5.1 Decimals  (Page 5/8)

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 $\mathrm{-2}$ lies to the right of $\mathrm{-3}$ on the number line, we know that $\mathrm{-2}>\mathrm{-3}.$ Similarly, smaller numbers lie to the left on the number line. For example, because $\mathrm{-9}$ lies to the left of $\mathrm{-6}$ on the number line, we know that $\mathrm{-9}<\mathrm{-6}.$

If we zoomed in on the interval between $0$ and $\mathrm{-1},$ we would see in the same way that $\mathrm{-0.2}>\mathrm{-0.3}\text{and}\mathrm{-0.9}<\mathrm{-0.6}.$

Round decimals

In the United States, gasoline prices are usually written with the decimal part as thousandths of a dollar. For example, a gas station might post the price of unleaded gas at $\text{\$3.279}$ per gallon. But if you were to buy exactly one gallon of gas at this price, you would pay $\text{\$3.28}$ , because the final price would be rounded to the nearest cent. In Whole Numbers , we saw that we round numbers to get an approximate value when the exact value is not needed. Suppose we wanted to round $\text{\$2.72}$ to the nearest dollar. Is it closer to $\text{\$2}$ or to $\text{\$3}?$ What if we wanted to round $\text{\$2.72}$ to the nearest ten cents; is it closer to $\text{\$2.70}$ or to $\text{\$2.80}?$ The number lines in [link] can help us answer those questions.

Can we round decimals without number lines? Yes! We use a method based on the one we used to round whole numbers.

Round $18.379$ to the nearest hundredth.

Solution

Locate the hundredths place and mark it with an arrow.
Underline the digit to the right of the 7.
Because 9 is greater than or equal to 5, add 1 to the 7.
Rewrite the number, deleting all digits to the right of the hundredths place.
	18.38 is 18.379 rounded to the nearest hundredth.

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Round $18.379$ to the nearest ⓐ tenth ⓑ whole number.

Solution

ⓐ Round 18.379 to the nearest tenth.
Locate the tenths place and mark it with an arrow.
Underline the digit to the right of the tenths digit.
Because 7 is greater than or equal to 5, add 1 to the 3.
Rewrite the number, deleting all digits to the right of the tenths place.
	So, 18.379 rounded to the nearest tenth is 18.4.

ⓑ Round 18.379 to the nearest whole number.
Locate the ones place and mark it with an arrow.
Underline the digit to the right of the ones place.
Since 3 is not greater than or equal to 5, do not add 1 to the 8.
Rewrite the number, deleting all digits to the right of the ones place.
	So 18.379 rounded to the nearest whole number is 18.

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