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Decimals: reading and writing decimals

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Sample set a

Read the following numbers.

6.8

6.8 is six and eight tenths. The 8 is in the tenths position.

Some people read this as "six point eight." This phrasing gets the message across, but technically, "six and eight tenths" is the correct phrasing.

14.116

14.116 is fourteen and one hundred sixteen thousandths. The six is in the thousandths position.

0.0019

0.0019 is nineteen ten thousandths. The nine is in the ten thousandths position.

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 = 81 . 0 size 12{"81"="81" "." 0} {}

Practice set a

Read the following decimal fractions.

12.9

twelve and nine tenths

4.86

four and eighty-six hundredths

7.00002

seven and two hundred thousandths

0.030405

thirty thousand four hundred five millionths

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.

Sample set b

Write each number.

Thirty-one and twelve hundredths.

The decimal position indicated is the hundredths position.

31.12

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.

2.00003

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.

6,027.000104

Seventeen hundredths.

The decimal position indicated is the hundredths position.

0.17

Practice set b

Write each decimal fraction.

Three hundred six and forty-nine hundredths.

306.49

Nine and four thousandths.

9.004

Sixty-one millionths.

0.000061

Exercises

For the following three problems, give the decimal name of the posi­tion of the given number in each decimal fraction.

1. 3.941
9 is in the position.
4 is in the position.
1 is in the position.

Tenths; hundredths, thousandths

17.1085
1 is in the position.
0 is in the position.
8 is in the position.
5 is in the position.

652.3561927
9 is in the position.
7 is in the position.

Hundred thousandths; ten millionths

For the following 7 problems, read each decimal fraction by writing it.

9.2

8.1

eight and one tenth

10.15

55.06

fifty-five and six hundredths

0.78

1.904

one and nine hundred four thousandths

10.00011

For the following 10 problems, write each decimal fraction.

Three and twenty one-hundredths.

3.20

Fourteen and sixty seven-hundredths.

One and eight tenths.

1.8

Sixty-one and five tenths.

Five hundred eleven and four thousandths.

511.004

Thirty-three and twelve ten-thousandths.

Nine hundred forty-seven thousandths.

0.947

Two millionths.

Seventy-one hundred-thousandths.

0.00071

One and ten ten-millionths.

Calculator problems

For the following 10 problems, perform each division using a calculator. Then write the resulting decimal using words.

3 ÷ 4 size 12{3¸4} {}

seventy-five hundredths

1 ÷ 8 size 12{1¸8} {}

4 ÷ 10 size 12{4¸"10"} {}

four tenths

2 ÷ 5 size 12{2¸5} {}

4 ÷ 25 size 12{4¸"25"} {}

sixteen hundredths

1 ÷ 50 size 12{1¸"50"} {}

3 ÷ 16 size 12{3¸"16"} {}

one thousand eight hundred seventy-five ten thousandths

15 ÷ 8 size 12{"15"¸8} {}

11 ÷ 20 size 12{"11"¸"20"} {}

fifty-five hundredths

9 ÷ 40 size 12{9¸"40"} {}

Exercises for review

( [link] ) Round 2,614 to the nearest ten.

2610

( [link] ) Is 691,428,471 divisible by 3?

( [link] ) Determine the missing numerator.
3 14 = ? 56 size 12{ { {3} over {14} } = { {?} over {"56"} } } {}

12

( [link] ) Find 3 16 of 32 39 size 12{ { {3} over {"16"} } " of " { {"32"} over {"39"} } } {}

( [link] ) Find the value of 25 81 + 2 3 2 + 1 9 size 12{ sqrt { { {"25"} over {"81"} } } + left ( { {2} over {3} } right ) rSup { size 8{2} } + { {1} over {9} } } {}

10 9   or   1 1 9 size 12{ { {"10"} over {9} } " or "1 { {1} over {9} } } {}

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Source:  OpenStax, Contemporary math applications. OpenStax CNX. Dec 15, 2014 Download for free at http://legacy.cnx.org/content/col11559/1.6
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