What Is the Order of the Numbers From Least to Greatest a=4.6

Example one: The Glosser Family unit drove to a gasoline station in their neighborhood. The station has three gas pumps, each marked in price per gallon. Which pump has the lowest price per gallon? Which pump has the highest toll per gallon?

$1.79,  $ane.96,  $ane.61

Analysis: We know that 1.79 < i.96 and that ane.79 > one.61. Writing i decimal below the other in gild, we get:

ane	.	half-dozen	one		least
ane	.	vii	9
1	.	9	6		greatest

Answer: The pump marked $1.61 has the everyman price per gallon. The pump marked $1.96 has the highest price per gallon.

In the example higher up, we ordered three decimal numbers from least to greatest by comparison them two at a time. Let's look at some more examples.

Case 2: Lodge these decimals from to the lowest degree to greatest:  0.5629,  0.5621,  0.6521

Allow'south examine these decimals in our place-value-chart.

0	.	5	6	ii	ix
0	.	5	half dozen	ii	ane
0	.	half-dozen	5	2	1

Now let'southward order these decimals from least to greatestwithout our identify-value chart. We volition do this by comparison two decimals at a time.

0	.	5	6	ii	1
0	.	5	6	2	9
0	.	six	v	2	1

Reply: Ordering these decimals from least to greatest we go:  0.5621,  0.5629,  0.6521.

In the examples in a higher place, the decimals in each problem had the aforementioned number of digits. Thus, they lined up nicely, one below the other. Let'southward look at some examples in which the decimals presented have a different number of decimal digits.

Example 3: Order these decimals from least to greatest:  vi.01,  0.601,  6.1

Let's start by writing one decimal below the other in their original order. Note that these three decimals take a different number of decimal digits.

half-dozen	.	0	ane	0
0	.	6	0	1
half dozen	.	1	0	0

Next, examine each decimal, writing i or more zeros to the correct of the last digit, so that all decimals have the same number of decimal digits.

6	.	0	1	0
0	.	six	0	1
6	.	one	0	0

Now nosotros can compare two decimals at a fourth dimension.

half-dozen	.	0	1	0
0	.	6	0	1
6	.	1	0	0

From to the lowest degree to greatest, we get:   0.6010,  6.010,  6.100.

Reply: Ordering these decimals from least to greatest we get:  0.601,  6.01,  6.one.

Sometimes it is helpful to place a number in a circle to the correct of each decimal yous are trying to lodge. This is done in Instance 4.

Example 4: Guild these decimals from least to greatest:  3.87,  3.0875,  3.87502,  3.807

We have been asked to order iv decimal numbers. Let'south starting time past writing one decimal beneath the other in their original order.

3	.	8	seven	0	0	0
iii	.	0	viii	7	5	0
3	.	viii	7	5	0	2
3	.	8	0	7	0	0

Next, examine each decimal, writing one or more zeros to the right of the last digit, then that all decimals take the aforementioned number of decimal digits.

three	.	8	seven	0	0	0
three	.	0	8	7	5	0
3	.	8	7	five	0	2
3	.	8	0	7	0	0

Now we can compare 2 decimals at a time. We will write a number in a circle next to each decimal to denote its order.

three	.	8	7	0	0	0
3	.	0	8	7	5	0
iii	.	8	7	5	0	2
3	.	8	0	7	0	0

From least to greatest, we get:  3.08750,  3.80700,  3.87000,  3.87502

Respond: Ordering these decimals from to the lowest degree to greatest we get:  3.0875,  3.807,  three.87,  3.87502

Example 5: Order these decimals from to the lowest degree to greatest:  5.364,  six.0364,  five.36,  five.00364,  5.40364

We have been asked to order five decimal numbers. Allow'due south starting time by writing one decimal beneath the other in their original order. Next, examine each decimal, writing 1 or more than zeros to the right of the concluding digit, as needed.

5	.	3	half dozen	4	0	0
six	.	0	three	six	4	0
v	.	3	vi	0	0	0
five	.	0	0	iii	half-dozen	iv
5	.	4	0	3	vi	4

Now we can compare two decimals at a time. We will write a number in a circumvolve next to each decimal to denote its order.

