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Why do whole numbers raised to an exponent get greater while fractions raised to an exponent to get smaller?
Whole numbers raised to an exponent increase because multiplying a positive whole number by itself repeatedly yields a larger value. In contrast, fractions (less than 1) raised to an exponent result in smaller values because each multiplication reduces the overall product. For example, (0.5^2 = 0.25), which is less than (0.5). Thus, the behavior of whole numbers and fractions under exponentiation reflects their inherent properties.
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Why do whole numbers raised to an exponent get greater and greater while fractions raised to an exponent get smaller?
Whole numbers raised to an exponent increase because multiplying a whole number by itself repeatedly results in a larger product. Conversely, fractions (a number less than one) raised to an exponent get smaller because each multiplication reduces the value further; for example, multiplying 0.5 by itself yields 0.25, which is less than 0.5. Thus, the behavior of whole numbers and fractions under exponentiation is fundamentally different due to their values relative to one.
Why do whole numbers raised to an exponent get greaterwhile fractions raised to an exponent get smaller?
Whole numbers greater than one raised to an exponent increase because multiplying a number by itself repeatedly results in a larger value. In contrast, fractions (numbers between 0 and 1) raised to an exponent decrease because each multiplication reduces the value further, as each factor is less than one. Thus, while whole numbers amplify their size, fractions diminish with each exponentiation.
What are the parts of fractions?
There are 3 Parts of fractions: 1:Improper Fractions Improper fractions are those fractions which numerator is greater than the denominator. 2:Proper Fractions Proper Fractions are those fractions which numerator is smaller than the denominator. 3:Mixed Numbers Mixed Numbers are those numbers which have a whole number and a part of fraction.
How do you compare numbers in scientific notation?
To compare numbers in scientific notation, first check the exponent. Whatever exponent is higher is the greater number. If the exponents are the same, check the first number. Whatever first number is higher is the greater number. 5.7 x 10^3 is greater than 3.89 x 10^3 2.66 x 10^5 is greater than 8.57 x 10^2
How can you tell which fractions is greater if both fractions have the same numerator?
Then the fraction with the smaller denominator is larger.
Why do whole numbers raised to an exponent get greater and greater while fractions raised to an exponent get smaller?
Whole numbers raised to an exponent increase because multiplying a whole number by itself repeatedly results in a larger product. Conversely, fractions (a number less than one) raised to an exponent get smaller because each multiplication reduces the value further; for example, multiplying 0.5 by itself yields 0.25, which is less than 0.5. Thus, the behavior of whole numbers and fractions under exponentiation is fundamentally different due to their values relative to one.
Why do whole numbers raised to an exponent get greaterwhile fractions raised to an exponent get smaller?
Whole numbers greater than one raised to an exponent increase because multiplying a number by itself repeatedly results in a larger value. In contrast, fractions (numbers between 0 and 1) raised to an exponent decrease because each multiplication reduces the value further, as each factor is less than one. Thus, while whole numbers amplify their size, fractions diminish with each exponentiation.
What are the parts of fractions?
There are 3 Parts of fractions: 1:Improper Fractions Improper fractions are those fractions which numerator is greater than the denominator. 2:Proper Fractions Proper Fractions are those fractions which numerator is smaller than the denominator. 3:Mixed Numbers Mixed Numbers are those numbers which have a whole number and a part of fraction.
How do you compare numbers in scientific notation?
To compare numbers in scientific notation, first check the exponent. Whatever exponent is higher is the greater number. If the exponents are the same, check the first number. Whatever first number is higher is the greater number. 5.7 x 10^3 is greater than 3.89 x 10^3 2.66 x 10^5 is greater than 8.57 x 10^2
Why do numbers get smaller when multiplied by a decimal?
It's because decimals are really fractions and all numbers get smaller when you multiply them by fractions.
How do you compare expressions in scientific notation?
A number with a small exponent is smaller than a number with a large exponent. If two numbers have the same exponent then compare the mantissae. The smaller mantissa represents the smaller number.
How can you tell which fractions is greater if both fractions have the same numerator?
Then the fraction with the smaller denominator is larger.
Why do whole numbers raised to exponents get greater while fractions raised to exponent get smaller?
An exponent just tells how many times a number is multiplied by itself. With whole numbers, if you keep multiplying them, they have to increase. 3 x 3 is 9, 3 x 3 x 3 is 27 and so on. Taking a half of anything makes it smaller. 1/2 x 1/2 is 1/4, 1/2 x 1/2 x 1/2 is 1/8 and so on.
What statement about multiplying fractions and mixed numbers is not true?
A common misconception is that multiplying fractions always results in a smaller number. While it is true that multiplying two proper fractions (less than one) results in a smaller fraction, multiplying a fraction by a mixed number can yield a larger product if the mixed number is greater than one. Therefore, the statement "Multiplying fractions always results in a smaller number" is not true.
What is smaller than 6.5 x 10 exponent -5?
There are infinitely many smaller numbers. One such is -6*103
Is infinity in between every number?
There's an infinite number of fractions possible between any two consecutive whole numbers.FOOTNOTE: Still, there are as many "whole" numbers are there are fractions. Paradoxically, there are more decimalnumbers greater than zero but smaller than one than there are "whole" numbers.
Why is six tenths greater?
Six tenths is greater than infinitely many fractions and it is also smaller than infinitely many.
