Decimals: Reading and Writing Decimals *

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1 OpenStax-CNX module: m Decimals: Reading and Writing Decimals * Wade Ellis Denny Burzynski This work is produced by OpenStax-CNX and licensed under the Creative Commons Attribution License 3.0 Abstract This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses how to read and write decimals. By the end of the module students should understand the meaning of digits occurring to the right of the ones position, be familiar with the meaning of decimal fractions and be able to read and write a decimal fraction. 1 Section Overview Digits to the Right of the Ones Position Decimal Fractions Reading Decimal Fractions Writing Decimal Fractions 2 Digits to the Right of the Ones Position We began our study of arithmetic () by noting that our number system is called a positional number system with base ten. We also noted that each position has a particular value. We observed that each position has ten times the value of the position to its right. This means that each position has 1 the value of the position to its left. * Version 1.2: Aug 18, 20 8:21 pm

2 OpenStax-CNX module: m Thus, a digit written to the right of the units position must have a value of of 1. Recalling that the word "of" translates to multiplication ( ), we can see that the value of the rst position to the right of the units digit is 1 of 1, or 1 1 = 1 The value of the second position to the right of the units digit is 1 of 1, or 1 1 = 1 = The value of the third position to the right of the units digit is 1 of 1, or = 1 = This pattern continues. We can now see that if we were to write digits in positions to the right of the units positions, those positions have values that are fractions. Not only do the positions have fractional values, but the fractional values are all powers of (, 2, 3,... ). 3 Decimal Fractions Decimal Point, Decimal If we are to write numbers with digits appearing to the right of the units digit, we must have a way of denoting where the whole number part ends and the fractional part begins. Mathematicians denote the separation point of the units digit and the tenths digit by writing a decimal point. The word decimal comes from the Latin prex "deci" which means ten, and we use it because we use a base ten number system. Numbers written in this form are called decimal fractions, or more simply, decimals. Notice that decimal numbers have the sux "th." Decimal Fraction A decimal fraction is a fraction in which the denominator is a power of. The following numbers are examples of decimals The 6 is in the tenths position = The 8 is in the tenths position. The 0 is in the hundredths position. The 1 is in the thousandths position. The 4 is in the ten thousandths position = ,000

3 OpenStax-CNX module: m The 9 is in the tenths position. The 3 is in the hundredths position = 93 0 note: Quite often a zero is inserted in front of a decimal point (in the units position) of a decimal fraction that has a value less than one. This zero helps keep us from overlooking the decimal point The 7 is in the tenths position. 0.7 = 7 note: We can insert zeros to the right of the right-most digit in a decimal fraction without changing the value of the number = 0.7 = 0.70 = = Reading Decimal Fractions Reading a Decimal Fraction To read a decimal fraction, 1. Read the whole number part as usual. (If the whole number is less than 1, omit steps 1 and 2.) 2. Read the decimal point as the word "and." 3. Read the number to the right of the decimal point as if it were a whole number. 4. Say the name of the position of the last digit. 4.1 Sample Set A Read the following numbers. Example note: Some people read this as "six point eight." This phrasing gets the message across, but technically, "six and eight tenths" is the correct phrasing. Example Example

4 OpenStax-CNX module: m Example 4 81 Eighty-one In this problem, the indication is that any whole number is a decimal fraction. Whole numbers are often called decimal numbers. 81 = Practice Set A Read the following decimal fractions. Exercise 1 (Solution on p. 8.) 12.9 Exercise 2 (Solution on p. 8.) 4.86 Exercise 3 (Solution on p. 8.) Exercise 4 (Solution on p. 8.) Writing Decimal Fractions Writing a Decimal Fraction To write a decimal fraction, 1. Write the whole number part. 2. Write a decimal point for the word "and." 3. Write the decimal part of the number so that the right-most digit appears in the position indicated in the word name. If necessary, insert zeros to the right of the decimal point in order that the right-most digit appears in the correct position. 5.1 Sample Set B Write each number. Example 5 Thirty-one and twelve hundredths. The decimal position indicated is the hundredths position Example 6 Two and three hundred-thousandths. The decimal position indicated is the hundred thousandths. We'll need to insert enough zeros to the immediate right of the decimal point in order to locate the 3 in the correct position Example 7 Six thousand twenty-seven and one hundred four millionths. The decimal position indicated is the millionths position. We'll need to insert enough zeros to the immediate right of the decimal point in order to locate the 4 in the correct position. 6,

