Estimating

$19.95 ≈ $20.00

 

Positions
2146.8

thousands

2146.87
   
   hundreds

2146.873
”””
”””tens

2146.873
””””’
””””’ones

2146.873
””””””’
””””””’tenths

2146.873
””””””””
””””””””hundredths

2146.873
””””””””””
””””””””””thousandths

 


Technique

Estimating is a technique that uses rounding to make calculations “cleaner” and easier to do.

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

The words about and approximately are often used to suggest that you estimate.

The ≈ sign is sometimes used with estimating.


Question
Without using the calculator, about how much is 205 + 303?
A.  400
B.  500
C.  600
D.  700

Answer
B.  500

Answer Process
The word about is often used to suggest that you estimate.

Because the answer choices are rounded to the nearest hundred, round the parts of the problem to the nearest hundred.
205 —> 200
303 —> 300

Addition
200 + 300 = 500
[205 + 303 ≈ 500]


Question
Without using the calculator, approximately how much is 7196 – 3205?
A.  2000
B.  3000
C.  4000
D.  5000

Answer
C.  4000

Answer Process
The word approximately is often used to suggest that you estimate.

Because the answer choices are rounded to the nearest thousand, round the parts of the problem to the nearest thousand.
7196 —> 7000
3205 —> 3000

Subtraction
7000 – 3000 = 4000
[7196 – 3205 ≈ 4000]


Question
Without using the calculator, what is the approximate value of 99 × 11?
A.  10
B.  100
C.  1000
D.  10000

Answer
C.  1000

Answer Process
The word approximate is often used to suggest that you estimate.

Because the answer choices are rounded to something that ends in zero, see if you can round the parts of the problem to something that ends in zero.
99 —> 100 (99 rounded to the nearest hundred)
11 —> 10 (11 rounded to the nearest ten)

Multiplication
100 × 10 = 1000
[99 × 11 ≈ 1000]


Question
Without using the calculator, what is the approximate value of 6123 ÷ 32?
A.  20
B.  200
C.  2000
D.  20000

Answer
B.  200

Answer Process
The word approximate is often used to suggest that you estimate.

Because the answer choices are rounded to something that ends in zero, see if you can round the parts of the problem to something that ends in zero.
6123 —> 6000 (6123 rounded to the nearest thousand)
32 —> 30 (32 rounded to the nearest ten)

Division
6000 ÷ 30 = 200
[6123 ÷ 32 ≈ 200]


Question
A steak at a restaurant costs $19.95.  About how much does it cost?

Answer
$20.00

Answer Process
The word about is often used to suggest that you estimate.

Round to the nearest ten
19.95 —> 20
[$19.95 ≈ $20.00]

Question
At a fancy restaurant, a steak costs $19.95, a baked potato costs $9.99, a side salad costs $9.95, a glass of wine costs $9.99, and dessert costs $9.95.  Without using the calculator, approximately how much did a meal consisting of all of these items cost?
A.  $30.00
B.  $40.00
C.  $50.00
D.  $60.00

Answer
D.  $60.00

Answer Process
The word approximately is often used to suggest that you estimate.

Because the answer choices are rounded to the nearest ten, round the parts of the problem to the nearest ten.
19.95 —> 20
9.99 —> 10
9.95 —> 10
9.99 —> 10
9.95 —> 10

Addition
20 + 10 + 10 + 10 + 10 = 60
[$19.95 + $9.99 + $9.95 + $9.99 + $9.95 ≈ $60.00] 


Practice – Questions

1.  Without using the calculator, about how much is 415 + 523?
A.  600
B.  700
C.  800
D.  900

2.  Without using the calculator, approximately how much is 8196 – 2315?
A.  3000
B.  4000
C.  5000
D.  6000

3.  Without using the calculator, what is the approximate value of 994 × 12?
A.  10
B.  100
C.  1000
D.  10000

4.  Without using the calculator, what is the approximate value of 8123 ÷ 23?
A.  40
B.  400
C.  4000
D.  40000

5.  At a restaurant, a sandwich costs $2.95, french fries cost $0.99, a side salad costs $1.95, a drink costs $0.99, and dessert costs $1.95.  Without using the calculator, approximately how much did a meal consisting of all of these items cost?
A.  $6.00
B.  $7.00
C.  $8.00
D.  $9.00

6.  Bill’s bowling score was 132.  The highest score in the bowling alley that day was 281.
Without using the calculator, about how much lower was Bill’s score than the highest score that day?
A.  100
B.  125
C.  150
D.  175

7.  The bowling alley bought 22 bowling balls at a cost of $49.99 apiece.  Without using the calculator, approximately how much did the bowling alley pay for all of the bowling balls?
A.  $100.00
B.  $1000.00
C.  $10000.00
D.  $100000.00

8.  The bowling alley has 398 pizzas in stock.  Without using the calculator, if 42 bowlers eat all of the pizzas, approximately how many pizzas were eaten by each bowler?
A.  10
B.  20
C.  30
D.  40

9.  The highest temperature on an August day was 109ºF.  Without using the calculator, about how many degrees above freezing (32ºF) was the temperature?
A.  50°
B.  60°
C.  70°
D.  80°

10.  The coldest temperature on an January day was -19ºF.  Without using the calculator, about how many degrees below freezing (32ºF) was the temperature?
A.  40°
B.  50°
C.  60°
D.  70°


Practice – Answers

1.  D.  900

2.  D.  6000

3.  D.  10000

B.  400

5.  D.  $9.00

6.  C.  150

7.  B.  $1000.00

8.  A.  10

9.  D.  80°

10.  B.  50°

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