Download Decimals and Fractions

Math 952
5.5 "Decimals, Fractions, and Scienti…c Notation"
Objectives:
*
Learn how to change decimal numbers to fraction and/or mixed number form.
*
Learn how to change fractions and mixed numbers to decimal notation.
*
Know how to write and read decimal numbers in scienti…c notation.
Decimals and Fractions
Changing From Decimal Form to Fraction Form:
A decimal number with digits to the right of the decimal point can be written in fraction form by writing a fraction with.
1: A numerator that consists of the whole number formed by all the digits of the decimal number and
2: A denominator that is the power of 10 that corresponds to the rightmost digit.
Example 1: (Converting decimal numbers to fractions)
Change each decimal to a fraction and reduce (if possible).
a) 0:125
b)
3:45
c)
0:029
Changing From Fraction Form to Decimal Form:
A fraction can be written in decimal form by dividing the numerator by the denominator.
1: If the remainder is 0, the decimal is said to be terminating.
2: If the remainder is not 0, the decimal is said to be nonterminating.
Example 2: (Converting fractions to decimals)
Change each fraction to a decimal.
5
a)
16
b)
9
16
c)
Page: 1
5
18
Notes by Bibiana Lopez
Prealgebra by Franklin Wright
5.5
Operations with Both Decimals and Fractions
NOTE: In cases where the decimal number has more than four decimal places or is non-terminating, we will agree to
round the decimal to thousandths.
Example 3: (Working with fractions and decimals)
Perform the following operation in two ways (decimal and fraction form):
1
3
+
+ 3:452
3 10
Example 4: (Working with fractions and decimals)
Perform the following operations by writing all numbers in decimal form.
3
3
3
2
1 2
a)
+8 +1
b) 2 10
(1:5)
100
5
4
Example 5: (Evaluating expressions)
Evaluate x2 y 2 + 2xy
5 when x = 1:5 =
3
2
and y = :
2
3
Page: 2
Notes by Bibiana Lopez
Prealgebra by Franklin Wright
5.5
Absolute Value
De…nition:
"Absolute Value"
The absolute value of a decimal number is its distance from 0.
1: If a is positive or 0, then jaj = a:
2: If a is negative, then jaj =
a:
Example 6: (Absolute value)
Perform the following operation:
4 12 + 3 12
j 10:7j
Scienti…c Notation
De…nition:
"Scienti…c Notation"
A positive number is written in scienti…c notation when it is written in the form N
where 1
10n ;
N < 10 and n is an integer (n = :::; 3; 2; 1; 0; 1; 2; 3; 4; :::)
Example 7: (Writing numbers in scienti…c notation)
Write each of the following numbers in scienti…c notation.
a) 76; 200
b) 0:000000912
c) 0:4321
Example 8: (Word problem)
The United States produces about 3.3 pounds of solid waste per capita per day. The U.S. population is about 281,000,000.
Translate these facts into the number of pounds of solid waste produced each day in the United States. Write the number in
both decimal notation and scienti…c notation.
Page: 3
Notes by Bibiana Lopez