5 OpenStax-CNX module: m Example 8 Seventeen hundredths. The decimal position indicated is the hundredths position Practice Set B Write each decimal fraction. Exercise 5 (Solution on p. 8.) Three hundred six and forty-nine hundredths. Exercise 6 (Solution on p. 8.) Nine and four thousandths. Exercise 7 (Solution on p. 8.) Sixty-one millionths. 6 Exercises For the following three problems, give the decimal name of the position of the given number in each decimal fraction. Exercise 8 (Solution on p. 8.) is in the position. 4 is in the position. 1 is in the position. Exercise is in the position. 0 is in the position. 8 is in the position. 5 is in the position. Exercise (Solution on p. 8.) is in the position. 7 is in the position. For the following 7 problems, read each decimal fraction by writing it. Exercise Exercise 12 (Solution on p. 8.) 8.1 Exercise Exercise 14 (Solution on p. 8.) Exercise

6 OpenStax-CNX module: m Exercise 16 (Solution on p. 8.) Exercise For the following problems, write each decimal fraction. Exercise 18 (Solution on p. 8.) Three and twenty one-hundredths. Exercise 19 Fourteen and sixty seven-hundredths. Exercise 20 (Solution on p. 8.) One and eight tenths. Exercise 21 Sixty-one and ve tenths. Exercise 22 (Solution on p. 8.) Five hundred eleven and four thousandths. Exercise 23 Thirty-three and twelve ten-thousandths. Exercise 24 (Solution on p. 8.) Nine hundred forty-seven thousandths. Exercise 25 Two millionths. Exercise 26 (Solution on p. 8.) Seventy-one hundred-thousandths. Exercise 27 One and ten ten-millionths. Calculator Problems For the following problems, perform each division using a calculator. Then write the resulting decimal using words. Exercise 28 (Solution on p. 8.) 3 4 Exercise Exercise 30 (Solution on p. 8.) 4 Exercise Exercise 32 (Solution on p. 8.) 4 25 Exercise Exercise 34 (Solution on p. 8.) 3 16 Exercise

7 OpenStax-CNX module: m Exercise 36 (Solution on p. 8.) Exercise Exercises for Review Exercise 38 (Solution on p. 8.) () Round 2,614 to the nearest ten. Exercise 39 () Is 691,428,471 divisible by 3? Exercise 40 (Solution on p. 8.) () Determine the missing numerator =? 56 Exercise 41 () Find 3 32 of Exercise 42 (Solution on p. 8.) () Find the value of ( 2 3 )

8 OpenStax-CNX module: m Solutions to Exercises in this Module Solution to Exercise (p. 4) twelve and nine tenths Solution to Exercise (p. 4) four and eighty-six hundredths Solution to Exercise (p. 4) seven and two hundred thousandths Solution to Exercise (p. 4) thirty thousand four hundred ve millionths Tenths; hundredths, thousandths Hundred thousandths; ten millionths eight and one tenth fty-ve and six hundredths one and nine hundred four thousandths seventy-ve hundredths four tenths sixteen hundredths one thousand eight hundred seventy-ve ten thousandths Solution to Exercise (p. 7) fty-ve hundredths Solution to Exercise (p. 7) 26 Solution to Exercise (p. 7) 12

9 OpenStax-CNX module: m Solution to Exercise (p. 7) 9 or 1 1 9

Based on Introduction to Fractions and Multiplication and Division of Fractions: Proper Fractions, Impr. Mixed Numbers *

Based on Introduction to Fractions and Multiplication and Division of Fractions: Proper Fractions, Impr. Mixed Numbers * OpenStax-CNX module: m7 Derived copy of Introduction to Fractions and Multiplication and Division of Fractions: Proper Fractions, Improper Fractions, and Mixed Numbers * Ann Simao Based on Introduction