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Decimals Module Overview

Acknowledgments This presentation is based on and includes content derived from the following OER resource: Pre-Algebra An OpenStax book used for this course may be downloaded for free at: https://openstax.org/https://openstax.org/details/books/psychology


To name a decimal number Step 1: Name the number to the left of the decimal point Step 2: Write “and” for the decimal point Step 3: Name the “number” part to the right of the decimal point as if it were a whole number Step 4: Name the decimal place of the last digit Example: 23.057 reads as: “twenty-three and fifty-seven thousandths” Image: Fig 5.2 Prealgebra, Openstax

Write a decimal number from its name Step 1: Locate the word “and” – it tells you where the decimal point lies. Place a decimal point under the word “and” Step 2: Translate the words before “and” into the whole number and place it to the left of the decimal point. Note: if there is no “and” write a “0” with a decimal point to its right. Step 3: Mark the number of decimal places needed to the right of the decimal point by noting the place value indicated by the last word Step 4: Translate the words after “and” into the number to the right of the decimal point. Write the number in the spaces, putting the final digit in the last place. Fill in zeros for place holders, as needed.

Example writing a decimal from its name Two hundred thirty-five and thirty-two thousandths 235.___ ___ ___ Tenths Hundredths Thousands 235.___ _3_ _2_ 235.032

Convert a decimal to a fraction or mixed number

Ordering decimals Step 1: Check to see if both numbers have the same number of decimal places. If not, write zeros at the end of the one with fewer digits to make them match. Step 2: Compare the numbers to the right of the decimal point as if they were whole numbers. Step 3: Order the numbers using the appropriate inequality sign. Example: 0.415 vs 0.41  0.415  0.415 > 0.410 0.410

Rounding decimals Step 1: Locate the given place value, and underline the digit to the right. Step 2: If the underlined digit is greater than or equal to 5, add 1 to the digit in the given place value. If the underlined digit is 4 or less, do not change the digit in the given place value. Step 3: Rewrite the number, removing all digits to the right of the given place value. Example: Round 3.478 to the nearest hundredth. Since 8 > 5, add one to the 7 to get 3.48

To add or subtract decimals Step 1: Write the numbers vertically so the decimal points line up Step 2: Use zeros as place holders, as needed Step 3: Add or subtract the numbers as if they were whole numbers. Place the decimal in the answer under the decimal points in the given numbers. Example: 23.1 – 19.43 23.1 23.10 -19.43  -19.43 3.67 1 12 10

To multiply decimals Step 1: Determine the sign of the product. Step 2: Write the numbers in vertical format, lining up the numbers on the right. Step 3: Multiply as if they were whole numbers, temporarily ignoring the decimal points. Step 4: Place the decimal point. The number of decimal places in the product is the sum of the number of decimal places in the factors. Use zeros as placeholders, as needed.

Multiplication example

To multiply a decimal by a power of 10

To divide a decimal by a whole number

Dividing Decimal Numbers

To convert a fraction to a decimal

Converting a fraction to a decimal example 2

Properties of circles Image: Chapter 5, Prealgebra, Openstax

Example problems

Solve Equations with Decimals

Examples using properties of equality

Mean

Median

Mode The mode of a set of numbers is the number(s) that occur(s) most frequently. Note: Some data sets have no mode because all values appear the same number of times. Other data sets have more than one mode. Example: Find the mode of the following data: 3, 7, 7, 7, 11, 11, 12, 12, 12, 15 Modes: 7 and 12

Probability

Rate and ratio

Unit rate

Unit price

Squares and radicals radicand radical sign

Radical example

How to study this module Read the syllabus or schedule of assignments regularly. Understand key terms; look up and define all unfamiliar words and terms. Take notes on your readings, assigned media, and lectures. Discuss topics with classmates. Frequently review your notes. Make flow charts and outlines from your notes to help you study for assessments. Complete all course assessments.

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