In the following exercises, write as the ratio of two integers. (a)-16 (b)4.399

Name: Problem 4, Chapter 7: Prealgebra
Uploaded: 2020-09-14T07:32:45-08:00
Duration: 3 min 41 s
Channel: Pratul Kasote
Description: In the following exercises, write as the ratio of two integers. (a)-16 (b)4.399

step 1 In this example, we are given two real numbers, minus 16 and 4 .399. And we are asked to express

In the following exercises, write as the ratio of two...

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Key Concepts

Converting Terminating Decimals to Fractions

Terminating decimals are decimals that have a finite number of digits after the decimal point. They can be converted into fractions by taking the decimal number without the decimal point as the numerator and using a power of ten corresponding to the number of decimal places as the denominator. This process always produces a fraction that represents the same value and can often be simplified further by reducing the fraction.

Fraction Representation of Integers

Every integer is naturally a rational number because it can be written as a fraction with a denominator of one. This simple representation highlights the fact that integers are a subset of rational numbers, and it helps illustrate more complex concepts by showing that the concept of fractions applies uniformly to both whole numbers and non-integer values.

Rational Numbers

Rational numbers are numbers that can be expressed as the quotient of two integers, where the denominator is not zero. They are a fundamental element in number theory and arithmetic, providing a way to represent fractions and proportions. Recognizing a number as rational allows one to work with it in a fractional form, which is useful for exact calculations and proofs.

Transcript

00:02 In this example, we are given two real numbers, minus 16 and 4 .399.

00:09 And we are asked to express these real numbers into the ratio of two integers.

00:16 Have a look on the first number.

00:20 The first example or the first number we are given is minus 16.

00:27 A simple question is asked.

00:30 We are asked to express or we are asked to write this number as a ratio of integers.

00:38 There is nothing in the denominator of minus 16, but for our convenience, we can write minus 16 as minus 16 upon 1.

00:47 Can we write it like this? the answer is yes, it makes no difference if we divide minus 16 by 1.

00:55 If we write 1 in the denominator of minus 16, nothing will happen to it.

01:02 And this is how we can convert.

01:04 We can express minus 16 as ratio of two integers.

01:08 You can observe that there is an integer in the numerator as well as there is an integer in the denominator.

01:17 This both the numbers that is minus 16 as well as one, both are integers, both belongs to the set of integers.

01:30 Now have a look on the second question.

01:34 This is the sign of belongs to capital i.

01:38 Capital i is nothing but set of integers.

01:43 One more example we'll discuss now...

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