Sorting

0.211, 0.201, 0.300, 0.310, 0.212  →  0.201, 0.211, 0.212, 0.300, 0.311


Positions

2146.8

thousands

2146.87

hundreds

2146.873
””’
””’tens

2146.873
”””’
”””’ones

2146.873
”””””’
”””””’tenths

2146.873
””””””’
””””””’hundredths

2146.873
””””””””
””””””””thousandths


Technique
Sorting is a technique that arranges a group of numbers in order from lowest to highest.

On the calculator-prohibited portion of the Mathematical Reasoning module, you might be required to use sorting to solve a problem. 


Question

You are given the numbers 246, 110, 248, 232, and 159.  Without using the calculator, what is the order of these numbers from smallest to largest?
A.  246, 110, 248, 232, 159
B.  110, 246, 248, 232, 159
C.  110, 159, 232, 248, 246
D.  110, 159, 232, 246, 248

Answer
D.  110, 159, 232, 246, 248

Answer Process
Note that the numbers variously fill the ones, tens, and hundreds positions.

Place the numbers, as given, in a column.
246
110
248
232
159

Sort the column from lowest (on the bottom) to highest (on the top) by comparing the hundreds position.  Note that, after sorting, 159 and 110 are lower than 232, 248, and 246.
246
248
232
110
159

Sort 159 and 110 from lowest to highest by comparing the tens position.  Sort 232, 248, and 246 from lowest to highest by comparing the tens position.  Note that, after sorting, 110 and 159 are in the correct order.
246
248
232
159
110

Sort 232, 248, and 246 from lowest to highest by comparing the ones position.  Note that, after sorting, 232, 246, and 248 are in the correct order, putting the entire column in the correct order.
248
246
232
159
110

Finish by putting the numbers from lowest to highest in a row.
110, 159, 232, 246, 248


Question

You are given the numbers 0.346, 0.210, 0.348, 0.332, and 0.259.  Without using the calculator, what is the order of these numbers from smallest to largest?
A.  0.259, 0.210, 0.332, 0.346, 0.348
B.  0.210, 0.259, 0.346, 0.332, 0.348
C.  0.210, 0.259, 0.332, 0.348, 0.346
D.  0.210, 0.259, 0.332, 0.346, 0.348

Answer
D.  0.210, 0.259, 0.332, 0.346, 0.348

Answer Process
Note that the numbers variously fill the tenths, hundredths, and thousandths positions.

Place the numbers, as given, in a column.
0.346
0.210
0.348
0.332
0.259

Sort the column from lowest (on the bottom) to highest (on the top) by comparing the tenths position.  Note that, after sorting, 0.259 and 0.210 are lower than 0.332, 0.348, and 0.346.
0.346
0.348
0.332
0.210
0.259

Sort 0.259 and 0.210 from lowest to highest by comparing the hundredths position.  Sort 0.332, 0.348, and 0.346 by comparing the hundredths position.  Note that, after sorting, 0.210 and 0.259 are in the correct order.
0.346
0.348
0.332
0.259
0.210

Sort 0.332, 0.348, and 0.346 from lowest to highest by comparing the thousandths position.  Note that, after sorting, 0.332, 0.346, and 0.348 are in the correct order, putting the entire column in the correct order.
0.348
0.346
0.332
0.259
0.210

Finish by putting the numbers from lowest to highest in a row.
0.210, 0.259, 0.332, 0.346, 0.348


Question

A scientist measures the lengths of five worms.  Their lengths in inches are 0.211, 0.201, 0.300, 0.310, and 0.212, respectively.  Without using the calculator, what is the order of these worms from shortest to longest?
A.  0.211, 0.201, 0.300, 0.310, 0.212
B.  0.201, 0.211, 0.300, 0.310, 0.212
C.  0.201, 0.211, 0.212, 0.300, 0.310
D.  0.201, 0.211, 0.212, 0.310, 0.300

Answer
C.  0.201, 0.211, 0.212, 0.300, 0.310

Answer Process
Note that the worms are measured in tenths, hundredths, and thousandths.

Place the numbers, as given, in a column.
0.211
0.201
0.300
0.310
0.212

Sort the column from lowest (on the bottom) to highest (on the top) by comparing the tenths position.  Note that, after sorting, 0.212, 0.201, and 0.211 are lower than 0.310 and 0.300.
0.300
0.310
0.211
0.201
0.212

Sort 0.212, 0.201, and 0.210 from lowest to highest by comparing the hundredths position.
Sort 0.310 and 0.300 by comparing the hundredths position.  Note that, after sorting, 0.300 and 0.310 are in the correct order.
0.310
0.300
0.211
0.212
0.201

Sort 0.201, 0.212, and 0.211 from lowest to highest by comparing the thousandths position.  Note that, after sorting, 0.201, 0.211, and 0.212 are in the correct order, putting the entire column in the correct order.
0.310
0.300
0.212
0.211
0.201

Finish by putting the numbers from lowest to highest in a row.
0.201, 0.211, 0.212, 0.300, 0.310


