How to Convert Fractions to Decimals

Converting fractions to decimals is one of the basic skills in mathematics that you should learn in order to pass the Civil Service Examination.  Being able to convert numbers to fractions, decimals, and percents, will give you an advantage to solve problems better and faster. In this post, we are going to discuss how to convert fractions to decimals.

Recall that in fractions, the number at the top of the fraction bar is called the numerator and the number at the bottom of the fraction bar is called the denominator. In converting fractions to decimals we divide: the numerator becomes the dividend and the denominator becomes the divisor (don’t switch!).

fraction to decimals 3

In converting fractions to decimals, you should divide the numerator by the denominator manually. Take note of this step because most solvers switch their places.

Example 1: Convert \frac{4}{5} to decimals.

First, 4 divided by 5 cannot be done, so we place 0 in the quotient.

Second, we add the decimal point and place 0 after the decimal point in the dividend. We also add the decimal point to the quotient aligned with the first decimal point.

Third, ignoring the decimal point, we divide 40 by 5, which gives us 8. We write 8 at the right of the decimal point and continue our calculation.

So, \frac{4}{5} in decimals is 0.8.

fraction to decimal 2

Example 2: Convert \frac{1}{8} to decimals.

Again, we align the decimals and divide 1 with 8 which cannot be, so we place 0 in the quotient. Next, we add the decimal point and 0 to the dividend. Now dividing 10 by 8, we get 1 a quotient as shown below.

fraction to decimals 4

After subtraction, we still have a remainder. So, we add another 0 in the dividend as shown. Performing division, we have the following calculation.

fraction to decimal 5Next, we still have a remainder. Adding 0, we have the following calculation.

Screen Shot 2015-03-12 at 12.18.31 AM

 

Therefore \frac{1}{8} = 0.125.

Example 3: There are cases that the decimal in non-terminating such as \frac{1}{3}. If you calculate this fraction, it will give you 0.333333 with never ending 3’s. So, you can just round to 0.33 or depending on the number of decimal places required.

Example 4: There are cases that the decimals are repeating. For example, if we convert \frac{1}{7} to fractions, we get 0.142857142857 with 142857 repeating. Again, in examinations, they usually tell you to round your answers to the nearest place values.

Example 5: For mixed fractions, you can just ignore the whole number, and then convert the fraction to decimals. After you have calculated the decimal, add the whole number.

For example, how do we convert 9 \frac{4}{5} to decimals.

First, we ignore the whole number. Then, we convert \frac{4}{5} to decimals which is 0.8 in Example 1.  Lastly, we add 9 and 0.8 which is equal to 9.8.

9 \frac{4}{5} = 9.8.

Downloadable Math Word Problem Tutorials

Many of you had been asking for downloadable PDF of tutorials. Well, this is what you’ve been waiting for! Admin Jess Christian Ramirez has prepared some tutorials on math word problems with examples which you can download in PDF form. You may download them, print them, and share them with your friends!

Also, you might want to join our Facebook Group. We have more than 10,000 members reviewing through question and answer about Civil Service Exams.

0.) Basic Mathematics

1.) Number Relation Problems

2.) Geometry Word Problems 

3.) Money Problems

4.) Age Problems

5.) Work Problems

6.) Investment Problems

7.) Mixture Problems

8.) Motion Problems

Enjoy studying and good luck every one.

Remember: Deadline for application for the May 3 exam is on March 12!

Video Series: How to Solve Consecutive Number Problems

PH Civil Service Review partners with the Sipnayan Youtube Channel in order to teach the basic concepts of mathematics easily. These tutorials are explained in mixed Tagalog and English, so viewers would be able to understand more. Below is one of the video series in the Sipnayan Youtube channel: a series of tutorials on how to solve consecutive number problems.

Part 1

The first video shown below discusses the definition of consecutive numbers. It also explains the difference of consecutive numbers, consecutive even numbers, and consecutive odd numbers. It discusses how to represent consecutive numbers algebraically and gives two sample problems.

