According to NASA, the distance between Earth and the closest star is 40,208,000,000,000 kilometers. Imagine how your eyes would sink into the back of your skull if you had to conduct math with that amount. To simply multiply or divide it by the speed of light, you’d need a calculator the size of your hand.
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 1013 kilometers.
Definition ? Standard Form
Standard form, often known as scientific notation, 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.
A x 10c
In this notation:
A is a number that’s known as the coefficient. The coefficient must be greater than or equal to 1 but less than 10.
- ‘x’ is the multiplication sign read as ‘times.’
- 10 is the base, and it must always be 10 in scientific notation.
- c is a number usually known as exponent, also referred to as the power of 10.
For example,
0.00004335 = 4.335 x 10-5
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.
Converting 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 359873236, for example, is frequently expressed as 359,873,236. 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 359,873,236 for example, are 3, 5, and 9.
Dealing with Exponents
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.
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 108 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.
Adding or Dividing numbers in Standard Form
Addition and Subtraction: 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 1295.8 x 105and 1.04 x 108.
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 1295.8 x 105.
= 1295.8 x 105 = 1.2958 x 108
Now we can add both numbers because the exponents of both numbers are identical.
= 1.2958 x 108 + 1.04 x 108
Simply add the numbers on the left side of the multiplication sign and write the 10 raised to the power 8 with the result.
= 2.3358 x 108
For subtraction, the same process should be followed. The only difference is we subtract numbers instead of summing them up.
Division and multiplication: When you multiply integers in standard form, you multiply the digits and add the exponents. When you divide one number by another, you do 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 3.87 x 104and 2.2 x 105.
Simply multiply numbers on the left side of the multiplication sign and add the exponents.
= 3.87 x 2.2 x 104+5
= 8.514 x 109
Divide 80.4 x 106and 1.2 x 103.
Divide numbers on the left side of the multiplication sign and subtract the exponents.
= (80.4 ? 1.2) x 106-3
= 67 x 103
Wrapping Up
If you are reading this section, it means that now you know why we need standard or scientific form when dealing with numbers. It is a very handy concept and is mostly used in various fields of science. Apart from numbers, the standard form is also applicable to linear equations, quadratic equations as well as polynomials. Its applications are wide and can be implemented according to the underlying requirements.
As the editor of the blog, She curate insightful content that sparks curiosity and fosters learning. With a passion for storytelling and a keen eye for detail, she strive to bring diverse perspectives and engaging narratives to readers, ensuring every piece informs, inspires, and enriches.
