Month: July 2021

Imagine how difficult it would be if you have to do math with an amount consisting of twenty digits. To perform any arithmetic operation on that kind of number, you would need a calculator that can accumulate that type of calculation.

Scientists deal with very big numbers, as well as extremely small numbers, by converting them to standard form, which is a decimal number followed by an exponent of 10. The decimal might be as precise as required, though it is commonly rounded to two. The exponent value denotes the magnitude of the number. The distance to the closest star in standard form is a considerably more reasonable 4.02 X 10 ¹³ kilometers.

What is Standard Form?

Standard form is also referred to as scientific notation. It is a technique of representing extremely big or extremely small integers. It’s used as shorthand in science and math, rather than writing down the whole number every time.

This form also makes it much easier to perform computations than working with a number that may have several place values. If you work with numbers with a lot of digits, either extremely large or very little, converting them to standard form will assist you in a big way.

The following notation is used to represent standard form,

B x 10 ^a

A is a number that’s known as the coefficient. The coefficient must be greater than or equal to 1 but less than 10.

• ‘B’ is the multiplication sign read as ‘times.’
• 10 is the base, and it must always be 10 in scientific notation.
• a is a number usually known as the exponent, also referred to as the power of 10.

For example,

0.00029876 = 2.9876 x 10 ^-4

Writing number in standard form could be much easier if you know how to convert a number into standard form. In the next section, we will explain the method to convert numbers in standard form.

How to convert numbers into Standard Form?

Before converting a number with an exponent, keep in mind another convention: use commas to separate number strings into groups of three or thousands. The number 2468561215, for example, is frequently expressed as 246,856,1215.

The first three digits of a number appear when the number is expressed in standard form. This is true even if the first group only has one or two numbers. The first three digits of the number 246,856,1215 for example, are 2, 4, and 6.

Small numbers, such as the radius of an atom, can be just as difficult to manage as huge ones. To convert those into standard form, you should employ the same technique. If the number is big, the decimal is placed after the first digit on the left, and the exponent is made positive. It is equal to the number of digits after the decimal. You can try out an online standard form calculator to see the steps of calculation if you are not sure about the answer.

In case the number is very small, the first three digits following the string of zeros are the same as the three used at the start of the number in normal form, and the exponent is negative. The exponent is the number of zeros multiplied by the first digit of the number series.

Here are several examples: Light travels at a speed of 299,792,458 meters per second. This is 3.00 X 10 ⁸ m/s in standard form. Be aware that you must round 299 to 300 because the fourth digit is more than 4. A hydrogen atom’s nucleus and electron are distant by 0.00000000005291772 meters. This is 5.29 X 10 ^-11 meters in standard form. You don’t need to round up because the digit after 9 in the original number is less than 5.

Performing arithmetic operations on Standard Form

·      Adding/Subtracting numbers in Standard Form

Adding and subtracting integers in standard form is simple as long as they have the same exponents. Simply add or subtract the digits. If the exponents of the numbers are not alike, convert one to the exponent of the other.

Add 1425.8 x 10 ⁵and 1.36 x 10 ⁸

As you can see, these numbers are in standard form. To add these numbers, we have to make the exponent of both numbers the same. To do so, let’s move the decimal in the number 1425.8 x 10 ⁵.

= 1425.8 x 10 ⁵ = 1.4258 x 10 ⁸

Now we can add both numbers because the exponents of both numbers are identical.

= 1.4258 x 10 ⁸ + 1.36 x 10 ⁸

Simply add the numbers on the left side of the multiplication sign and write the 10 raised to the power 8 with the result.

= 2.7858 x 10 ⁸

Subtraction is as same as addition. Just put the subtraction sign instead of the addition sign. Let’s use two standard form numbers for subtraction.

Subtract 3.93 x 10 ⁴ and 1.25 x 10 ²

To subtract these numbers, we have to make the exponent of both numbers the same as we did for adding numbers. To do so, let’s move the decimal point in the number 3.93 x 10 ⁴.

3.93 x 10 ⁴ = 393 x 10 ²

As you can see, both of the numbers now have the exponent of 2. Subtract the value before the multiplication sign and place the 10 raised to the power 2 as it is.

