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Round decimals

Rounding decimals is very much like rounding whole numbers. We will round decimals with a method based on the one we used to round whole numbers.

How to round decimals

Round 18.379 to the nearest hundredth.

A table is given with four steps. The first step reads “Step 1: Locate the given place value and mark it with an arrow.” To the right of this, we have the number 18.379; above it, are the words hundreds place, which has an arrow pointing to the 7. The second step reads “Step 2. Underline the digit to the right of the given place value.” To the right of this, we have 18.379 with the 9 underlined. The third step reads “Step 3. Is this digit greater than or equal to 5? Below this reads, “Yes: add 1 to the digit in the given place value.” Below this reads, “No: do not change the digit in the given place value.” To the right of this, it says “Because 9 is greater than or equal to ” To the right of this, we have the number 18.379 with the 9 marked “delete” and the 7 marked “add 1.” Finally, the last step reads “Step 4. Rewrite the number, removing all digits to the right of the rounding digit.” To the right of this, we have 18.38 followed by “18.38 is 18.379 rounded to the nearest hundredth.”
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Round to the nearest hundredth: 1.047 .

1.05

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Round to the nearest hundredth: 9.173 .

9.17

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We summarize the steps for rounding a decimal    here.

Round decimals.

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

Round 18.379 to the nearest tenth whole number.

Solution

Round 18.379

  1. to the nearest tenth
    Locate the tenths place with an arrow. .
    Underline the digit to the right of the given place value. .
    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 rounding digit. .
    Notice that the deleted digits were NOT replaced with zeros. So, 18.379 rounded to the nearest tenth is 18.4.


  2. to the nearest whole number
    Locate the ones place with an arrow. .
    Underline the digit to the right of the given place value. .
    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 rounding digit. .
    So, 18.379 rounded to the nearest whole number is 18.
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Round 6.582 to the nearest hundredth tenth whole number.

6.58 6.6 7

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Round 15.2175 to the nearest thousandth hundredth tenth.

15.218 15.22 15.2

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Add and subtract decimals

To add or subtract decimals, we line up the decimal points. By lining up the decimal points this way, we can add or subtract the corresponding place values . We then add or subtract the numbers as if they were whole numbers and then place the decimal point in the sum.

Add or subtract decimals.

  1. Write the numbers so the decimal points line up vertically.
  2. Use zeros as place holders, as needed.
  3. Add or subtract the numbers as if they were whole numbers. Then place the decimal point in the answer under the decimal points in the given numbers.

Add: 23.5 + 41.38 .

Solution

Write the numbers so the decimal points line up vertically. 23.5 + 41.38 ______ Put 0 as a placeholder after the 5 in 23.5. Remember, 5 10 = 50 100 so 0.5 = 0.50 . 23.50 + 41.38 ______ Add the numbers as if they were whole numbers. Then place the decimal point in the sum. 23.50 + 41.38 ______ 64.88

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Add: 4.8 + 11.69 .

16.49

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Add: 5.123 + 18.47 .

23.593

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Subtract: 20 14.65 .

Solution

20 14.65 Write the numbers so the decimal points line up vertically. 20. 14.65 ______ Remember, 20 is a whole number, so place the decimal point after the 0. Put in zeros to the right as placeholders. 20.00 −14.65 ______ Subtract and place the decimal point in the answer. 2 1 0 10 9 . 0 10 9 0 10 1 4 . 6 5 __________ 5 . 3 5

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Subtract: 10 9.58 .

0.42

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Subtract: 50 37.42 .

12.58

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Multiply and divide decimals

Multiplying decimals is very much like multiplying whole numbers—we just have to determine where to place the decimal point. The procedure for multiplying decimals will make sense if we first convert them to fractions and then multiply.

Practice Key Terms 3

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Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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