More on Rounding Decimals

Site: Saylor Academy
Course: RWM101: Foundations of Real World Math
Book: More on Rounding Decimals
Printed by: Guest user
Date: Monday, June 17, 2024, 6:09 AM

Description

Then read this text up to Sample Set A. The second paragraph gives a set of rules for determining how to round a decimal. The first two worked examples under Sample Set A show step-by-step directions for rounding numbers. Complete the practice problems and check your answers.

Rounding Decimals

Rounding Decimal Numbers

We first considered the concept of rounding numbers in [link] where our concern with rounding was related to whole numbers only. With a few minor changes, we can apply the same rules of rounding to decimals.

To round a decimal to a particular position:

Mark the position of the round-off digit (with an arrow or check).

Note whether the digit to the immediate right of the marked digit is

a. less than 5. If so, leave the round-off digit unchanged.
b. 5 or greater. If so, add 1 to the round-off digit.

If the round-off digit is

a. to the right of the decimal point, eliminate all the digits to its right.
b. to the left of the decimal point, replace all the digits between it and the decimal point with zeros and eliminate the decimal point and all the decimal digits.


Sample Set A

Round each decimal to the specified position. (The numbers in parentheses indicate which step is being used).

Round 32.116 to the nearest hundredth.

1: 

2b: The digit immediately to the right is 6, and 6 > 5, so we add 1 to the round-off digit: 1+1=2

3a: The round-off digit is to the right of the decimal point, so we eliminate all digits to its right. 32.12

The number 32.116 rounded to the nearest hundredth is 32.12.


Round 633.14216 to the nearest hundred.

1: 633.14216 hundreds position

2a: The digit immediately to the right is 3, and 3 < 5 so we leave the round-off digit unchanged.

3b: The round-off digit is to the left of 0, so we replace all the digits between it and the decimal point with zeros and eliminate the decimal point and all the decimal digits.

600

The number 633.14216 rounded to the nearest hundred is 600.

1,729.63 rounded to the nearest ten is 1,730.

1.0144 rounded to the nearest tenth is 1.0.

60.98 rounded to the nearest one is 61.

Sometimes we hear a phrase such as "round to three decimal places". This phrase means that the round-off digit is the third decimal digit (the digit in the thousandths position).

67.129 rounded to the second decimal place is 67.13.

67.129558 rounded to 3 decimal places is 67.130.



Source: Rice University, https://cnx.org/contents/XeVIW7Iw@4.6:bt1ND9pC@2/Rounding-Decimals
Creative Commons License This work is licensed under a Creative Commons Attribution 4.0 License.

Practice Set A

Round each decimal to the specified position.

  1. 4.816 to the nearest hundredth.
  2. 0.35928 to the nearest ten thousandths.
  3. 82.1 to the nearest one.
  4. 753.98 to the nearest hundred.
  5. Round 43.99446 to three decimal places.
  6. Round 105.019997 to four decimal places.
  7. Round 99.9999 to two decimal places.

Answers

  1. 4.82
  2. 0.3593
  3. 82
  4. 800
  5. 43.994
  6. 105.0200
  7. 100.00