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Topic

Rounding Decimals

Topic Progress:

Name Decimals

You probably already know quite a bit about decimals based on your experience with money. Suppose you buy a sandwich and a bottle of water for lunch. If the sandwich costs $3.45, the bottle of water costs $1.25, and the total sales tax is $0.33, what is the total cost of your lunch?

A vertical addition problem is shown. The top line shows $3.45 for a sandwich, the next line shows $1.25 for water, and the last line shows $0.33 for tax. The total is shown to be $5.03.

The total is $5.03. Suppose you pay with a $5 bill and pennies. Should you wait for change? No, $5 and 3 pennies is the same as $5.03.

Because 100 pennies=$1, each penny is worth of a dollar. We write the value of one penny as $0.01since 0.01=.

Writing a number with a decimal is known as decimal notation. It is a way of showing parts of a whole when the whole is a power of ten. In other words, decimals are another way of writing fractions whose denominators are powers of ten. Just as the counting numbers are based on powers of ten, decimals are based on powers of ten. Table shows the counting numbers.

Counting number Name
1 One
10 = 10 Ten
10 x 10 = 100 One hundred
10 x 10 x 10 = 1000 One thousand
10 x 10 x 10 x 10 = 10,000 Ten thousand

How are decimals related to fractions? Table shows the relation.

Decimal Fraction Name
0.1 One tenth
0.01 One hundredth
0.001 One thousandth
0.0001 One ten-thousandth

When we name a whole number, the name corresponds to the place value based on the powers of ten. In Whole Numbers, we learned to read 10,000 as ten thousand. Likewise, the names of the decimal places correspond to their fraction values. Notice how the place value names in Figure relate to the names of the fractions from Table.

A chart is shown labeled “Place Value”. There are 12 columns. The columns are labeled, from left to right, Hundred thousands, Ten thousands, Thousands, Hundreds, Tens, Ones, Decimal Point, Tenths, Hundredths, Thousandths, Ten-thousandths, Hundred-thousandths.
This chart illustrates place values to the left and right of the decimal point.

Notice two important facts shown in Figure.

  • The “th” at the end of the name means the number is a fraction. “One thousand” is a number larger than one, but “one thousandth” is a number smaller than one.
  • The tenths place is the first place to the right of the decimal, but the tens place is two places to the left of the decimal.

Remember that $5.03 lunch? We read $5.03 as five dollars and three cents. Naming decimals (those that don’t represent money) is done in a similar way. We read the number 5.03 as five and three hundredths.

We sometimes need to translate a number written in decimal notation into words. As shown in Figure, we write the amount on a check in both words and numbers.

An image of a check is shown. The check is made out to Jane Doe. It shows the number $152.65 and says in words, “One hundred fifty two and 65 over 100 dollars.”
When we write a check, we write the amount as a decimal number as well as in words. The bank looks at the check to make sure both numbers match. This helps prevent errors.
Let’s try naming a decimal, such as 15.68.
We start by naming the number to the left of the decimal. fifteen______
We use the word “and” to indicate the decimal point. fifteen and_____
Then we name the number to the right of the decimal point as if it were a whole number. fifteen and sixty-eight_____
Last, name the decimal place of the last digit. fifteen and sixty-eight hundredths

The number 15.68 is read fifteen and sixty-eight hundredths.

Name a Decimal Number

  • Name the number to the left of the decimal point.
  • Write “and” for the decimal point.
  • Name the “number” part to the right of the decimal point as if it were a whole number.
  • Name the decimal place of the last digit.

Name each decimal: ⓐ4.3 ⓑ2.45 ⓒ0.009 ⓓ−15.571.

Solution
4.3
Name the number to the left of the decimal point. four_____
Write "and" for the decimal point. four and_____
Name the number to the right of the decimal point as if it were a whole number. four and three_____
Name the decimal place of the last digit. four and three tenths
2.45
Name the number to the left of the decimal point. two_____
Write "and" for the decimal point. two and_____
Name the number to the right of the decimal point as if it were a whole number. two and forty-five_____
Name the decimal place of the last digit. two and forty-five hundredths
0.009
Name the number to the left of the decimal point. Zero is the number to the left of the decimal; it is not included in the name.
Name the number to the right of the decimal point as if it were a whole number. nine_____
Name the decimal place of the last digit. nine thousandths
15.571
Name the number to the left of the decimal point. negative fifteen
Write "and" for the decimal point. negative fifteen and_____
Name the number to the right of the decimal point as if it were a whole number. negative fifteen and five hundred seventy-one_____
Name the decimal place of the last digit. negative fifteen and five hundred seventy-one thousandths

Name each decimal: ⓐ6.7 ⓑ19.58 ⓒ0.018 ⓓ−2.053

six and seven tenths
nineteen and fifty-eight hundredths
eighteen thousandths
negative two and fifty-three thousandths

Name each decimal:ⓐ5.8 ⓑ3.57 ⓒ0.005 ⓓ−13.461

five and eight tenths three and fifty-seven hundredths
three and fifty-seven hundredths
five thousandths
negative thirteen and four hundred sixty-one thousandths

Rounding 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 $3.279 per gallon. But if you were to buy exactly one gallon of gas at this price, you would pay $3.28 because the final price would be rounded to the nearest cent. Suppose we wanted to round $2.72 to the nearest dollar. Is it closer to $2 or to $3? What if we wanted to round $2.72 to the nearest ten cents; is it closer to $2.70 or to $2.80? The number lines in Figure can help us answer those questions.

In part a, a number line is shown with 2, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9 and 3. There is a dot between 2.7 and 2.8 labeled as 2.72. In part b, a number line is shown with 2.70, 2.71, 2.72, 2.73, 2.74, 2.75, 2.76, 2.77, 2.78, 2.79, and 2.80. There is a dot at 2.72.
We see that 2.72 is closer to 3 than to 2. So, 2.72 rounded to the nearest whole number is 3.

We see that 2.72 is closer to 2.70 than 2.80. So we say that 2.72 rounded to the nearest tenth is 2.7.

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

Round a Decimal
  1. Locate the given place value and mark it with an arrow.
  2. Underline the digit to the right of the given place value.
  3. Is this digit greater than or equal to 5?
    • Yes - add 11 to the digit in the given place value.
    • No - do not change the digit in the given place value
  4. Rewrite the number, removing all digits to the right of the given place value.

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.

Round to the nearest hundredth: 1.047.

1.05

Round to the nearest hundredth: 9.173.

9.17

Lets take a look at another example:

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.

Round 6.582 to the nearest ⓐ hundredth ⓑ tenth ⓒ whole number.

6.58
6.6
7

Round 15.2175 to the nearest ⓐ thousandth ⓑ hundredth ⓒ tenth.

15.218
15.22
15.2

Before you progress to the next lesson, make sure you are comfortable with rounding. Watch how Sal Khan rounds to the nearest tenth.

 

Attribution

Creative Commons License The text has been derived from "Prealgebra" by OpenStax. © Nov 10, 2016 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License 4.0 license. Download for free at http://cnx.org/contents/yqV9q0HH@9.662:0L7hpyVK@14/Decimal-Operations

Creative Commons License The video "Worked example: Rounding decimals to nearest tenth" by Sal Khan is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. To see comments and other related activities please visit http://www.khanacademy.org.

Creative Commons License All other material in this work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. If you would like  to use this material, please provide attribution as follows: Richmond, J. (2016). https://www.ceces.ca/courses/med-math/. Continuing Education Centre for Emergency Services.