Book cover for Prealgebra

Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

ISBN #9781938168994

1st Edition

5,729 Questions

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210,912 Students Helped

Homework Questions

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Summary
Learning Objectives
Key Concepts
Example Problems
Explanations
Common Mistakes

Summary

This section covers the fundamentals of decimals, including how to name, write, convert, locate, order, and round decimals. It emphasizes the connection between decimal notation and fractions by using the power-of-ten system, and shows practical applications in everyday circumstances like financial transactions. Understanding these concepts builds a strong foundation for performing arithmetic operations with decimals.

Learning Objectives

1

Name and write decimal numbers, including translating between words and numeric form.

2

Convert decimals to fractions or mixed numbers by identifying place values.

3

Locate and order decimals on a number line, including comparison of negative decimals.

4

Round decimals to a specified place value and apply these skills in real-world contexts such as money.

5

Perform basic operations with decimals, including addition, subtraction, multiplication, and division.

Key Concepts

CONCEPT

DEFINITION

Decimal Notation

A way of writing numbers that shows parts of a whole with a decimal point, representing fractions whose denominators are powers of ten.

Place Value

The value of a digit based on its position relative to the decimal point, both to the left (whole numbers) and right (fractional parts).

Equivalent Decimals

Decimals that have the same value, even if a different number of zeros are written at the end (e.g., 0.31 and 0.310).

Rounding Decimals

The process of approximating a decimal to a specified place value by increasing or leaving the digit based on the next digit’s value.

Conversion to Fraction

Translating a decimal to a fraction by using the place value of the last digit as the denominator (a power of ten) and the digits to the right as the numerator.

Example Problems

Example 1

In the following exercises, name each decimal. $$5.5$$

Example 2

In the following exercises, name each decimal. $$7.8$$

Example 3

In the following exercises, name each decimal. $$5.01$$

Example 4

In the following exercises, name each decimal. $$14.02$$

Example 5

In the following exercises, name each decimal. $$8.71$$
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Step-by-Step Explanations

QUESTION

How do you name the decimal 15.68?

STEP-BY-STEP ANSWER:

Step 1: Name the whole number part: 'fifteen'.
Step 2: Use the word 'and' to indicate the decimal point.
Step 3: Name the digits to the right of the decimal as if they were a whole number: 'sixty-eight'.
Step 4: Identify the place value for the last digit; since the last digit is in the hundredths place, use 'hundredths'.
Final Answer: The decimal 15.68 is read as 'fifteen and sixty-eight hundredths'.

Naming a Decimal

QUESTION

Convert the decimal 0.03 to a fraction.

STEP-BY-STEP ANSWER:

Step 1: Identify the place value of the last digit; here, 3 is in the hundredths place.
Step 2: Write the decimal as a fraction with 3 as the numerator and 100 as the denominator.
Step 3: Simplify the fraction if necessary.
Final Answer: 0.03 = 3/100.

Converting a Decimal to a Fraction

QUESTION

Round 18.379 to the nearest hundredth.

STEP-BY-STEP ANSWER:

Step 1: Identify the hundredth place; here, the digit is 7 in 18.379.
Step 2: Look at the digit immediately to the right, which is 9.
Step 3: Since 9 is greater than or equal to 5, add 1 to the hundredth digit.
Step 4: Remove all digits to the right of the hundredth place.
Final Answer: 18.379 rounded to the nearest hundredth is 18.38.

Rounding a Decimal

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Common Mistakes

  • Failing to line up decimal points correctly when adding or subtracting decimals.
  • Incorrectly naming the decimal part by forgetting to mention the proper place value (e.g., confusing tenths and hundredths).
  • Neglecting zeros as placeholders which can lead to errors in identifying the correct place value.
  • Assuming that appending zeros to the right of a decimal changes its value, instead of recognizing they are equivalent decimals.