Practice – Questions
1.  You are given the numbers 2246, 1110, 2248, 2232, and 1159.  Without using the calculator, what is the order of these numbers from smallest to largest?
A.  1110, 2246, 2248, 2232, 1159
B.  1110, 1159, 2248, 2232, 2246
C.  1110, 1159, 2232, 2248, 2246
D.  1110, 1159, 2232, 2246, 2248

2.  You are given the numbers 0.446, 0.310, 0.448, 0.432, and 0.359.  Without using the calculator, what is the order of these numbers from smallest to largest?
A.  0.446, 0.310, 0.448, 0.432, 0.359
B.  0.310, 0.359, 0.432, 0.446, 0.448
C.  0.310, 0.448, 0.448, 0.432, 0.359
D.  0.310, 0.359, 0.432, 0.448, 0.446

3.  A scientist measures the lengths of five worms.  Their lengths in inches are 0.311, 0.301, 0.400, 0.410, and 0.412, respectively.  Without using the calculator, what is the order of these worms from shortest to longest?
A.  0.311, 0.301, 0.400, 0.410, 0.312
B.  0.301, 0.311, 0.400, 0.410, 0.312
C.  0.301, 0.311, 0.312, 0.400, 0.410
D.  0.301, 0.311, 0.312, 0.410, 0.400

4.  Five people weigh 196, 242, 142, 247, and 231 pounds, respectively.  Without using the calculator, what is the order of these weights from lightest to heaviest?
A.  142, 196, 231, 242, 247
B.  242, 196, 142, 247, 231
C.  142, 196, 231, 247, 242
D.  196, 242, 142, 247, 231

5.  Five worms weigh 0.296, 0.342, 0.242, 0.347, and 0.331 ounces, respectively.  Without using the calculator, what is the order of these worms from lightest to heaviest?
A.  0.296, 0.342, 0.242, 0.347, 0.331
B.  0.242, 0.296, 0.331, 0.342, 0.347
C.  0.342, 0.296, 0.242, 0.347, 0.331
D.  0.296, 0.342, 0.331, 0.347, 0.342

6.  Five items at the hardware store cost $12.96, $13.42, $12.42, $13.47, and $13.31, respectively.  Without using the calculator, what is the order of their cost from least expensive to most expensive?
A.  $12.96, $13.42, $12.42, $13.47, $13.31
B.  $13.42, $12.96, $12.42, $13.47, $13.31
C.  $12.42, $12.96, $13.31, $13.42, $13.47
D.  $12.42, $12.96, $13.31, $13.47, $13.42

7.  Five items at the hardware store cost $22.97, $33.43, $12.42, $23.48, and $13.31, respectively.  Without using the calculator, what is the order of their cost from least expensive to most expensive?
A.  $22.97, $33.43, $12.42, $23.48, $13.31
B.  $33.43, $22.97, $12.42, $23.48, $13.31
C.  $12.42, $13.31, $22.97, $33.43, $23.48
D.  $12.42, $13.31, $22.97, $23.48, $33.43

8.  Five items on a restaurant menu cost $1.97, $0.97, $1.96, $0.98, and $0.99, respectively.  Without using the calculator, what is the order of their cost from least expensive to most expensive?
A.  $0.97, $0.98, $0.99, $1.96, $1.97
B.  $0.97, $1.97, $1.96, $0.98, $0.99
C.  $0.97, $0.98, $1.96, $0.99, $1.97
D.  $0.97, $0.98, $0.99, $1.97, $1.96

9.  Five items on a restaurant menu cost $19.97, $9.97, $19.96, $1.98, and $1.99, respectively.  Without using the calculator, what is the order of their cost from least expensive to most expensive?
A.  $1.98, $1.99, $9.97, $19.97, $19.96
B.  $9.97, $19.97, $19.96, $1.98, $1.99
C.  $9.97, $19.97, $19.96, $1.99, $1.98
D.  $1.98, $1.99, $9.97, $19.96, $19.97

10.  A scientist measures the lengths of five ants.  Their lengths in centimeters are 0.512, 0.502, 0.601, 0.611, and 0.513, respectively.  Without using the calculator, what is the order of these ants from shortest to longest?
A.  0.512, 0.502, 0.601, 0.611, 0.513
B.  0.502, 0.512, 0.601, 0.611, 0.513
C.  0.502, 0.512, 0.513, 0.611, 0.601
D.  0.502, 0.512, 0.513, 0.601, 0.611


Practice – Answers
1.  D.  1110, 1159, 2232, 2246, 2248

2.  B.  0.310, 0.359, 0.432, 0.446, 0.448

3.  C.  0.301, 0.311, 0.312, 0.400, 0.410

4.  A.  142, 196, 231, 242, 247

5.  B.  0.242, 0.296, 0.331, 0.342, 0.347

6.  C.  $12.42, $12.96, $13.31, $13.42, $13.47

7.  D.  $12.42, $13.31, $22.97, $23.48, $33.43

8.  A.  $0.97, $0.98, $0.99, $1.96, $1.97

9.  D.  $1.98, $1.99, $9.97, $19.96, $19.97

10.  D.  0.502, 0.512, 0.513, 0.601, 0.611

About Scott Solomon

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