A decimal fraction differs from an ordinary fraction in that its denominator is a place value.
For example:
Decimal fractions are separated from ordinary fractions into a separate form, which led to their own rules for comparing, adding, subtracting, multiplying and dividing these fractions. In principle, you can work with decimal fractions using the rules of ordinary fractions. Own rules for converting decimal fractions simplify calculations, and rules for converting ordinary fractions to decimals, and vice versa, serve as a link between these types of fractions.
Writing and reading decimal fractions allows you to write them down, compare them, and perform operations on them according to rules very similar to the rules for operations with natural numbers.
The system of decimal fractions and operations on them was first outlined in the 15th century. Samarkand mathematician and astronomer Dzhemshid ibn-Masudal-Kashi in the book “The Key to the Art of Counting”.
The whole part of the decimal fraction is separated from the fractional part by a comma; in some countries (the USA) they put a period. If a decimal fraction does not have an integer part, then the number 0 is placed before the decimal point.
You can add any number of zeros to the fractional part of a decimal on the right; this does not change the value of the fraction. The fractional part of a decimal is read at the last significant digit.
For example:
0.3 - three tenths
0.75 - seventy-five hundredths
0.000005 - five millionths.
Reading the whole part of a decimal is the same as reading natural numbers.
For example:
27.5 - twenty seven...;
1.57 - one...
After the whole part of the decimal fraction, the word “whole” is pronounced.
For example:
10.7 - ten point seven
0.67 - zero point sixty-seven hundredths.
Decimal places are the digits of the fractional part. The fractional part is not read by digits (unlike natural numbers), but as a whole, therefore the fractional part of a decimal fraction is determined by the last significant digit on the right. The place system of the fractional part of the decimal is somewhat different than that of natural numbers.
- 1st digit after busy - tenths digit
- 2nd decimal place - hundredths place
- 3rd decimal place - thousandths place
- 4th decimal place - ten-thousandth place
- 5th decimal place - hundred thousandths place
- 6th decimal place - millionth place
- 7th decimal place - ten millionth place
- The 8th decimal place is the hundred millionth place
The first three digits are most often used in calculations. The large digit capacity of the fractional part of decimals is used only in specific branches of knowledge where infinitesimal quantities are calculated.
Converting a decimal to a mixed fraction consists of the following: the number before the decimal point is written as an integer part of the mixed fraction; the number after the decimal point is the numerator of its fractional part, and in the denominator of the fractional part write a unit with as many zeros as there are digits after the decimal point.
Is the conjunction “and” necessary when writing decimal places after the decimal point in a fractional number? Example: 10.5 (ten point five) square meters. m? Thank you!
No union needed: ten point five.
| Question No. 292725 | ||
The team of the portal "Gramota.ru", hello! I have an issue that has been troubling me for a long time: coordinating the verb form with complex (including fractional) numerals. I carefully studied the information on the topic http://new.gramota.ru/spravka/letters/64-bolshinstvo. But the question regarding fractional numbers remains open for me, I think, not only for me. These are the examples. 1). "In 2016, 58.2 thousand employees participated in scientific research and development on a reimbursable basis." (If there were only 58 people, then we would put “O”, but there is a nuance here: there are 2 tenths and thousands. What should we coordinate with?) 2). "In 2016, 51.7 thousand graduate students studied at universities and scientific organizations of the Ministry of Education and Science of the Russian Federation, of which 42.1 thousand people studied in full-time graduate school." (Here is “51 whole”, but there is also “7 tenths of a thousand”. Then “studied”? Then “42 point one thousand”. Then already “studied”?) 3). “1,580.1 thousand students completed full-time education.” Here there are already “1 million 580 point 1 thousand.” What should we do here? What to get attached to? And one more interesting aspect: the coordination of the participle with a complex numeral: “In 2016, 2,354 small enterprises operated at universities, created in the form of business entities and partnerships.” Here "... four small... created" or "four... enterprises created?" What to agree with??? Please help me figure it out! I'm tired of such cases. I also ask for a link to any reliable sources on these issues. We definitely need to make things clear!!!
