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chapter3.6b
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à 3.6è Changing Fractions to Decimal Form.
äèPlease change the following fractions to Decimal Form
êê and round the answers to the nearest thousandths place.
âêêêêè.375
#êêêï3êè ┌───────êêè 3
#ïChange the fraction, ─êï8 │ 3.000êë Thus, ─ï=ï.375
#êêêï8êë ╩╪╠╪╪êêë8
#ïto Decimal Form.êêê60è ┌──¥ ╠╚
#êêêêêè ═╬╪è│
#êêêêêë40 ──┘
éS To change the fraction,ï3/8, to Decimal Form, you should
#divide the bottom into the top.è ┌────
#êêêêë8 │ 3
Since the directions say to round answers to the nearest thousandths, we
will have to add zeros out to the ten-thousandths place.
#êêêêë ┌────────
#êêêêè 8 │ 3.0000
Now, you should divide as was done in earlier problems involving decimal
numbers.êêêê .3750
#êêêêë ┌────────
#êêêêè 8 │ 3.0000
#êêêêê ╩╪╠╪╪╪ë The answer rounded to
êêêêêè60ê the nearest thousandths
#êêêêêè═╬╪╪ë place is .375
êêêêêè 40
#êêêêêè ╠╚╪
êêêêêë 0
Thus, the Decimal Form of the Fraction,ï3/8, is .375.
1êêêï4
#êêêèChangeï─ïto decimal form.
êêêêè 5
êA)ï.945êèB)ï.8êëC)ï.875êèD)ïå
ü
êêêêê.800êë4
#êêêêè ┌───────êè ─è=è.8
#êêêêï5 │ 4.000êë5
#êêêêë ╠╪╚╪╪
Ç B
2êêê 3
#êêê Changeï──ïto decimal form.
êêêêï10
êA)ï.496êèB)ï.395êèC)ï.3êëD)ïå
ü
êêêêê.300êë3
#êêêêè ┌───────êè──è=è.3
#êêêê 10 │ 3.000êè 10
#êêêêë ╦╪╚╪╪
Ç C
3êêê 7
#êêêïChangeï─ïto decimal form.
êêêêè8
êA)ï.875êèB)ï.786êèC)ï.912êèD)ïå
ü
êêêêê.875êë7
#êêêêè ┌───────êè ─è=è.875
#êêêêï8 │ 7.000êë8
#êêêêë ╬╪╠╪╪
êêêêê 60
#êêêêê ═╬╪
êêêêêï40
#êêêêêï╠╚
Ç A
4êêêï11
#êêêèChangeï──ïto decimal form.
êêêêè 20
êA)ï.445êèB)ï.455êèC)ï.55êè D)ïå
ü
êêêêê .5500êï11
#êêêêè ┌─────────ê ──è=è.55
#êêêê 20 │ 11.0000êï20
#êêêêë ╔╚╪╚╪╪╪
êêêêê1 00
#êêêêê╔╪╚╚╪╪
êêêêêë0
Ç C
5êêêè7
#êêêèChangeï──ïto decimal form.
êêêêè 16
êA)ï.438êèB)ï.437êèC)ï.4485êïD)ïå
ü
êêêêê.4375êïThe answer rounded to
#êêêêè ┌────────ê the nearest thousandths
#êêêê 16 │ 7.0000êïplace is .438
#êêêêë ╬╪╠╪╪╪
êêêêê 60
#êêêêê ╠╨╪╪
êêêêê 120
#êêêêê ╔╔╩╪
êêêêêè80
#êêêêêè╨╚
Ç A
6êêêï17
#êêêèChangeï──ïto decimal form.
êêêêè 32
êA)ï.435êèB)ï.531êèC)ï.532êèD)ïå
ü
êêêêê .5312êïThe answer rounded to
#êêêêè ┌────────ê the nearest thousandths
#êêêê 32 │ 17.0000êïplace is .531
#êêêêë ╔╬╪╪╪╪╪
êêêêê1 00
#êêêêê╪╪╤╬╪╪
êêêêêè40
#êêêêêï╪╦╩╪
êêêêêè 80
#êêêêêè ╬╠
êêêêêè 16
Ç B
7êêêè9
#êêêèChangeï──ïto decimal form.
êêêêè 16
êA)ï.573êèB)ï.574êèC)ï.563êèD)ïå
ü
êêêêê.5625êïThe answer rounded to
#êêêêè ┌────────ê the nearest thousandths
#êêêê 16 │ 9.0000êïplace is .563
#êêêêë ╨╪╚╪╪╪╪
êêêêë 1 00
#êêêêë ╪╪╤╬╪╪
êêêêêï40
#êêêêê ╪╦╩╪
êêêêêè80
#êêêêêè╨╚
Ç C
8êêêè 3
#êêêèChangeï7 ─èto decimal form.
êêêêë 4
êA)ï7.35êèB)ï7.75êèC)ï7.85êèD)ïå
ü
êêêêê.7500êïThe answer rounded to
#è First, find theêë ┌────────ê the nearest thousandths
#decimal expansion forêï4 │ 3.0000êïplace is 7.75
#the fractional part.êê╩╪╨╪╪╪
Then add 7 to thisêêè 20
#decimal expansion.êêè╪╩╚╪╪
Ç B
9êêêë7
#êêêèChangeï4 ──ïto decimal form.
êêêêë 16
êA)ï4.438êïB)ï7.438êïC)ï4.738êïD)ïå
ü
êêêêê.4375êïThe answer rounded to
#è First, find theêë ┌────────ê the nearest thousandths
#decimal expansion forê 16 │ 7.0000êïplace is 4.438
#the fractional part.êê╬╪╠╪╪╪
Then add 4 to thisêêè 60
#decimal expansion.êêè╪╠╨╪╪
êêêêê 120
#êêêêê ╔╔╩╪
êêêêêè80
#êêêêêè╨╚
Ç A
äè Please write the following fractions in decimal form
using the "bar" notation.
