Math 104Section 1.1

Place Value, Estimation, Rounding, Decimals & Order of Operations

Place ValuesImmediately to the left of the decimal point is

the ones place. To its thousands, hundred thousands, and million places. To the right of the decimal point, it is important is no “oneths” place.

History

The number system, we use today, are called the Hindu-Arabic System is a base 10(or a decimal) system.

EstimationEstimation is done to determine an

approximate value of a calculation. It is used to make our life easier while

computing.

Example

You are grocery shopping and realize you only have $10. You want to buy a gallon of milk for $3.69, a bag chips for 99cents, a sandwich from the Deli for $3.99. Quickly estimate the total cost of your items to see if you will have enough money.

You can estimate the milk to cost $4, the chips to cost $1, and the sandwich to cost $4, making the total $9. So $10 should be enough.

RoundingRounding involves a specified place value.

We must have a place value to which to round. Note: if there is no directive to round to a

specified place value, it is incorrect to do.

Procedure for rounding1. Determine the round off digit.2. If the 1st digit to the right of the round-off

digit is less than 5, do not change the round-off digit, but delete all the remaining digits to its right. If you are rounding to a whole number, such as tens or hundreds, all the digits between the round-off digit and the decimal point should become zeros, and no digits will appear after the decimal point.

Procedure for rounding cont.3. If the first digit to the right of the round-off digit

is 5 or more, increase the round-off digit by 1, and delete all the remaining digits to its right. Again if you are rounding to a non-decimal number, such as tens or hundred, all the digits between the round-off digit and the decimal point should become zeros, and no digits will appear after the decimal point.

4. For decimals, double-check to make sure the right-most digit of the decimal falls in the place value column to which you were directed to round, and there are no other digits to its right.

ExampleRound 103.4736999 to the nearest tenth,

hundredth, and then hundred.

For the tenth: 4 is in the 10th place. The 7

immediately to its right indicates we are to change 4 to 5, and remove rest of the digits. 103.5

For hundredth: “7” – the value is 103.47For hundred: “1”- the value is 100.

Example

Round 13.99 to the nearest whole number and then hundred.

For the whole number – 14For the hundred - 0

Leading Digit Estimation

In this technique, we actually arrive at our estimated answer by rounding each number in the problem based on the first digit in each number.

Example

Use leading digit estimation to estimate the sum:

2319+345+12+421+5698=?2000+300+10+400+6000=8710Actually sum gives us 8795

Arithmetic with DecimalsSubtract 7.67 from 19.8

19.80-7.6712.13

Order of Operations The order that we do math problems matters. You can

solve problems in the correct order by remembering…

Please Excuse My Dear Aunt Sally(OR)

P E MD AS P ( ) Do what is in the parenthesis first.

E 32 Exponents next.

M/D Then do multiplication and division from left to right.

A/S Adding and Subtracting from left to right is last.

Example Expression48 ÷ (8+4) × 6 +32

48 ÷12 ×6 +32

48 ÷ 12 × 6 + 9

4 × 6 + 924 +9

33

P: Do what is in the parentheses first. (8+4)= 12

E: Do the exponents. 32= 3 x 3=9MD: Next do multiplication and division from left to right. 48 ÷ 12 = 4.4 x 6= 24.

AS: Last do addition and subtraction from left to right. There is only addition so you do 24 + 9 = 33

Example

1. 5+6.2 × 1.7

2. 13-5+6

3. 5 ×(2+3)4 –(6-4)+1

4. 4 × 4 - 3 × 3 - 16 ÷ 4

HW5-11, 13-18,20-23