Chapter 3 Decimals (194)
Objectives
Use decimal notation
Compare, order, and round decimals
Add/subtract decimals
Multiply decimals
Divide decimals
Convert fractions to decimals and the order of operations
Estimate and solve applied problems involving decimals
3.1 Using Decimal Notation (195)
Objectives
Write a decimal in words
Change from fractional notation to decimal notation
Change from decimal notation to fractional notation
3,1.1 Writing a Word Name for a Decimal Fraction (195)
Our number system is based on 10s. Probably because we have ten fingers.
Decimal fractions use tenths, hundredths, thousandths, ten-thousandths, etc. Same as for
whole numbers with no “units” and adding “th”.
One tenth is equivalent to 1/10 or 0.1
A decimal fraction is a fraction whose denominator is a power of ten. (10, 1000, 1000000, etc.)
The decimal separates the whole part of a number from the fractional (decimal ) part. Like the
whole part, you have to put place markers between the digits. Examples: 106, 2.105, -12.001
Note you can put as many zeroes in front of the whole part (00002.2) and as many zeroes after
any terminating decimal part (23.400000) In physics the number of digits after the decimal will
indicate the accuracy, but in computers, there is no significance unless you represent the value in a
different computer format.
If there is no whole portion of a decimal number, it is normal to put a 0 as the whole part. 0.13
Frequently the word “and” indicates the decimal point. 23.4
PP1 Write a word name for each decimal (196)
a) 0.073 seventy-three thousandths
b) 4.68
four and sixty-eight hundredths
c) 0.0017 seventeen ten-thousandths
d) 561.78 five hundred sixty-one and seventy-eight hundredths
How many days in a year? It’s not 365 otherwise why have a leap year? It is approximately
365 1/4, but then why don’t we have a leap year in most years ending in 00. According to
astronomers a tropical year rounded to the nearest hundred-thousandth is 365.24122 days.
Note the relationship between fractions and their equivalent decimal format: 7/10 and 0.7;
23/100 and 0.23; and 147/1000 and 0.147 (one, two, three digits)
Does anyone have a check book? How do you make out a check if the cost is fifty-two dollars
and sixty-two cents?
PP2 Write a word name for the amount of a check made out for $7863.04 (197)
Seven thousand eight hundred sixty-three {and 4/100} dollars and four cents
3.1.2 Changing from Fractional Notation to Decimal Notation (197)
In this portion the denominators will be in powers of ten, but soon we will have other ones.
PP3 Write as a decimal (197)
a) 9/10
0.9
b) 136/1000
0.136
c) 2 56/100
2.56
d) 34 86/1000 34.086
3.1.3 Changing from Decimal Notation to Fractional Notation (197)
Note: In the future you will have to simplify the fractions. Example. 0.5 = 5/10 = 1/2
PP4 Write in fractional notation (197)
a) 0.37
37/100
b) 182.3
182 3/10
c) 0.7131
7131/10000
d) 42.019
42 19/1000
Here comes the simplification
PP5 Write in fractional notation. Reduce whenever possible (ALWAYS) (198)
a)
b)
c)
d)
8.5
0.58
36.25
106.013
8 5/10 = 8 1/2
58/100 = 29/50
36 25/100 = 36 1/4
106 13/1000
PP6 A chemist found that the concentration of PCBs in a water sample was 2 parts per billion.
What fraction would represent the concentration of PCBs. 2/1,000,000.000 = 1/500,000,000 (198)
Developing Your Study Skills: Build one step at a time. Master each one before moving on.
Engineers learning a long time ago that you need a good foundation. The six steps are: (198)
1. Attend class everyday and pay attention
2. Read the textbook – peruse before class, read for understanding afterwards
3. Take notes in class
4. Do assigned homeword every day, don’t put it off
5. Get help immediately from your teacher, the math help center, your friend, or classmate
6. Review regularly