= 393 x 10 ² – 1.25 x 10 ²

Take 10 ² as common.

= (393 – 1.25) x 10 ²

= 391.75 x 10 ²

Move the decimal to convert the number into standard form for the final output.

= 3.9175 x 10 ^{2 + 2}

= 3.9175 x 10 ⁴

·      Multiplying/dividing numbers in Standard Form

When you multiply integers in standard form, you multiply the digits and add the exponents. When you divide one number by another, you perform the division on the number strings and subtract the exponents.

It is as simple as it gets. There is no need to complicate things when dealing with scientific form. In the case of multiplication and division, there is no need to make exponents equal. Add exponents in case of multiplication and subtract them in case of division.

Multiply 2.25 x 10 ⁴and 1.5 x 10 ⁵

Simply multiply numbers on the left side of the multiplication sign and add the exponents.

= 2.25 x 1.5 x 10 ⁴⁺⁵

= 3.375 x 10 ⁹

Divide 39.5 x 10 ⁶and 2.3 x 10 ³

Divide numbers on the left side of the multiplication sign and subtract the exponents of both of the 10s.

= (39.5 ÷ 2.3) x 10 ^{6 – 3}

= 1.7173913043 x 10 ⁴

Summary

If you’re reading this, you already understand why we need standard or scientific form when working with numbers. It is a very useful notion that is commonly utilized in many sectors of science. Aside from numbers, the standard form can also be applied to linear equations, quadratic equations, and polynomials. It has a wide range of applications that can be implemented based on the underlying needs.

Mathematics is one such subject that most students have trouble working with and understanding. This issue prevails in an offline mode of teaching and learning and seems to amplify in the online modus. It is primarily because online courses are exceedingly different than traditional classrooms.

There are a colossal number of problems that can arise during online classes. They can include the students being unable to have a face-to-face conversation with the teachers or them being unable to voice their doubts. In most cases, distractions common to online classes hinder their path of seeking knowledge on the subject.

Hence, we present the 8 best tips to ensure a successful online Math class. Overall, they allow the teachers to teach efficiently and the students to comprehend each module perfectly. They do not leave any room for uncertainties at the end of a class.

1. Look at the Courses from a Separate Angle

Online classes proffer a different ambiance and environment compared to conventional classrooms. Here, students and teachers cannot see each other directly and cannot understand what the other thinks about at any moment by looking at their expressions. Hence, the educators have to change their manner of delivery of the course materials and teaching style.

The Maths tutors have to cut down on the unnecessary parts of the course. It curbs the wastage of time that they would have transpired in the traditional classrooms. This minimalistic approach allows the teachers to dedicate their time and effort to the essential portions and explain them to the students as many times as required. Thus, it removes the possibility of even one student not understanding the concept. Similarly, the pupils must pay attention to what the tutors are elucidating with a focused mind. 

2. Learn About the Technical Aspects and Be Proficient In It

Since webcams and computer screens replace chalk and boards in online classes, the teachers and students have to utilize all available features of the platform that they are using for the purpose. It can include the “raise a hand,” chat, participant list, vote, and other such functions and attributes. The available platforms comprise Google Meet, Zoom, Cisco Webex, Microsoft Team, etc.

Unless both parties are proficient in the new teaching and learning system, no tricks or step jumps in Mathematics will help. The students and teachers can achieve it by having mock or test sessions with their friends and colleagues. Conversely, they can merely fiddle around with the features and characteristics of the platform in their free time to understand what it does. A net search on the topic can also solve this problem. 

3. Prepare The Course Material Beforehand

Preparation and browsing of the modules and course materials before the online class helps considerably. It stands true for both the teacher and the students. It allows the former to plan out how they will proffer the knowledge and make the pupils understand. It helps the latter get a better idea of what they need to prepare for the class. 

Indeed, the students cannot comprehend what the course entails by looking at the materials beforehand. Nevertheless, they can at least relate to the parts that they had skimmed through earlier. It helps in better memorization and overall understanding.

