Represent numbers in standard form 3590. Standard form for positive numbers - Knowledge Hypermarket

Would you like to learn how to write huge or very small numbers in a simple way? This article contains the necessary explanations and very clear rules on how to do this. The theoretical material will help you understand this rather easy topic.

Very large values

Let's say there is some number. Could you quickly tell how it reads or how important it is?

100000000000000000000

Nonsense, isn't it? Few people will be able to cope with such a task. Even if there is a specific name for such a magnitude, in practice it may not be remembered. This is why it is customary to use the standard view instead. It's much easier and faster.

Standard view

The term can mean many different things, depending on what area of \u200b\u200bmathematics we are dealing with. In our case, this is another name for the scientific notation of a number.

It's really simple. It looks like this:

In these designations:

a is a number called a coefficient.

The coefficient must be greater than or equal to 1, but less than 10.

"X" - multiplication sign;

10 is the basis;

n - exponent, power of ten.

Thus, the resulting expression reads "a by ten to the nth power".

Let's take a specific example for a complete understanding:

2 x 10 3

Multiplying the number 2 by 10 to the third power, we get the result 2000. That is, we have a couple of equivalent variants of writing the same expression.

Conversion algorithm

Let's take some number.

300000000000000000000000000000

It is inconvenient to use such a number in calculations. Let's try to bring it to the standard form.

1. Let's count the number of zeros to the right of the triplet. We get twenty nine.
2. Let's discard them, leaving only a single-digit number. It is equal to three.
3. Add the multiplication sign and ten to the power found in step 1.

It’s that easy to get the answer.

If there were still others before the first nonzero digit, the algorithm would change slightly. One would have to perform the same actions, however, the value of the indicator would be calculated by zeros on the left and would have a negative value.

0.0003 \u003d 3 x 10 -4

Converting a number facilitates and speeds up mathematical calculations, makes the solution writing more compact and clear.

The number of three-digit numbers. Accommodation. How many schedule options can you make? How many ways you can arrange 5 volumes on a bookshelf. Selecting and rearranging objects. The composition of the selected objects. Number of permutations. Combinations. Permutation formula. The number of possible combinations. There are seven teams participating in the tournament. Combinations. There are many ways you can form a brigade.

"" Probability "Grade 9" - Find the expected number of crucians. The lowest of the two points dropped. The number of points is a multiple of 3. Bernoulli's test. The number of points dropped. The number of points dropped on one die. The likelihood of success. Dispersion properties. Probability theory and statistics. The mathematical expectation of a random variable. Distribution of a random variable. Dispersion of the number of successes. The highest of the two points dropped. The sum of the points dropped by two throws of the dice.

"Algebra" Geometric Progression "" - Write down the first five terms of the geometric progression. Choose the statement that suits you. Definition of a geometric progression. Execution check. Write any sequence of numbers in one of the columns. Geometric progression. “Math cannot be learned by watching a neighbor do it…” Ivan Niven. Mathematical dictation. Personal goals. Physical education. Compare math objects in each group.

"The concept of an algebraic fraction" - Raising a rational fraction to a negative power. Perform division. Degree with natural and whole exponents. Bring to a standard polynomial. Actions with algebraic fractions. Methods for factoring a polynomial. An algebraic fraction is an expression. Perform verbally. Find the numerical value of the expression after simplifying it. The sum of monomials is called a polynomial. Check if the action is correct.

"" Quadratic function "Grade 9" - Y \u003d a (x-m) 2 + n. Properties of a quadratic function. Function y \u003d ax2 + g. The branches of the parabola are directed upwards. Shift of the graph of the function y \u003d ax2 along the coordinate axes. Function properties. Schedule. A quadratic function is a function that can be specified by a formula. Function y \u003d a (x - p). Function graph. Graph and properties of the function y \u003d ax2. Plot the function y \u003d x2-4x + 5. Parabola construction scheme. Function y \u003d x2. Constructing a parabola by points.

"Numerical functions" Grade 9 "- Abscissas of points of intersection with the OX axis. Function definition. Function zeros. Function definition area. The function y \u003d f (x) is called odd. Function properties. Function range. Monotone. Even and odd functions (even and odd). Numeric functions.

Back forward

Attention! The slide preview is used for informational purposes only and may not represent all the presentation options. If you are interested in this work, please download the full version.

Lesson type: a lesson in explanation and primary consolidation of new knowledge.

Equipment: route sheet (MR) ( Appendix 1 ); technical equipment of the lesson - a computer, a projector for demonstrating a presentation, a screen. Computer presentation in Microsoft PowerPoint.

DURING THE CLASSES

I. Organization of the beginning of the lesson

Hello! Please check that you have handouts on your desk and that you are ready for the lesson.

II. Communication of the topic, purpose and objectives of the lesson

- Before starting to study a new topic, complete the tasks on the first page of the route sheet (check on the screen). If you completed the tasks correctly, then you should receive the word - STANDARD.
What is a standard? Where did you meet this word? What does it mean? (SCREEN)
Standard (from English - standard) A sample, a standard, a model with which they are compared, similar objects, processes are compared. (Universal encyclopedic dictionary). That is, when they talk about a standard, it is easier for people to imagine what it is about. And today we will talk about the standard form of a number. So this is the topic of today's lesson.

III. Actualization of students' knowledge. Preparation for active educational and cognitive activities at the main stage of the lesson

- Let's make a lesson plan:

1. Reiteration
2. Determination of the degree of a number;
3. Determination of the degree of a number with a negative exponent;
4. Degree properties;
5. Determination of the standard form of a number;
6. Actions with numbers written in standard form;
7. Application.

In the world around us, we are faced with very large and very small numbers. We already know how to write large and small numbers using the power of the number.

- Is it convenient to write numbers like this? Why? (Takes up a lot of space, takes a lot of time, and is difficult to remember.)
- What do you think you found a way out of this situation? (Write numbers using powers.)

Write down the mass of the Earth using a power number. 598 10 25 g. Now write down the mass of the hydrogen atom. 17 10 –20 g. Is it possible to write these numbers differently, using powers? Try it! 59.8 10 26, 5.98 10 27; 0.598 10 28; 5980 10 24.
17 10 –20 ; 1,7 10 –19 ; 0,17 10 –18 ; 170 10 –21 ;

- All results are correct. But can we talk about a standard recording? How to be? (Agree on a single notation for numbers.)
- Try to discuss with your neighbor, what kind of record should be uniform, standard?
- What should be the factor in front of the power of the number 10, so that it is convenient and REMEMBER the number and represent it?

IV. Assimilation of new knowledge

- Open, please, textbooks p. 35 and find the definition of the standard type of number and write it down in the route sheets.
- The standard form of a number is a record of the form and 10 n, where 1 < and < 10, n – целое. n – называют порядком числа.

- Any positive number can be written in the standard form !!!
Why? (By definition. Since the first factor is a number belonging to the interval from)