Part 2 (click here to watch video), discusses in details two more examples. The first is four consecutive numbers with a sum of 70 and the third one is 3 consecutive numbers with a sum of 51.

Part 3 (click here to watch video) discusses two consecutive number problems describing their terms.

Aside from these videos, PH Civil Service Review has also a tutorial series on “The Solving Consecutive Number Problems Series” which discusses more examples in details. You can also subscribe to the Sipnayan Youtube Channel to be updated to the latest videos.

Grammar Tutorial: Past Progressive Tense

Written by Leny Ortega

Past Progressive Tense of the verb is used when something was going on before another action happened. Remember, these two actions are both in the past. Only the action that was going on uses the past progressive tense while the other action uses the simple past tense.

1st past action (on-going)             2nd past action
Form:  (singular) was + verb – ing                     simple past (talked, walked, etc)
                    (plural )  were + verb – ing

Examples:
1. The teacher was discussing the lesson when the group of rowdy men entered the classroom.

2. The civilians were crossing the river when they heard a loud explosion.

3. The UN peace troopers were meeting their members when foreign terrorists attacked the camp.

Exercises: Use the correct form of the verb inside the parentheses.

1. Melissa (sing) her contest piece when the audience (shout) delightfully at her performance.

2. The GLEE Club members (prepare) their repertoire when the adviser (ask) them to revise the list.

3. The ballerina (practice) her routine when her partner accidentally (slip) on the floor.

4. The news reporter (deliver) the news when a storm surge (reach) his place.

5. The militant groups (ask) for a signature campaign against the president when the presidential
spoke person (call) for a press conference.

Answers:

1. The answers are was singing and shouted respectively. Melissa is singular that is why was is used. The first verb sing is formed as was singing and the other verb is in simple past, shouted. This means that Melissa was actually singing (on- going) then a shout was heard from the audience.

2. In this number “were preparing” is the first on- going past action. We could imagine here that members were on the process of selecting the songs and dance number to include in the repertoire when all of a sudden the club adviser asked them to revise the items included in the list. Therefore, the correct answers here are: were preparing and asked.

3. In this number, both the ballerina and her partner were dancing (Meaning on-going). The ballerina was busy doing her part of the routine then the partner accidentally slipped. So, the correct answers are was practicing (ballerina –singular) and slipped.

4. In sentence number 4, we can actually imagine a television news reporter doing her usual account of a typhoon when a big wave of water was seen on the background reached his place. Therefore, the news reporting was on- going when a storm surged occurred. Answers: was delivering and reached.

5. The answers to this number are: were asking and called. We use “were asking” because the subject is plural (militant groups). The idea here is that the groups were busy asking people to sign in favor of their campaign against the president. Then, probably after hearing this propaganda against the president the spoke person announced of an urgent press conference.

How to Convert Decimal Numbers to Percent

Conversions of decimals, fractions, and percent is a very important basic skill in mathematics and many problems in the Civil Exams require this skill. Being able to convert from one form to another will help you speed up in calculations.   For example, instead of multiplying a number by 25%, you just have to get its 1/4 or simply divide it by 4.

Percent usually appears in discount and interest problems while fractions and decimals appear in various types of problems.

How to Convert Decimals to Percent

To convert decimal percent, you just have to multiply the decimal by 100.

Example 1

What is 0.25 in percent?

Solution

0.25 × 100 = 25

So, the answer is 25%.

Example 2

What is 0.08 in percent?

0.08 × 100 = 8

Therefore, the answer is 8%.

Of course, there are cases that the given is more than one such as the next example

Example 3

What is 1.8 in percent?

Solution

1.8 × 100 = 180

Therefore, the answer is 180%.

Example 4

What is 0.009 in percent?

Solution

0.009× 100 = 0.9%

Notice that some percent can also have decimal point such as shown in Example 4. In dealing with many decimals, if we multiply them with 100, we just move two decimal places to the right.

In the next post, we are going to discuss the other way around. That is, how to convert, percent to decimals.

