Example 1: The Glosser Kinsfolk swarm to a gasoline station in their neighborhood. The station has three gas pumps, each marked in cost per gallon. Which pump has the last terms per gallon? Which pump has the highest price per gallon?
$1.79, $1.96, $1.61
Depth psychology: We know that 1.79 < 1.96 and that 1.79 > 1.61. Writing extraordinary decimal below the other in order, we get:
| 1 | . | 6 | 1 |  |  least |
| 1 | . | 7 | 9 | | |
| 1 | . | 9 | 6 | | greatest |
Answer: The pump marked $1.61 has the lowest price per gallon. The pump marked $1.96 has the highest terms per gallon.
In the example preceding, we sequential three decimal numbers from least to greatest past comparison them two at a time. Let's view some more examples.
Example 2: Regularize these decimals from to the lowest degree to superlative: 0.5629, 0.5621, 0.6521
Let's examine these decimals in our put away-value-chart.
 |  |  |  |  |  |
| 0 | . | 5 | 6 | 2 | 9 |
| 0 | . | 5 | 6 | 2 | 1 |
| 0 | . | 6 | 5 | 2 | 1 |
Now permit's order these decimals from least to greatestwithout our come in-appreciate graph. We will do this past comparing two decimals at a time.
| 0 | . | 5 | 6 | 2 | 1 |
| 0 | . | 5 | 6 | 2 | 9 |
| 0 | . | 6 | 5 | 2 | 1 |
Answer: Ordering these decimals from least to greatest we get: 0.5621, 0.5629, 0.6521.
In the examples above, the decimals in each problem had the same number of digits. Thus, they lined up nicely, one below the other. Let's look at some examples in which the decimals presented undergo a different number of decimal digits.
Example 3: Order these decimals from least to greatest: 6.01, 0.601, 6.1
Let's start by written material one decimal beneath the other in their original order. Note that these three decimals have a different list of denary digits.
| 6 | . | 0 | 1 | 0 |
| 0 | . | 6 | 0 | 1 |
| 6 | . | 1 | 0 | 0 |
Next, study each decimal fraction, writing one or more zeros to the right wing of the last digit, so that all decimals have the same identification number of decimal digits.
| 6 | . | 0 | 1 | 0 |
| 0 | . | 6 | 0 | 1 |
| 6 | . | 1 | 0 | 0 |
Now we can compare two decimals at a time.
| 6 | . | 0 | 1 | 0 |
| 0 | . | 6 | 0 | 1 |
| 6 | . | 1 | 0 | 0 |
From least to greatest, we bugger off: 0.6010, 6.010, 6.100.
Answer: Ordering these decimals from to the lowest degree to greatest we draw: 0.601, 6.01, 6.1.
Sometimes it is helpful to locate a number in a circle to the reactionist of for each one decimal you are disagreeable to order. This is done in Example 4.
Example 4: Order these decimals from least to greatest: 3.87, 3.0875, 3.87502, 3.807
We have been asked to order cardinal decimal numbers. Let's take up by composition one decimal beneath the other in their original order.
| 3 | . | 8 | 7 | 0 | 0 | 0 |
| 3 | . | 0 | 8 | 7 | 5 | 0 |
| 3 | . | 8 | 7 | 5 | 0 | 2 |
| 3 | . | 8 | 0 | 7 | 0 | 0 |
Next, examine all decimal, writing one or more zeros to the right of the last digit, so that all decimals birth the same number of quantitative digits.
| 3 | . | 8 | 7 | 0 | 0 | 0 |
| 3 | . | 0 | 8 | 7 | 5 | 0 |
| 3 | . | 8 | 7 | 5 | 0 | 2 |
| 3 | . | 8 | 0 | 7 | 0 | 0 |
Now we tail compare two decimals at a time. We will spell a number in a circle next to from each one denary to denote its order.
| 3 | . | 8 | 7 | 0 | 0 | 0 |  |
| 3 | . | 0 | 8 | 7 | 5 | 0 |  |
| 3 | . | 8 | 7 | 5 | 0 | 2 |  |
| 3 | . | 8 | 0 | 7 | 0 | 0 |  |
From to the lowest degree to sterling, we get: 3.08750, 3.80700, 3.87000, 3.87502
Do: Ordering these decimals from least to greatest we get: 3.0875, 3.807, 3.87, 3.87502
Example 5: Order these decimals from least to greatest: 5.364, 6.0364, 5.36, 5.00364, 5.40364
We have been asked to order five decimal Numbers. Let's protrude by writing one decimal below the other in their original lodg. Next, examine each quantitative, composition one or more zeros to the right of the senior digit, as required.
