Basic Mathematics for College Students



320 Chapter 4 Decimals

The Language of Mathematics Decimals are often read in an informal way.

For example, we can read 184.3 as “one hundred eighty-four point three” and

9.69 as “nine point six nine.”

The procedure for reading a decimal can be applied in reverse to convert from

written-word form to standard form.

Solution

a.. The whole-number part is 184. The fractional part is 3.

The digit the farthest to the right, 3, is in the tenths place.

One hundred eighty-four and three tenths

Written as a mixed number, 184.3 is

b.. The whole-number part is 9. The fractional part is 69.

The digit the farthest to the right, 9, is in the hundredths place.

Nine and sixty-nine hundredths

Written as a mixed number, 9.69 is

c.. The whole-number part is 0. The fractional part is 43.

The digit the farthest to the right, 4, is in the ten-thousandths place.

Forty-three ten-thousandths Since the whole-number part is 0, we need not write it

nor the word and.

Written as a fraction, 0.0043 is

d.. This is a negative decimal.

Negativethirty-seven and seven tenths.

Written as a negative mixed number,37.7is  37 107.

 37 7

43

10,000^.

0 0043

9 10069.

9 69

184 103.

184 3

EXAMPLE (^4) Write each number in standard form:
a.One hundred seventy-two and forty-three hundredths
b.Eleven and fifty-one thousandths
StrategyWe will locate the word andin the written-word form and translate the
phrase that appears before it and the phrase that appears after it separately.
WHYThe whole-number part of the decimal is described by the phrase that
appears before the word and.The fractional part of the decimal is described by the
phrase that follows the word and.
Solution
a.
172.43
This is the hundredths place-value column.
b.Sometimes, when changing from written-word form to standard form, we must
insert placeholder 0’s in the fractional part of a decimal so that that the last
digit appears in the proper place-value column.

11.051

This is the thousandths place-value column.

A place holder 0 must be inserted here so that the

last digit in 51 is in the thousandths column.

Eleven and fifty-one thousandths

One hundred seventy-two and forty-three hundredths

Self Check 4

Write each number in standard

form:

a.Eight hundred six and ninety-

two hundredths

b.Twelve and sixty-seven ten-

thousandths

Now TryProblems 41, 45, and 47

Caution! If a placeholder 0 is not written in 11.051, an incorrect answer of

11.51 (eleven and fifty-one hundredths,not thousandths) results.

Now TryProblems 31, 35, and 39