Grammar Rules: Present Perfect Tense

Written by Leny Ortega
Like simple tenses, perfect or sometimes called compound tenses have three categories namely: Present Perfect, Past Perfect, and Future Perfect. Each of these has a corresponding usage depending on the time of action is completed or intended to be done.

PRESENT PERFECT TENSE

Present Perfect Tense is used to express an action happened at an unspecific time before now. The exact time is not important.  Unlike the simple past tense, the action is done at a particular time. Hence, time expression such as yesterday, last month, etc. must be stated. The only time expressions accepted in this tense are: ever, never, once, many times, several times, before, so far, already, yet, etc.

FORM: for singular subject =Has + past participle of the given verb
                For plural subject   = Have + past participle of the given verb
***

Example 1: I have seen the movie Serendipity more than ten times.
Present perfect tense is also used to talk about change that has happened over a period of time.

Example 2: My English has improved since I migrated to America.
We also use the present perfect tense of the verb to tell an action that began in the past but continues up to the present.

Example 3: I have been in Japan since October.

Exercise: Choose the correct form of the present perfect tense in the following sentences.

  1. My friend Claire (has been, have been, was) in England for six months.
  2. Many policemen (have died, has died, died) in the Mindanao siege.
  3. The army (has attacked, have attacked, attacked) that city five times.
  4. The principal (has been, have been, was) in the meeting since this morning.
  5. The baby (has grown, have grown, grew) so fast!

Answer:

1.) The correct answer to this number is Has been for the following reasons: first, the subject, Claire is singular that is why we use HAS not HAVE. Second, the exact time she moved to England was not stated. But, the action began six months ago and until now she is still in England.

2.) The answer here is Have died. The subject is plural (policemen) therefore, have must be used together with the past participle of the verb die. We cannot use the simple past tense here (died) because the specific time is not mentioned.

3.) The answer is has attacked. Again, there is no specific time when the attacked happened. But the idea here is that from the first time the city was attacked until now it happened only six times.

4.) The correct answer is Has been. The subject (principal) is singular so, has been is used. This sentence means that the meeting started in the morning until the time of speaking the meeting is still on-going.

5.) The sentence tells us that the change happened for a period of time (but unspecified).

The Difference Between ITS and IT’S

ITS is the contracted possessive form that modifies or describes the subject of the sentence.

Sample sentence:
She will talk to you about its natural habitat in a few minutes.

IT’S is simply a contracted form of “it is” and is used as a helping verb; it is used to show ownership or possession of specific qualities.

Sample sentence:
It’s only proper to greet older people with a smile.

There is no such word as ITS’.

Practice Test: ITS or IT’S

1.) The ostrich is also known for (its, it’s) inability to fly.

2.) Do you think (its, it’s) going to be easy?

3.) (Its, It’s) outstanding qualities give competing cars a run for their money.

4.) I think (its, it’s) going to rain.

5.) This pillow is too big for (its, it’s) case.

Short answer key: (1) its, (2) it’s, (3) its (4) it’s (5) its.

For more exercises about its and it’s, take this grammar quiz.

The Solving Consecutive Number Problems Series

The Solving Consecutive Number Problems Series is a series of post discussing how to solve consecutive number word problems in Algebra. Consecutive number problems are very common in many exams including the Subprofessional and Professional Civil Service Exams. Below is the list of posts including their descriptions.

How to Solve Consecutive Number Problems Part 1 is an introduction to the concept and algebraic representation of numbers. This post discusses the difference between consecutive integers, consecutive odd integers, and consecutive even integers. Two sample problems with complete and detailed solutions were discussed in this post.

How to Solve Consecutive Number Problems Part 2 discusses more examples about consecutive numbers and consecutive odd numbers.

How to Solve Consecutive Number Problems Part 3 discusses examples about consecutive odd numbers and consecutive even numbers.

Each of this posts has a video from Youtube that you can watch if you are not fond of reading.

I hope you enjoy these posts.

If you want me to discuss a particular topic, please comment them below.

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