Russian language help desk response
The coordination of the counting turnover with the value of a certain quantity with the predicate is influenced by many different factors. In the above contexts, agreement is possible in both singular and plural. number. Wed. examples from reference books: There are 28 thousand students studying at the university And One hundred of our students will go on internships abroad this year. The features of agreement with the subject - fractional numerals are not described in reference books, so you can be guided by these general recommendations. Unit form numbers emphasize the total number of persons, a set of objects, indicate that they are experiencing some kind of impact, state; units The number of the predicate focuses attention on the number of objects or persons in question. In the plural form. numbers highlight the persons and objects being counted as producers of the action, the separateness of the objects or persons indicated in the subject, the separateness of their performance of the action are emphasized.
In a sentence In 2016, there were 2,354 small enterprises operating at universities, created in the form of business entities and partnerships Both forms of participle are possible. To the right books indicate that the definition (usually isolated), standing after the counting phrase with the numeral 2, 3, 4 or ending in 2, 3, 4, is often put in the form named after. plural case numbers, but the form is gen. case is not prohibited.
| Question No. 291932 | ||
Which case should you choose when writing units of measurement after numerals in contracts if fractions are present? For example: “The company undertakes to sell 20100.52 (Twenty thousand one hundred) 52/100 barrel(s) of oil? On the one hand, it reads as “twenty thousand one hundred barrels”, on the other - “twenty thousand one hundred point fifty two barrel." Which option is correct?
Russian language help desk response
Since a fractional number is used here, the noun is put in the singular genitive form: barrel.
| Question No. 287513 | ||
Which is correct to say: “the first eight and seven POINTS earned” or “the first eight and seven POINTS earned”? Thank you!
Russian language help desk response
Do you mean seven points or seven tenths of a point? If the second option, then true: first earnedeight point seven points.
| Question No. 285308 | ||
Dear “Certificate”, explain why of the two options “two hundred nine and a half thousand” and “two hundred nine and a half thousand” the first option is correct (this is question No. 285264), and of the options “five and a half meters” and “five and a half meters" is correct 5.5 meters (question no. 285260). Can you explain please!
Russian language help desk response
Right: two hundred nine and a half thousand, five and a half meters. But if we use a number form to write, where there is an integer and a fraction, it is correct: 209.5 thousand, 5.5 meters. A noun is governed by a fraction: two hundred and nine point five thousand, five point five meters.
| Question No. 285002 | ||
Russian language help desk response
The number reads like this: four point four billion.
| Question No. 279612 | ||
Which is correct - “three point two tenths” or “three point two tenths”?
According to almost all sources, -Х is correct. It seems to me that they are correct, as with adjectives: two little girls. According to Wiktionary, the words "tenth" and "hundredth" are nouns. Then the correct option would be "three point two", but I've never heard that at all. Or are the words “whole,” “tenth,” and “hundredth” NUMERAL and subject to their own rules? Help determine the part of speech and the correct option, and, most importantly, WHY this or that is correct.
Russian language help desk response
Correct in them. P.: three point two. The choice of case form is determined by tradition and is probably due to the influence of numerals five, six, seven etc. ( whole tenths).
| Question No. 274366 | ||
What would be the correct way to write: “One point three thousandths of a gram” or “One point three thousandths of a gram.” Thank you
Russian language help desk response
Right: one point three thousandths of a gram.
| Question No. 266266 | ||
Ilya received 3.7 thousand rubles as a teacher (three point seven thousand rubles or three point seven hundred thousand rubles)
how to read correctly?
Thank you!
Russian language help desk response
| Question No. 262214 | ||
Hello! I have difficulty pronouncing numbers (word combinations) out loud: 233,627.4 thousand rubles, 33.9%. Please tell me how to do it correctly?
Russian language help desk response
Pronounced like this: two hundred thirty-three thousand six hundred twenty-seven point four thousand rubles, thirty-three point nine percent.
| Question No. 252566 | ||
Which is correct: “from two point five to three point” or “from two point five to three point”?
Russian language help desk response
Right: from two point five to three.
| Question No. 252037 | ||
Please tell me how to write correctly
“TWO point five percent per annum” or “TWO point five percent per annum”?
Thank you
Russian language help desk response
Right: two wholes (parts).
| Question No. 251723 | ||
Good afternoon
I'm interested in the correct declension of a noun when used together with a fraction.