â
êêë 5
#êëWriteï──ïin decimal form using the "bar" notation.
êêë11
#êêêêêêê╪╪
êêë 5/11è=è.454545∙∙∙è=è.45
éS Many fractions likeï3/4ïandè3/8ïhave decimal expansions
that divide evenly.
êêë 3êêë3
#êêë ─è=è.75èandè─è=è.375
êêë 4êêë8
These fractions, that divide evenly, are said to have terminating
decimal expansions.ïOther fractions likeï1/3ïandï5/11ïhave
decimal expansions that continue.
êêêê1
#êêêê─è=è.3333∙∙∙
êêêê3
êêêê5
#êêêë ──è=è.454545∙∙∙
êêêë 11
These patterns keep going forever.ïFractions like this are said to
have repeating decimal expansions.ïA convenient notation for this
kind of number is the "bar" notation.ïJust put a bar over the repeating
#numbers.êë 1êêêï╪
#êêê─è=è.3333∙∙∙è=è.3
êêê3
#êêê5êêêè ╪╪
#êêë ──è=è.454545∙∙∙è=è.45
#êêë 11è ╪êêêë ╪╪
Thus,ï1/3ïis equal toï.3ïandï5/11ïis equal toï.45
10ê 4
#êè Writeï─ïin decimal form using the "bar" notation.
êêè 9
#êè ╪╪êêè╪╪êêè╪
ë A)ï.29êëB)ï.36êëC)ï.4êè D)ïå
ü
êêêêë .444∙∙∙
#êêêêè┌─────────
#êêêê 9 │ 4.0000ê The "bar" notation for
#êêêêë╦╪╬╪╪êêê╪
êêêêê40êè.444∙∙∙ is .4
#êêêêê╦╬╪
êêêêê 40
Ç C
11êï1
#êè Writeï── in decimal form using the "bar" notation.
êêè 18
#êè ╪╪êêè ╪êêè╪╪╪
ë A)ï.18êëB)ï.05êëC)ï.056êïD)ïå
ü
êêêêë .0555∙∙∙
#êêêêè┌─────────
#êêêê18 │ 1.0000ê The "bar" notation for
#êêêêë╪╪╤╚╪╪êêê ╪
êêêêê100êï.0555∙∙∙ is .05
#êêêêê╪╤╚╪
êêêêê 100
Ç B
12êï3
#êè Writeï── in decimal form using the "bar" notation.
êêè 11
#êè ╪╪êêè╪êêè╪╪
ë A)ï.27êëB)ï.3êëC)ï.11êèD)ïå
ü
êêêêë .2727∙∙∙
#êêêêè┌─────────
#êêêê11 │ 3.0000ê The "bar" notation for
#êêêêë╩╪╩╪╪╪êêê╪╪
êêêêê 80êï.2727∙∙∙ is .27
#êêêêê╪╧╧╪
êêêêêï30
#êêêêêï╩╩
êêêêêè8
Ç A
13êï7
#êè Writeï── in decimal form using the "bar" notation.
êêè 15
#êè ╪╪êêè ╪êêï╪╪
ë A)ï.46êëB)ï.46êè C)ï.15êèD)ïå
ü
êêêêë .4666∙∙∙
#êêêêè┌─────────
#êêêê15 │ 7.0000ê The "bar" notation for
#êêêêë╬╪╚╪╪╪êêê ╪
êêêêë1 00êè.4666∙∙∙ is .46
#êêêêê╤╚╪╪
êêêêê100
#êêêêê╪╤╚╪
êêêêê 100
Ç B
äè Please change the following decimal numbers to fraction
êêïform.
âêêêê6ê3
#êêêè .6è=è──è=è─
êêêêë 10ê5
êêêêê395ê 79
#êêêï.395è=è────è=è───
êêêêë 1000ê200
éS To writeï.6ïin fraction form, you should just read the number.
For example,ï.6ïis read "six tenths".ïThusï.6ïis equal toï6/10.
This fraction can be reduced.
êêêêêï6ê3
#êêêë .6è=è──è=è─
êêêêê 10ê5
The number, .395, is read three hundred ninety-five thousandths.ïThus,
.395 is equal toï395/1000.ïThis fraction can be reduced.
êêêêêè395ê 79
#êêêë.395è=è────è=è───
êêêêêï1000ê200
ï14
êêêChange .3 to fraction form.
êï1êêï1êêè3
#ëA)ï─êëB)ï─êëC)ï──êëD)ïå
êï5êêï3êêï10
ü
êêêêêë3
#êêêêï.3è=è──
êêêêêè 10
Ç C
ï15
êêêChange .97 to fraction form.
êè9êêè97êê 7
#ëA)ï──êëB)ï───êèC)ï──êëD)ïå
êï10êêï100êê10
ü
êêêêêë97
#êêêê .97è=è───
êêêêêè 100
Ç B
ï16
êêêChange .75 to fraction form.
êï3êêè4êêï3
#ëA)ï─êë B)ï─êëC)ï─êë D)ïå
êï4êêè3êêï5
ü
êêêêê75ê3
#êêêè.75è=è───è=è─
êêêêë 100ê4
Ç A
ï17
êêêChange .425 to fraction form.
êï16êêï17êê 19
#ëA)ï──êëB)ï──êè C)ï──êëD)ïå
êï33êêï40êê 50
ü
êêêêê425ê17
#êêêï.425è=è────è=è──
êêêêë 1000ê40
Ç B