5	.	three	vi	4	0	0
half-dozen	.	0	3	half-dozen	four	0
5	.	iii	6	0	0	0
5	.	0	0	3	vi	iv
5	.	4	0	3	six	four

From to the lowest degree to greatest, we get:  five.00364,  five.36000,  v.36400,  5.40364,  6.03640

Answer: Ordering these decimals from to the lowest degree to greatest nosotros get:  5.00364,  five.36,  v.364,  5.40364,  6.0364

Let's look at some not-routine problems that involve comparison and ordering decimals.

Example 6: Write 3 decimals between 4.35 and four.36 in order from least to greatest.

Analysis: Nosotros need to write a zippo in the thousandths place for each of the given numbers.

4 . 3 5 0 four . 3 6 0

At present nosotros must find 3 numbers that are between the given numbers. We can utilise whatever digit between ane and 9.

4 . 3 5 0 4 . 3 5 ane 4 . 3 5 2 4 . 3 5 3 4 . 3 5 four iv . 3 5 5 4 . three five 6 4 . 3 5 7 iv . 3 five 8 4 . 3 5 9 4 . 3 6 0

The question asks united states to write 3 decimals between 4.35 and 4.36 in gild from least to greatest. We can cull any 3 numbers in red from above every bit long as they are in order from least to greatest. Appropriately, our answers will vary. Below are some sample answers.

Sample Answer 1: 4.351,  4.352,  4.353

Sample Answer two: 4.354,  iv.356,  four.358

Example 7: Write 3 decimals betwixt 7.418 and vii.419 in lodge from to the lowest degree to greatest.

Assay: We need to write a null in the x-thousandths place for each of the given numbers.

7 . iv ane eight 0 7 . 4 i 9 0

Now nosotros must find 3 numbers that are betwixt the given numbers. We can use any digit between 1 and ix.

vii . 4 one 8 0 seven . four 1 8 1 7 . 4 i 8 2 seven . 4 one 8 3 7 . 4 1 eight 4 7 . 4 1 8 five 7 . 4 i eight 6 seven . iv 1 eight seven 7 . four 1 8 eight seven . 4 ane eight 9 7 . 4 one nine 0

The question asks us to write iii decimals between 7.418 and 7.419 in order from least to greatest. We can choose whatsoever 3 numbers in ruddy from above as long as they are in order from to the lowest degree to greatest. Accordingly, our answers will vary. Beneath are some sample answers.

Sample Answer 1:7 .4182,  7.4183,  7.4184

Sample Answer 2: 7 .4185,  seven.4187,  7.4189

Case viii: Write the smallest possible decimal between zero and one that uses the digits v, 0, four, ane, 9, and vi exactly one time.

Answer: .014569. Note that a leading nil wasnot used here.

Example 9: Write the greatest possible decimal betwixt null and one that uses the digits 9, 0, 2, 7, 3 and
5 exactly once.

Answer: .975320 (without a leading zero) or 0.97532 (with a leading zero). Note that these ii decimals are equivalent.

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Summary: When ordering decimals, outset write ane decimal below the other in their original order. Then compare them two at a time. When ordering iv or more decimals, it is helpful to write a number in a circle next to each to order them.

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Exercises

Directions: Read each question below. You lot may use newspaper to help you notice the answers. Select your reply by clicking on its push. Feedback to your answer is provided in the RESULTS BOX. If you make a mistake, cull a dissimilar button.

1.	Which of the post-obit is the smallest decimal number?

2.	Which of the following is the largest decimal number?

iii.	Which of the following choices lists these decimals in society from least to greatest: 0.910,  0.091,  0.9?

4.	Which of the following choices lists these decimals in order from to the lowest degree to greatest: 3.45,  3.0459,  3.5,  3.4059?

5.	Which of the post-obit choices lists these decimals in gild from to the lowest degree to greatest:  7.102,  7.0102,  7.012,  seven.00102,  7.102021?
	7.102021, vii.00102, 7.012, seven.0102, 7.102 7.00102, 7.0102, vii.012, 7.102, seven.102021 seven.102021, seven.102, 7.012, vii.0102, 7.00102 None of the above. RESULTS BOX:

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Source: https://www.mathgoodies.com/lessons/decimals/order

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