- 102.6 grams or 102.6 grams?
And accordingly, I would like to know the correct form of pronunciation:
- “One hundred two point six grams” or “One hundred two point six grams”
P.S. I myself am inclined to the first option in both the first and second cases, but I would like to read the commentary of a specialist.
Russian language help desk response
Noun gram controls the fractional part of the numeral. Right: six tenths of a gram.
| Question No. 251219 | ||
Good afternoon
Please tell me how the surname Yurgala is declined.
And how correct: “31.8 (thirty-one point eight) sq.m.” or "31.8 (thirty-one point eight"?
Thank you.
Russian language help desk response
This surname is declined according to the first school declension (like the word Mother).
Right: thirty-one point eight.
| Question No. 235934 | ||
Please tell me how to correctly read this entry out loud: 2.4 liters of milk. 2 options come to mind: 1) two and four tenths of a liter, 2) two and four tenths of a liter. However, both seem somehow unnatural. ON THE.
Russian language help desk response
Correct: _two point four liters_.
“I am satisfied with the ruins of Ak Bars,” they say, this inscription in Finnish appeared quite recently on the wall of the Sports Palace of Trade Unions. But seriously... However, why do you have to be serious after such a victory? Last time I tried to tell in full detail about my acquaintance with the Ak Bars that was torn up in Nizhny. This time, of course, it was “Salavat Yulaev’s” turn. Firstly, it turned out to be no less interesting, and secondly, when will another opportunity arise?
My acquaintance with the Ufa club occurred during the season when Spartak, which returned there, headed by Nikolai Solovyov, was spectacular in the Super League. We, at Sport Express, were friends with the club, so the team often took us to away matches.
And we had a pleasure flying. After all, back then the red-whites had not just a charter, but a representative plane of the Ministry of Emergency Situations. Even though it was a Yak-42 (it wouldn’t be a good night to remember it), it had a wonderful interior, imported, and therefore comfortable, and not sadistic, as is customary in our aircraft industry, seats. And the front salon for management is something special. Leather sofas, video clips, tables that are very comfortable to play cards on...
In addition, the head coach of Spartak Nikolai Dmitrievich Solovyov (known as VAT) had a non-hockey fixed idea at that time: to beat me at preference. And this, I will say without false modesty, is an extremely difficult task. The fact is that during my last years of study at the military school of logistics, which was once located on Lyadov Square, I worked in the computer center located on the first floor of our residential building. And he earned money by writing algorithms for the computer “Marriage”. The very first one that was published even before the beginning of the era “ Windows" That is, he mathematically substantiated, if I’m not mistaken over the years, all 72 thousand-odd options for the initial layout of cards with three options for approaching and further developments of events. Go beat this one! And while VAT and Sergei Shepelev were enthusiastically loading each other (not without my help) with “steam locomotives” on minuscules, your humble servant “drove into paradise on someone else’s hump.” That is, by the time the plane landed in the next city, the only one closed in a good plus (experts will understand).
That season turned out to be both enchanting and tragic at the same time for Spartak. Let me remind you: it was a three-round event, without any conferences. So, after the first round, Spartak took a confident first place in the standings. And in the end, I didn’t even make it to the playoffs. And somewhere after the New Year, towards the end of the second round, just before the start of Spartak’s protracted “pike”, we flew to Ufa. While the plane was taxiing to the parking lot, the flight preference was “knocked out” and it turned out that VAT, together with Shepelev, was again in the deepest disadvantages. VAT once again called me a sharper, once again said that “he would never sit down to play with me” (although we never played for money, but exclusively for the next trip). The team, along with all the equipment, loaded onto the Salavatov bus and went straight to the Ice Palace to leave their uniforms in the locker room and go light to the hotel.
And at that time... a storm broke out in the Ice Palace. The storm hit the then head coach of Salavat, Sergei Alekseevich Nikolaev (popularly known as Seich). Before our arrival, he received a copy of the annual report of the hockey school for children and youth, from which he learned that the Salavat Youth Sports School, it turns out, worked 37.4 percent better last year than before. This caused a storm of indignation.
