Express the number as a ratio of integers.

In summary, expressing a number as a ratio of integers means to represent it as a fraction with whole numbers in the numerator and denominator. This can be done by converting a decimal or mixed number to an improper fraction and simplifying it. The difference between a proper and an improper fraction is that a proper fraction is always less than 1, while an improper fraction can also represent whole numbers or numbers greater than 1. Not all numbers can be expressed as a ratio of integers, such as irrational numbers and numbers with an infinite number of decimal places. Some real-life applications of expressing numbers as ratios of integers include scaling recipes, calculating interest rates, and representing data in statistics.
  • #1
bobbarkernar
48
0
hi I am having trouble with this question:
Q:Express the number as a ratio of integers. 9.4(78)bar so 9.4787878787878787878

what is confusing me is the 9.4, and where i should start the series at 78/10^(?)

please if someone could help me.

ty
 
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  • #2
Try multiplying it by 99. Specifically, multiply it by 100 and then subtract the original number. The repeating part should go away.
 
  • #3
yea i think i got it
9.4+(78/10^3)+(78/10^5)
so according to the geo series a=(78/10^3) and r=(1/10^2)
it should be (94/10)+(13/165)
 

Related to Express the number as a ratio of integers.

1. Can you explain what it means to express a number as a ratio of integers?

Expressing a number as a ratio of integers means to represent the number as a fraction, where both the numerator and denominator are whole numbers. This is often used to simplify or compare numbers.

2. How do you convert a decimal or mixed number to a ratio of integers?

To convert a decimal or mixed number to a ratio of integers, you can first rewrite the decimal or mixed number as an improper fraction. Then, you can simplify the fraction by finding the greatest common factor (GCF) of the numerator and denominator and dividing both by the GCF.

3. What is the difference between a proper and an improper fraction?

A proper fraction is a fraction where the numerator is smaller than the denominator, while an improper fraction has a numerator that is equal to or greater than the denominator. In other words, a proper fraction is always less than 1, while an improper fraction can also represent whole numbers or numbers greater than 1.

4. Can all numbers be expressed as a ratio of integers?

No, not all numbers can be expressed as a ratio of integers. For example, irrational numbers such as pi or square root of 2 cannot be represented as a fraction with integers in the numerator and denominator. Additionally, numbers with an infinite number of decimal places cannot be accurately expressed as a ratio of integers.

5. What are some real-life applications of expressing numbers as ratios of integers?

Expressing numbers as ratios of integers is commonly used in cooking and baking to scale recipes, in finance to calculate interest rates, and in engineering to simplify and compare measurements. It is also used in statistics to represent data as fractions or percentages.

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