| 5 | . | 3 | 6 | 4 | 0 | 0 |
| 6 | . | 0 | 3 | 6 | 4 | 0 |
| 5 | . | 3 | 6 | 0 | 0 | 0 |
| 5 | . | 0 | 0 | 3 | 6 | 4 |
| 5 | . | 4 | 0 | 3 | 6 | 4 |
Now we fanny compare two decimals at once. We bequeath write a number in circles incoming to each decimal fraction to denote its order.
| 5 | . | 3 | 6 | 4 | 0 | 0 | |
| 6 | . | 0 | 3 | 6 | 4 | 0 |  |
| 5 | . | 3 | 6 | 0 | 0 | 0 | |
| 5 | . | 0 | 0 | 3 | 6 | 4 | |
| 5 | . | 4 | 0 | 3 | 6 | 4 | |
From to the lowest degree to greatest, we get: 5.00364, 5.36000, 5.36400, 5.40364, 6.03640
Answer: Ordering these decimals from least to greatest we get: 5.00364, 5.36, 5.364, 5.40364, 6.0364
Allow's look at some not-number problems that call for comparing and ordering decimals.
Example 6: Write 3 decimals between 4.35 and 4.36 in order from to the lowest degree to sterling.
Analysis: We call for to write a zero in the thousandths range for to each one of the given Numbers.
| |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Forthwith we mustiness find oneself 3 numbers pool that are 'tween the given numbers. We ass manipulation any digit between 1 and 9. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| |||||||||||||||||||||||||||||||||||||||||||||||||||||||
| The motion asks us to write 3 decimals between 4.35 and 4.36 systematic from least to superlative. We tail end opt any 3 numbers in red from above as long as they are in order from least to greatest. Accordingly, our answers will alter. To a lower place are some sample answers. |
Sample Respond 1: 4.351, 4.352, 4.353
Sampling Answer 2: 4.354, 4.356, 4.358
Example 7: Write 3 decimals between 7.418 and 7.419 ready from least to greatest.
Analysis: We penury to write a goose egg in the cardinal-thousandths place for each of the given numbers game.
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Now we must obtain 3 numbers that are between the given numbers. We can wont whatsoever finger's breadth 'tween 1 and 9. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| The oppugn asks us to write 3 decimals between 7.418 and 7.419 ready from to the lowest degree to greatest. We can select any 3 numbers in red from to a higher place As long as they are in plac from least to greatest. Accordingly, our answers wish vary. Below are some sample answers. |
Sample Answer 1:7 .4182, 7.4183, 7.4184
Try Answer 2: 7 .4185, 7.4187, 7.4189
Model 8: Write the smallest possible decimal between zero and one that uses the digits 5, 0, 4, 1, 9, and 6 exactly at one time.
Answer: .014569. Note that a ahead zero wasnot used Hera.
Example 9: Pen the greatest possible decimal fraction between zero and combined that uses the digits 9, 0, 2, 7, 3 and
5 exactly once.
Answer: .975320 (without a leading zero) operating theatre 0.97532 (with a leading zero point). Note that these two decimals are equivalent weight.
Summary: When ordering decimals, first write one decimal fraction beneath the former in their original order. Then compare them two at a time. When ordering four operating theatre more decimals, IT is helpful to write a number in a circle side by side to to each one to order them.
Exercises
Directions: Translate each head below. You may usance paper to help you find the answers. Select your answer by clicking on its button. Feedback to your serve is provided in the RESULTS BOX. If you make a error, choose a different button.
| 1. | Which of the pursuit is the smallest decimal number? |
| | |
| 2. | Which of the following is the largest decimal list? |
| | |
| 3. | Which of the following choices lists these decimals in rate from least to greatest: 0.910, 0.091, 0.9? |
| | |
| 4. | Which of the following choices lists these decimals in social club from least to greatest: 3.45, 3.0459, 3.5, 3.4059? |
| | |
| 5. | Which of the following choices lists these decimals ready from to the lowest degree to sterling: 7.102, 7.0102, 7.012, 7.00102, 7.102021? |
| | |
Sign Up For Our Self-governing Newsletter!
Sign in Up For Our FREE Newsletter!
how to order negative decimals from least to greatest
Source: https://www.mathgoodies.com/lessons/decimals/order
