5.1 Decimals  (Page 4/8)

Locate decimals on the number line

Since decimals are forms of fractions, locating decimals on the number line is similar to locating fractions on the number line.

Order decimals

Which is larger, $0.04$ or $0.40?$

If you think of this as money, you know that $\text{\$0.40}$ (forty cents) is greater than $\text{\$0.04}$ (four cents). So,

In previous chapters, we used the number line to order numbers.

Where are $0.04$ and $0.40$ located on the number line?

We see that $0.40$ is to the right of $0.04.$ So we know $0.40>0.04.$

How does $0.31$ compare to $0.308?$ This doesn’t translate into money to make the comparison easy. But if we convert $0.31$ and $0.308$ to fractions, we can tell which is larger.

	$0.31$	$0.308$
Convert to fractions.	$\frac{31}{100}$	$\frac{308}{1000}$
We need a common denominator to compare them.		$\frac{308}{1000}$
	$\frac{310}{1000}$	$\frac{308}{1000}$

Because $310>308,$ we know that $\frac{310}{1000}>\frac{308}{1000}.$ Therefore, $0.31>0.308.$

Notice what we did in converting $0.31$ to a fraction—we started with the fraction $\frac{31}{100}$ and ended with the equivalent fraction $\frac{310}{1000}.$ Converting $\frac{310}{1000}$ back to a decimal gives $0.310.$ So $0.31$ is equivalent to $0.310.$ 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 $0.31$ and $0.310$ are equivalent decimals.

Remember, writing zeros at the end of a decimal does not change its value.