4. Have an Interactive Session

Mathematics becomes a tedious and monotonous subject if only one person speaks throughout the class and the others listen or pretend to do so. Interaction between students and teachers is the aspect that brings out the elements of interest and enjoyment in a Math class. However, the said communication does not refer to a viva session. It merely implies a lesson with general discussions where the students can share their views on the taught material. Additionally, the teacher can explain the real-life uses and applications of the module to pique the interests of their pupils. 

One can initiate the interactive session in the online platform via the chat feature or by switching on their audio and video. Both options come in handy as some students are shy and may prefer typing out their doubts. On the other hand, others may fancy asking a question orally.

5. Engage in Collaborative Assignments

Similar to interaction, collaboration with their peers can help students develop an interest and added understanding of online Mathematics. Of course, the assignments must be on an online platform. Thus, group assignments, discussions, test preparations, and so on during or after class hours aid in this facet. 

Maths tuition can motivate students and get their attentiveness renewed by giving follow-up tests or quizzes on a ranking basis to arouse and maintain their competitive nature. 

6. Review the Course Material

Reviewing and practicing the modules and portions taught in a class at the end of it helps significantly for Mathematics. Although it applies to both online and offline lessons, the individuals profit more in the former case. It is primarily because the students do not have to waste time traveling back home after the class. 

7. Take Ample Notes

In any online class, teachers share their screens to show the students the course material they refer to for teaching. They also give it to the pupils before or after a class to check while reviewing. However, these course materials come from sources that write them in a standard style or manner. In most cases, only those who have prior knowledge of the module can understand it.

Thus, it is necessary to take running notes during class. It allows the students to write down the steps they have to follow while solving a problem. It also proffers a hands-on experience, promotes active and continual thinking, and extends attention span. 

8. Create a Dedicated Study Space

It is arduous to concentrate in all online classes, especially Math, with distractions in the background. In any case, students have a hard time concentrating without the face-to-face teaching and learning system.  

Therefore, a calm, quiet, and clean study space aids in this aspect to a great extent. It is applicable for both the students and the teachers. Both parties can create a clutter-free area and sit with their required particulars like water bottles, pens, notebooks, chargers, snacks, and so on for the entire duration of the class. It prevents them from getting up frequently, keeping their attention focused on only one thing at hand and dedicating their all to it. 

Preparing for the SAT exam is one of the hardest things for a student. While the test itself might not be that hard, it is a very big undertaking, and students don’t know where to begin. Moreover, the test judges a student’s analytical, critical, creative, and concrete thinking on top of putting a time constraint on him. If you are preparing for an SAT exam, there are some tips and tricks that are going to help you come up with a proper strategy to tackle it. In this article, I am going to highlight some of the most helpful tips that you can use to get a good score. So, without further ado, let’s get right down to it.

Understand the Paper Pattern

The very first and the most basic thing that you need to know is the paper pattern. There are lots of candidates who only focus on preparing study material, but they don’t have a clear idea about what to expect from an SAT exam. The exam consists of two sections that are further divided into different parts that have to be completed in the allotted time. You can click on the linked article to learn about the SAT paper pattern in detail.

Follow the Elimination Rule

Once you have understood the paper pattern and what to expect from the exam, you need to figure out how to solve the questions. A very important tip that you have to remember is that there is only one correct option out of four. Even if you don’t know the exact answer to a specific question, you can follow the elimination rule. All the incorrect options are incorrect for a certain reason. If you are able to find the reason, you can find the right answer with the process of elimination.

Skip Difficult Questions

One of the major reasons why the SAT Singapore exam is so difficult is due to the time pressure. After you enter the examination room, you have to put your ego on one side and focus on your strengths. When you are solving the paper, you should start from the top and solve questions that don’t take much time. If a question is taking too much time, you should just skip it. After you have answered all the easier questions, you will have ample time to think about the hard questions and come up with a solution.

Fill the Bubbles at the End

A good tip to help you save some time is to skip the bubble filling part till the very end after you have answered all the questions. You can just circle or mark the right answer on the booklet. Filling the bubbles takes a considerable amount of time, and if you try to fill them back and forth, you are only going to make things harder for yourself. Filling them all at once is going to take less time so that you don’t feel any pressure.