Estimation and Rounding Notes

Now that you have put down what you believe each term means let’s discuss some more precise definitions and steps.

Place Value: A specific location or name of a digit within a number.

Digit: A digit is not the same a number. In our number system there are 10 digits (0 – 9). Numbers are composed of a single digit or many digits.

Now it is your turn to try using the number 457,123.098:

a) What digit is in the tens place? _____

b) What digit is in the tenths place? _____

c) The 7 is in the ______place.

Rounding:

Ø  The process of replacing one number with another number that has approximately the same value. When asked to round you will always be given a place value to round to.

Ø  Rounding usually takes place after you have solved the problem.

STEPS TO ROUNDING:

1) Identify the place value that you need to round to.

2) Locate the digit that is in that place value.

3) Look at the digit immediately to the right of that digit.

- if the number is 5 or larger round up

- if the number is 4 or less keep the number the same

4) If the number is after the decimal point, remove all digits after the place value you rounded to… if the number is before the decimal point, replace all digits (after the place value rounded to) with zeros until you reach the decimal point.

Now it is your turn to try using the number 457,123.098:

a) round to the nearest tens place ______

b) round to the nearest tenths place ______

c) round to the nearest ten-thousands place ______


Estimation:

Ø  The process of approximating an answer to a mathematical sentence. The process often involves changing numbers to other numbers that are close in value but easier to work with.

Ø  Estimation involves changing the numbers before performing any operations.

Ø  You do not have to follow the rules of rounding

STEPS TO ESTIMATION:

a) Identify the numbers that you need to use.

b) Change the numbers so that they become easier to work with (this can involve rounding).

c) Perform the given operation to find an approximate value for the problem in question.

Now it is your turn to estimate some solutions:

Original Expression / Estimation Expression / Approximate Answer
4.589 + 15.4982
9.8 • 5.468
23.65489 – 8.65
47 ÷ 6
12.123 + 7.321
45.78 – 6.32
3.399 • 15.12
546 ÷ 92

Directions: Choose the best answer.

1)  Rounding and estimation have the same definition.

a.  True

b.  False

2)  When rounding you change the numbers…

a.  before performing any operations.

b.  while you are performing any operations.

c.  after performing any operations.

d.  you don’t change any of the numbers.

3)  When estimating…

a.  you must follow the rules of rounding.

b.  you are told what place value to estimate to.

c.  there are many good estimates, but some are better than others

d.  you change the numbers after performing any operations

Directions: Use complete sentences to answer each question.

How are rounding and estimation similar?

______

______

How are rounding and estimation different?

______

______