, we can tell which is larger.[latex]0.31[/latex] | [latex]0.308[/latex] | |
Convert to fractions. | [latex]\frac{31}{100}[/latex] | [latex]\frac{308}{1000}[/latex] |
We need a common denominator to compare them. | [latex]\frac{31\cdot\color{red}{10}}{100\cdot\color{red}{10}}[/latex] | [latex]\frac{308}{1000}[/latex] |
[latex]\frac{310}{1000}[/latex] | [latex]\frac{308}{1000}[/latex] |
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 [latex]<\text{or}\text{>:}[/latex] ⓐ [latex]0.64__0.6[/latex] ⓑ [latex]0.83__0.803[/latex]Answer: Solution
ⓐ | |
[latex]0.64__0.6[/latex] | |
Check to see if both numbers have the same number of decimal places. They do not, so write one zero at the right of [latex]0.6[/latex]. | [latex]0.64__0.60[/latex] |
Compare the numbers to the right of the decimal point as if they were whole numbers. | [latex]64>60[/latex] |
Order the numbers using the appropriate inequality sign. | [latex]0.64>0.60[/latex] [latex]0.64>0.6[/latex] |
ⓑ | |
[latex]0.83__0.803[/latex] | |
Check to see if both numbers have the same number of decimal places. They do not, so write one zero at the right of [latex]0.83[/latex]. | [latex]0.830__0.803[/latex] |
Compare the numbers to the right of the decimal point as if they were whole numbers. | [latex]830>803[/latex] |
Order the numbers using the appropriate inequality sign. | [latex]0.830>0.803[/latex] [latex]0.83>0.803[/latex] |
try it
[ohm_question]146232[/ohm_question] [ohm_question]146237[/ohm_question] [ohm_question]146238[/ohm_question]example
Use [latex]<\text{or}>[/latex]; to order. [latex]-0.1__ - 0.8[/latex].Answer: Solution
[latex]-0.1__ - 0.8[/latex] | |
Write the numbers one under the other, lining up the decimal points. | [latex]-0.1[/latex] [latex]-0.8[/latex] |
They have the same number of digits. | |
Since [latex]-1>-8,-1[/latex] tenth is greater than [latex]-8[/latex] tenths. | [latex]-0.1>-0.8[/latex] |
try it
[ohm_question]146239[/ohm_question]Licenses & Attributions
CC licensed content, Original
- Question ID 146237, 146238, 146239. Authored by: Lumen Learning. License: CC BY: Attribution.
CC licensed content, Shared previously
- Example: Identify Decimals on the Number Line. Authored by: James Sousa (Mathispower4u.com). License: CC BY: Attribution.
- Decimal Notation: Ordering Decimals. Authored by: James Sousa (Mathispower4u.com). License: CC BY: Attribution.
CC licensed content, Specific attribution
- Prealgebra. Provided by: OpenStax License: CC BY: Attribution. License terms: Download for free at http://cnx.org/contents/[email protected].