No, 0.999999 is not equal to 1. Although they appear to be the same number, 0.999999 is actually a tiny bit less than 1. To demonstrate that they are not the same number, we can write them in scientific notation.
0.999999 = 9.9999 x 10^-1 and 1 = 1.0000 x 10^0. This clearly illustrates that 0.999999 is 0.0001 less than 1.0
How do you prove .99999 is 1?
Proof by contradiction:
First, suppose we assume that .99999 is not equal to 1. Therefore, we could say that .99999 is not equal to (1 + x) for any value x.
Next, let’s take the limit of (1 + x) as x approaches 0. Since the limit of (1 + x) as x approaches 0 is 1, we can conclude that .99999 will have to approach 1.
However, this contradicts our original assumption that .99999 is not equal to 1, leading us to the conclusion that .99999 is, in fact, equal to 1.
Why 0.9999 is 1?
0.9999 is considered equal to 1 because it is effectively a representation of 1. Mathematically speaking, it is the same number, given that 0.9999 can be written as 1 – 0.0001. Therefore, 1 minus a small number still out of bounds from the decimal system will still be considered the same as 1, since it is effectively 1.
This is a result of the theoretical concept of mathematical limits, where the number approaches a certain figure but does not completely reach it, either due to restrictions with the decimal system or finite numbers.
Therefore, in a theoretical sense, 0.9999 is essentially equal to 1, although in reality it is a small fraction off.
Why is 0.9 and 0.90 the same?
0.9 and 0.90 are the same because they both signify nine-tenths of a number. In math, a decimal is a sequence of numbers used to represent fractions of a whole number. 0.9 is a decimal that can be expressed in terms of a fraction; it is equal to 9/10 or nine-tenths.
Similarly, 0.90 is a decimal that is also equal to 9/10 or nine-tenths. So, in mathematics 0.9 and 0.90 are the same because they both are expressed as nine-tenths of a number.
Why is 1 such a special number?
One is often considered a special number because it is the first positive integer and the first whole number, making it a fundamental building block of mathematics. Throughout history and across many different cultures, one has been recognized as having a unique significance.
One is a symbol of unity, often representing the union of mind, body, and spirit and the universe around us. It is also symbolic of beginnings and has been used to signify new and creative ideas. One is also the smallest prime number and an important factor in the Fibonacci sequence, which is a sequence of numbers that creates the Golden Ratio, a ratio of two numbers found in nature.
Furthermore, the number one is the lowest number with no multiples other than itself; it is a symbol of exclusivity, suggesting something is singular or special in nature. Many numbers hold significant meaning, but one is a timeless representation of unity and the beginning of something truly special.
How can you prove that 0.99999 is not equal to 1?
Strictly speaking, 0.99999 is not equal to 1 because they are decimals with an infinite number of decimal places and therefore an infinite number of digits, while 0.99999 has five 9s following the decimal point and 1 has one 0 following the decimal point.
Mathematically, there is evidence to suggest that 0.99999 is not equal to 1. If you were to divide 1 by 0.99999, the result would be 1.00001, which is greater than 1, indicating that 0.99999 is not equal to 1.
Additionally, the product of 0.99999 multiplied by 0.99999 will equal 0.9999800001 which is not equal to 1. Neither of these equations would hold true if 0.99999 was equal to 1. This demonstrates that 0.99999 is not equal to 1.
Why was 1 not considered a number?
This may seem like an odd question to ask, as 1 is of course universally considered a number. Up until the 16th century, however, that wasn’t always the case. This is because in Ancient Greek mathematics, numbers only consisted of the positive whole numbers, or counting numbers, from 2 onwards.
So, 1 wasn’t included. This might seem strange to us, but at the time it made perfect sense – entire systems of mathematics were based on this rule.
In the 15th century, it was still generally believed that 1 could not be considered a number in an arithmetic context. However, this ruling was challenged by French mathematician Nicolas Chuquet. Chuquet argued that 1 should be considered a number alongside the other positive whole numbers, and this argument eventually caught on.
Today, 1 is accepted as a number across the world.
Are 1 and .9 repeating the same?
No, 1 and .9 are not repeating the same. The number 1 is an integer, meaning it is a whole number that can not be divided any further. The number .9 is a non-integer or a decimal, meaning it can be divided to a certain degree of accuracy.
The difference between the two is that 1 is a whole number, while .9 is technically not a whole number. Additionally, an integer is a number without a fractional part while a non-integer or decimal has a fractional part as it is written in tenths, hundredths, thousandths, and so on.
Therefore, even though 1 and .9 are both single digits, they are not the same because one is a whole number, and one is not.
Why is a repeating decimal over 9?
A repeating decimal is over 9 because it is a number that, when divided, produces a fraction that cannot be fully represented by a decimal notation. The decimal notation will repeat certain numbers, signifying that the fraction cannot be represented in the decimal notation.
Thus, the decimal will repeat a finite number of digits continuously, producing a number that is greater than 9. This is why a repeating decimal is over 9.
Is .999 the same as 1?
No, .999 is not the same as 1. .999 is a repeating decimal and is not an exact number, while 1 is an exact numerical value. As decimals can be endless (they do not terminate or repeat in a pattern), they do not equate to precise values.
Therefore, as .999 is an estimation of 1, it is not equal to the exact value of 1. Mathematically speaking, it can be said that .999 is less than 1 but approaches it.
What is the value of 0.9 bar?
The value of 0.9 bar is equal to 90 kilopascals (kPa). It is equivalent to 9.0 x 10^5 Pascals (Pa) or 9.0 x 10²³ forces per square meter (N/m²). It is the same as 131.3 pounds per square inch (psi). 0.9 bar is a metric unit of pressure, commonly used in the measurement of gas pressures or for calculating the absolute pressure in open or vented systems.
It is equivalent to around 13.3 times the atmospheric pressure at sea level, which is equivalent to 1 atmosphere (atm) or 101.3 kilopascals (kPa).
What is 0.9 bar into fraction?
0.9 bar can be converted into a fraction by first expressing it as a decimal. 0.9 bar is equal to 0.9 atmospheres, which expressed as a decimal is 0.9. 0.9 can then be expressed as a fraction with the denominator of 1, which gives a fraction of 0.9/1, which simplifies to 9/10.
What are numerals of 1 to 9?
The numerals from 1 to 9 are 1, 2, 3, 4, 5, 6, 7, 8, and 9. These are the basic digits which make up all other numbers, as each number after 9 will include some combination of the numerals from 1 to 9.
Numerals are symbols that represent Numbers, such as the numerals shown above, and they may also be combined with other symbols (such as the plus sign) to form mathematical expressions. Numerals are used to create and label quantities, whether they are physical objects, measurements, or mathematical equations.