Since decimals are forms of fractions, locating decimals on the number line is similar to locating fractions on the number line.
In the next video we show more examples of how to locate a decimal on the number line.
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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]0.40>0.04[/latex]
In previous chapters, we used the number line to order numbers.
[latex]begin{array}{} a<btext{ , }atext{ is less than }btext{ when }atext{ is to the left of }btext{ on the number line}hfill a>btext{ , }atext{ is greater than }btext{ when }atext{ is to the right of }btext{ on the number line}hfill end{array}[/latex]
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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]{Largefrac{31}{100}}[/latex] [latex]{Largefrac{308}{1000}}[/latex] We need a common denominator to compare them. [latex]{Largefrac{31cdotcolor{red}{10}}{100cdotcolor{red}{10}}}[/latex] [latex]{Largefrac{308}{1000}}[/latex] [latex]{Largefrac{310}{1000}}[/latex] [latex]{Largefrac{308}{1000}}[/latex]
Because [latex]310>308[/latex], we know that [latex]{Largefrac{310}{1000}}>{Largefrac{308}{1000}}[/latex]. Therefore, [latex]0.31>0.308[/latex].
Notice what we did in converting [latex]0.31[/latex] to a fraction—we started with the fraction [latex]Largefrac{31}{100}[/latex] and ended with the equivalent fraction [latex]Largefrac{310}{1000}[/latex]. Converting [latex]Largefrac{310}{1000}[/latex] back to a decimal gives [latex]0.310[/latex]. So [latex]0.31[/latex] is equivalent to [latex]0.310[/latex]. Writing zeros at the end of a decimal does not change its value.
[latex]{Largefrac{31}{100}}={Largefrac{310}{1000}}text{ and }0.31=0.310[/latex]
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If two decimals have the same value, they are said to be equivalent decimals.
[latex]0.31=0.310[/latex]
We say [latex]0.31[/latex] and [latex]0.310[/latex] are equivalent decimals.
Remember, writing zeros at the end of a decimal does not change its value.
When we order negative decimals, it is important to remember how to order negative integers. Recall that larger numbers are to the right on the number line. For example, because [latex]-2[/latex] lies to the right of [latex]-3[/latex] on the number line, we know that [latex]-2>-3[/latex]. Similarly, smaller numbers lie to the left on the number line. For example, because [latex]-9[/latex] lies to the left of [latex]-6[/latex] on the number line, we know that [latex]-9<-6[/latex].
If we zoomed in on the interval between [latex]0[/latex] and [latex]-1[/latex], we would see in the same way that [latex]-0.2>-0.3text{and}-0.9<-0.6[/latex].
In the following video lesson we show how to order decimals using inequality notation by comparing place values, and by using fractions.
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Category: WHICH