The storm did not spare anyone who was still in the Palace late in the evening. The ice makers hid behind their cars, the trainers, they say, jumped out of the windows, the cleaners scurried away from Seich into their cubicles with equipment. While the team was unloading their bags, the author of these lines, not knowing the danger, brazenly burst inside and immediately ran into the epicenter of the storm.
So you explain it to me, an uneducated fool! If I now have our students on my team - wow! - and a hardened Nikolaev doula appeared in front of my nose. - That’s 37.4 percent more - how’s that?!
Realizing what was happening, your humble servant tried to take the raging Seich under the elbow. Explaining along the way that this is all mathematics and accounting, that accountants are not from this world at all, that they have not twelve months in a year, but ten plus 20 percent of VAT (value added tax, of course) ...
What the hell is accounting, what mathematics?! - Seich did not calm down. - Need to work! Work, do you understand? And they either have Eid al-Adha for a couple of months, or Eid al-Adha, or some other Eid al-Fitr - and they can’t work. Then they have a two-week period - ugh! - Halloween, then the Chinese New Year, which turns into Yom Kippur, and then the May holidays have already arrived - and the season is over. And there is no time to work...
For some reason, what killed Seich the most was not the number itself, but four tenths after the decimal point.
I would chop off these four tenths of a percent from the front...
Yes, this director... this youth sports school... But I saw him for the last time last year. In a tavern. They celebrated Catholic Christmas there with the whole school. The school hasn’t been able to let anyone out in recent years, we’re staring here, day and night, without bending over, the stars are shining right into our ass, and they only have bayrams. And yet we can’t get into the playoffs, but they work 37 percent better, can you imagine? And four tenths... I'll kill you, you nit! - Nikolaev exploded again and rushed off somewhere deep into the dark palace. And a minute later, from there, from the dark depths, an amplified echo came:
No, did you see it?!! 37 and four, damn it, tenths!.. And you, Seich, even go to bed yourself, but let’s have the playoffs...
This is how, to put it mildly, my acquaintance with both Ufa and “Salavat Yulaev” turned out to be extraordinary. Of course, many, many years have passed since then, people and priorities have changed, and the very attitude towards the matter has changed. For Salavat, the problem of reaching the playoffs has long ceased, the youth Tolpar is now one of the leaders of the MHL, the main team has won the championship twice, hockey has become almost the main driving force of the republic, but...
As the writer Konetsky said, “the path we have traveled cannot be taken away from us.” And if you are interested in my serious thoughts about today’s Salavat, they will again be in the program for the match.
See you at hockey!
From: Source: HC Torpedo 11/18/2011, 971 views
Let's look at examples of how to round numbers to tenths using rounding rules.
Rule for rounding numbers to tenths.
To round a decimal fraction to tenths, you must leave only one digit after the decimal point and discard all other digits that follow it.
If the first of the discarded digits is 0, 1, 2, 3 or 4, then the previous digit is not changed.
If the first of the discarded digits is 5, 6, 7, 8 or 9, then we increase the previous digit by one.
Examples.
Round to the nearest tenth:
To round a number to tenths, leave the first digit after the decimal point and discard the rest. Since the first digit discarded is 5, we increase the previous digit by one. They read: “Twenty-three point seven five hundredths is approximately equal to twenty three point eight tenths.”
To round this number to tenths, leave only the first digit after the decimal point and discard the rest. The first digit discarded is 1, so we do not change the previous digit. They read: “Three hundred forty-eight point thirty-one hundredths is approximately equal to three hundred forty-one point three tenths.”
When rounding to tenths, we leave one digit after the decimal point and discard the rest. The first of the discarded digits is 6, which means we increase the previous one by one. They read: “Forty-nine point nine, nine hundred sixty-two thousandths is approximately equal to fifty point zero, zero tenths.”
We round to the nearest tenth, so after the decimal point we leave only the first of the digits, and discard the rest. The first of the discarded digits is 4, which means we leave the previous digit unchanged. They read: “Seven point twenty-eight thousandths is approximately equal to seven point zero tenths.”
To round a given number to tenths, leave one digit after the decimal point, and discard all those following it. Since the first digit discarded is 7, therefore, we add one to the previous one. They read: “Fifty-six point eight thousand seven hundred six ten thousandths is approximately equal to fifty six point nine tenths.”
And a couple more examples for rounding to tenths:
